From 231d0634198babf31a72f367a86bbbf10dbbea21 Mon Sep 17 00:00:00 2001 From: Gert-Jan Date: Thu, 23 Jan 2020 15:34:10 +0000 Subject: [PATCH] Updated example --- examples/Burgers_no_Lreg.ipynb | 751 -------------- examples/Example.ipynb | 459 +++++++++ examples/Example_Advection_Diffusion.ipynb | 352 ------- examples/Example_Burgers.ipynb | 1044 -------------------- examples/data/Advection_diffusion.mat | Bin 5077184 -> 0 bytes examples/data/burgers.npy | Bin 0 -> 1111839 bytes 6 files changed, 459 insertions(+), 2147 deletions(-) delete mode 100644 examples/Burgers_no_Lreg.ipynb create mode 100644 examples/Example.ipynb delete mode 100644 examples/Example_Advection_Diffusion.ipynb delete mode 100644 examples/Example_Burgers.ipynb delete mode 100644 examples/data/Advection_diffusion.mat create mode 100644 examples/data/burgers.npy diff --git a/examples/Burgers_no_Lreg.ipynb b/examples/Burgers_no_Lreg.ipynb deleted file mode 100644 index ec23e50..0000000 --- a/examples/Burgers_no_Lreg.ipynb +++ /dev/null @@ -1,751 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import torch\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "from deepymod_torch.library_function import library_1D_in\n", - "from deepymod_torch.neural_net import deepmod_init, train\n", - "\n", - "try:\n", - " torch.set_default_tensor_type('torch.cuda.FloatTensor') # enable for GPU\n", - "except:\n", - " pass\n", - "\n", - "\n", - "#%% Settings for reproducibility\n", - "np.random.seed(42)\n", - "torch.manual_seed(0)\n", - "torch.backends.cudnn.deterministic = True\n", - "torch.backends.cudnn.benchmark = False" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "data = np.load('data/processed/burgers.npy', allow_pickle=True).item()" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(25856, 2) (25856, 1)\n" - ] - } - ], - "source": [ - "X = np.transpose((data['t'].flatten(), data['x'].flatten()))\n", - "y = np.real(data['u']).reshape((data['u'].size, 1))\n", - "\n", - "print(X.shape, y.shape)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "noise_level = 0.25\n", - "y_noisy = y + noise_level * np.std(y) * np.random.randn(y.size, 1)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "number_of_samples = 1000\n", - "\n", - "idx = np.random.permutation(y.size)\n", - "X_train = torch.tensor(X[idx, :][:number_of_samples], dtype=torch.float32, requires_grad=True)\n", - "y_train = torch.tensor(y_noisy[idx, :][:number_of_samples], dtype=torch.float32)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "optim_config = {'lambda': 10**-5, 'max_iterations': 20000}\n", - "network_config = {'input_dim': 2, 'hidden_dim': 20, 'layers': 5, 'output_dim': 1}\n", - "library_config = {'type': library_1D_in, 'poly_order': 2, 'diff_order': 2}" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch | Total loss | MSE | PI | L1 \n", - "0 2.0E+00 8.1E-02 1.9E+00 1.3E-02\n", - "tensor([[-1.3764],\n", - " [-0.5860],\n", - " [ 0.0993],\n", - " [ 0.0393],\n", - " [ 1.1484],\n", - " [-0.2577],\n", - " [-0.1894],\n", - " [-0.0037],\n", - " [-1.7295]], requires_grad=True)\n", - "500 1.7E-01 1.2E-01 5.3E-02 1.2E-04\n", - "tensor([[-0.8180],\n", - " [-1.3032],\n", - " [ 0.5077],\n", - " [ 0.8928],\n", - " [ 1.4966],\n", - " [-1.0501],\n", - " [ 0.5603],\n", - " [-0.6519],\n", - " [-2.4926]], requires_grad=True)\n", - "1000 5.9E-02 4.6E-02 1.4E-02 1.3E-04\n", - "tensor([[-0.5263],\n", - " [-1.4761],\n", - " [ 0.5361],\n", - " [ 1.2344],\n", - " [ 1.5825],\n", - " [-1.1920],\n", - " [ 0.7059],\n", - " [-0.6853],\n", - " [-2.5626]], requires_grad=True)\n", - "1500 3.4E-02 2.7E-02 7.1E-03 1.3E-04\n", - "tensor([[-0.3365],\n", - " [-1.5661],\n", - " [ 0.5910],\n", - " [ 1.3476],\n", - " [ 1.6691],\n", - " [-1.1682],\n", - " [ 0.7293],\n", - " [-0.6830],\n", - " [-2.5392]], requires_grad=True)\n", - "2000 2.7E-02 2.0E-02 6.6E-03 1.6E-04\n", - "tensor([[-0.2321],\n", - " [-1.5496],\n", - " [ 1.0348],\n", - " [ 1.3358],\n", - " [ 1.8208],\n", - " [-1.0771],\n", - " [ 0.7128],\n", - " [-0.6696],\n", - " [-2.4880]], requires_grad=True)\n", - "2500 2.2E-02 1.5E-02 6.9E-03 1.8E-04\n", - "tensor([[-0.1935],\n", - " [-1.3786],\n", - " [ 1.6556],\n", - " [ 1.2392],\n", - " [ 2.1088],\n", - " [-0.9262],\n", - " [ 0.6735],\n", - " [-0.6429],\n", - " [-2.3999]], requires_grad=True)\n", - "3000 1.7E-02 1.1E-02 5.6E-03 1.9E-04\n", - "tensor([[-0.1807],\n", - " [-1.1432],\n", - " [ 2.3145],\n", - " [ 1.0590],\n", - " [ 2.5077],\n", - " [-0.7567],\n", - " [ 0.6085],\n", - " [-0.6033],\n", - " [-2.2840]], requires_grad=True)\n", - "3500 1.1E-02 8.6E-03 2.6E-03 2.0E-04\n", - "tensor([[-0.1692],\n", - " [-0.9606],\n", - " [ 2.7894],\n", - " [ 0.8552],\n", - " [ 2.8288],\n", - " [-0.6612],\n", - " [ 0.5407],\n", - " [-0.5746],\n", - " [-2.2105]], requires_grad=True)\n", - "4000 1.1E-02 8.6E-03 1.8E-03 1.7E-04\n", - "tensor([[-0.1536],\n", - " [-0.8646],\n", - " [ 2.8359],\n", - " [ 0.7116],\n", - " [ 2.8698],\n", - " [-0.6840],\n", - " [ 0.5017],\n", - " [-0.5988],\n", - " [-2.2272]], requires_grad=True)\n", - "4500 9.0E-03 7.5E-03 1.3E-03 1.6E-04\n", - "tensor([[-0.1360],\n", - " [-0.8042],\n", - " [ 2.6268],\n", - " [ 0.5901],\n", - " [ 2.6588],\n", - " [-0.7680],\n", - " [ 0.4754],\n", - " [-0.6783],\n", - " [-2.2869]], requires_grad=True)\n", - "5000 8.0E-03 6.7E-03 1.2E-03 1.5E-04\n", - "tensor([[-0.1154],\n", - " [-0.7347],\n", - " [ 2.2951],\n", - " [ 0.4514],\n", - " [ 2.2686],\n", - " [-0.8443],\n", - " [ 0.4426],\n", - " [-0.8105],\n", - " [-2.3153]], requires_grad=True)\n", - "5500 6.9E-03 5.8E-03 1.0E-03 1.3E-04\n", - "tensor([[-0.0896],\n", - " [-0.6213],\n", - " [ 1.8838],\n", - " [ 0.2949],\n", - " [ 1.7245],\n", - " [-0.8245],\n", - " [ 0.4000],\n", - " [-0.9991],\n", - " [-2.1824]], requires_grad=True)\n", - "6000 5.6E-03 4.5E-03 9.3E-04 1.1E-04\n", - "tensor([[-0.0582],\n", - " [-0.4340],\n", - " [ 1.3463],\n", - " [ 0.1302],\n", - " [ 1.0660],\n", - " [-0.6055],\n", - " [ 0.3478],\n", - " [-1.2427],\n", - " [-1.7372]], requires_grad=True)\n", - "6500 3.4E-03 2.8E-03 4.9E-04 6.3E-05\n", - "tensor([[-0.0219],\n", - " [-0.2128],\n", - " [ 0.5673],\n", - " [-0.0247],\n", - " [ 0.4283],\n", - " [-0.0596],\n", - " [ 0.2782],\n", - " [-1.4658],\n", - " [-0.8339]], requires_grad=True)\n", - "7000 2.2E-03 2.0E-03 1.3E-04 3.7E-05\n", - "tensor([[ 2.9893e-05],\n", - " [-1.9418e-01],\n", - " [ 7.4746e-02],\n", - " [-7.7934e-02],\n", - " [ 1.5050e-01],\n", - " [ 2.6424e-01],\n", - " [ 2.3771e-01],\n", - " [-1.3700e+00],\n", - " [-1.9277e-01]], requires_grad=True)\n", - "7500 2.0E-03 1.9E-03 9.5E-05 2.9E-05\n", - "tensor([[ 6.0529e-04],\n", - " [-1.7182e-01],\n", - " [ 6.2208e-02],\n", - " [-7.5555e-02],\n", - " [-1.2768e-02],\n", - " [ 1.9984e-01],\n", - " [ 2.2148e-01],\n", - " [-1.2410e+00],\n", - " [-9.5648e-02]], requires_grad=True)\n", - "8000 2.0E-03 1.9E-03 7.9E-05 2.5E-05\n", - "tensor([[ 4.8484e-04],\n", - " [-1.4845e-01],\n", - " [ 7.0296e-02],\n", - " [-6.9553e-02],\n", - " [-1.1760e-01],\n", - " [ 1.2112e-01],\n", - " [ 1.9634e-01],\n", - " [-1.1370e+00],\n", - " [-2.3033e-02]], requires_grad=True)\n", - "8500 2.0E-03 1.9E-03 6.9E-05 2.2E-05\n", - "tensor([[ 2.0654e-04],\n", - " [-1.2587e-01],\n", - " [ 7.6724e-02],\n", - " [-5.9186e-02],\n", - " [-2.2010e-01],\n", - " [ 8.1835e-02],\n", - " [ 1.6517e-01],\n", - " [-1.0311e+00],\n", - " [ 8.9746e-05]], requires_grad=True)\n", - "9000 2.0E-03 1.9E-03 5.9E-05 2.1E-05\n", - "tensor([[ 1.2925e-04],\n", - " [-1.0866e-01],\n", - " [ 7.6569e-02],\n", - " [-4.5814e-02],\n", - " [-3.1411e-01],\n", - " [ 7.1486e-02],\n", - " [ 1.2849e-01],\n", - " [-9.1827e-01],\n", - " [ 1.3619e-04]], requires_grad=True)\n", - "9500 1.9E-03 1.9E-03 5.2E-05 1.9E-05\n", - "tensor([[-5.9767e-06],\n", - " [-9.3196e-02],\n", - " [ 7.8101e-02],\n", - " [-3.0523e-02],\n", - " [-4.0498e-01],\n", - " [ 6.0333e-02],\n", - " [ 8.9905e-02],\n", - " [-8.0591e-01],\n", - " [ 2.0889e-05]], requires_grad=True)\n", - "10000 1.9E-03 1.9E-03 4.6E-05 1.7E-05\n", - "tensor([[-1.3042e-04],\n", - " [-8.0381e-02],\n", - " [ 7.8727e-02],\n", - " [-1.5562e-02],\n", - " [-4.8708e-01],\n", - " [ 4.9457e-02],\n", - " [ 5.0765e-02],\n", - " [-6.8953e-01],\n", - " [ 6.4376e-06]], requires_grad=True)\n", - "10500 1.9E-03 1.9E-03 4.2E-05 1.6E-05\n", - "tensor([[-3.0487e-04],\n", - " [-6.9669e-02],\n", - " [ 7.8986e-02],\n", - " [-1.1347e-03],\n", - " [-5.6141e-01],\n", - " [ 3.9094e-02],\n", - " [ 1.3291e-02],\n", - " [-5.7560e-01],\n", - " [-5.8180e-05]], requires_grad=True)\n", - "11000 1.9E-03 1.8E-03 4.0E-05 1.5E-05\n", - "tensor([[-2.6932e-04],\n", - " [-5.8455e-02],\n", - " [ 7.9992e-02],\n", - " [ 2.3351e-03],\n", - " [-6.3229e-01],\n", - " [ 3.2484e-02],\n", - " [ 6.3180e-06],\n", - " [-4.7461e-01],\n", - " [ 1.1854e-04]], requires_grad=True)\n", - "11500 1.9E-03 1.9E-03 3.9E-05 1.5E-05\n", - "tensor([[-1.4697e-04],\n", - " [-4.6569e-02],\n", - " [ 7.9081e-02],\n", - " [ 1.6375e-03],\n", - " [-7.0130e-01],\n", - " [ 3.4139e-02],\n", - " [-3.2741e-04],\n", - " [-3.9296e-01],\n", - " [ 1.8937e-04]], requires_grad=True)\n", - "12000 1.9E-03 1.8E-03 4.0E-05 1.5E-05\n", - "tensor([[-2.1397e-04],\n", - " [-3.2243e-02],\n", - " [ 8.2107e-02],\n", - " [ 1.9294e-03],\n", - " [-7.6722e-01],\n", - " [ 3.0378e-02],\n", - " [-3.8099e-06],\n", - " [-3.2410e-01],\n", - " [ 5.8312e-05]], requires_grad=True)\n", - "12500 1.9E-03 1.8E-03 4.1E-05 1.5E-05\n", - "tensor([[-2.0881e-04],\n", - " [-2.1848e-02],\n", - " [ 8.2053e-02],\n", - " [ 2.1128e-03],\n", - " [-8.2733e-01],\n", - " [ 3.1845e-02],\n", - " [ 7.3221e-06],\n", - " [-2.5313e-01],\n", - " [-1.7014e-05]], requires_grad=True)\n", - "13000 1.9E-03 1.8E-03 4.2E-05 1.5E-05\n", - "tensor([[-1.8524e-04],\n", - " [-1.3073e-02],\n", - " [ 8.1566e-02],\n", - " [ 2.2998e-03],\n", - " [-8.8116e-01],\n", - " [ 3.4004e-02],\n", - " [-3.7960e-06],\n", - " [-1.8718e-01],\n", - " [ 5.9954e-05]], requires_grad=True)\n", - "13500 1.9E-03 1.8E-03 4.2E-05 1.5E-05\n", - "tensor([[-1.5703e-04],\n", - " [-5.8444e-03],\n", - " [ 8.0980e-02],\n", - " [ 2.4175e-03],\n", - " [-9.2848e-01],\n", - " [ 3.5915e-02],\n", - " [-3.6726e-05],\n", - " [-1.2597e-01],\n", - " [-2.3702e-05]], requires_grad=True)\n", - "14000 1.9E-03 1.8E-03 4.3E-05 1.5E-05\n", - "tensor([[-1.4701e-04],\n", - " [ 2.0135e-06],\n", - " [ 8.0413e-02],\n", - " [ 2.6034e-03],\n", - " [-9.7026e-01],\n", - " [ 3.8268e-02],\n", - " [ 4.3432e-05],\n", - " [-7.0021e-02],\n", - " [ 4.2157e-05]], requires_grad=True)\n", - "14500 1.9E-03 1.8E-03 4.3E-05 1.5E-05\n", - "tensor([[-9.6790e-05],\n", - " [-4.5762e-05],\n", - " [ 7.8555e-02],\n", - " [ 2.6385e-03],\n", - " [-9.8979e-01],\n", - " [ 4.1589e-02],\n", - " [ 2.9379e-05],\n", - " [-2.9554e-02],\n", - " [-5.9865e-05]], requires_grad=True)\n", - "15000 1.9E-03 1.8E-03 4.4E-05 1.5E-05\n", - "tensor([[-1.2849e-04],\n", - " [ 4.8326e-05],\n", - " [ 7.6716e-02],\n", - " [ 3.0143e-03],\n", - " [-1.0011e+00],\n", - " [ 4.5407e-02],\n", - " [-9.1067e-05],\n", - " [-7.4136e-03],\n", - " [-1.1882e-04]], requires_grad=True)\n", - "15500 1.9E-03 1.8E-03 4.4E-05 1.5E-05\n", - "tensor([[-8.9885e-05],\n", - " [-3.4886e-05],\n", - " [ 7.4951e-02],\n", - " [ 3.5153e-03],\n", - " [-1.0048e+00],\n", - " [ 4.8821e-02],\n", - " [ 5.5874e-05],\n", - " [-4.3433e-05],\n", - " [-3.4738e-05]], requires_grad=True)\n", - "16000 1.9E-03 1.8E-03 4.6E-05 1.5E-05\n", - "tensor([[-2.4067e-04],\n", - " [-1.7940e-04],\n", - " [ 7.3316e-02],\n", - " [ 3.9657e-03],\n", - " [-1.0023e+00],\n", - " [ 5.2971e-02],\n", - " [-5.3019e-05],\n", - " [-1.0180e-03],\n", - " [ 1.0161e-04]], requires_grad=True)\n", - "16500 1.9E-03 1.8E-03 4.6E-05 1.5E-05\n", - "tensor([[-1.0207e-04],\n", - " [-1.0212e-05],\n", - " [ 7.3125e-02],\n", - " [ 3.7981e-03],\n", - " [-1.0036e+00],\n", - " [ 5.3121e-02],\n", - " [ 2.3265e-05],\n", - " [-2.2369e-04],\n", - " [-5.8185e-05]], requires_grad=True)\n", - "17000 1.9E-03 1.8E-03 4.8E-05 1.5E-05\n", - "tensor([[-1.1044e-04],\n", - " [-8.8982e-04],\n", - " [ 7.1109e-02],\n", - " [ 4.1078e-03],\n", - " [-1.0020e+00],\n", - " [ 5.6920e-02],\n", - " [ 2.2418e-05],\n", - " [-2.0069e-03],\n", - " [-1.9804e-04]], requires_grad=True)\n", - "17500 1.8E-03 1.8E-03 4.8E-05 1.5E-05\n", - "tensor([[-7.0449e-05],\n", - " [-2.1211e-05],\n", - " [ 7.1265e-02],\n", - " [ 4.1726e-03],\n", - " [-1.0031e+00],\n", - " [ 5.7023e-02],\n", - " [ 1.9343e-05],\n", - " [-2.5518e-04],\n", - " [-8.0919e-06]], requires_grad=True)\n", - "18000 1.8E-03 1.8E-03 4.7E-05 1.5E-05\n", - "tensor([[-1.3211e-04],\n", - " [ 2.5024e-05],\n", - " [ 7.0499e-02],\n", - " [ 4.5311e-03],\n", - " [-1.0026e+00],\n", - " [ 5.8403e-02],\n", - " [ 8.9930e-06],\n", - " [-2.3458e-04],\n", - " [ 3.5934e-06]], requires_grad=True)\n", - "18500 1.9E-03 1.8E-03 4.8E-05 1.5E-05\n", - "tensor([[-1.5548e-04],\n", - " [-9.0773e-06],\n", - " [ 6.9832e-02],\n", - " [ 4.6332e-03],\n", - " [-1.0026e+00],\n", - " [ 5.9665e-02],\n", - " [ 1.1546e-04],\n", - " [-1.0662e-04],\n", - " [ 3.5255e-05]], requires_grad=True)\n", - "19000 1.9E-03 1.9E-03 5.6E-05 1.5E-05\n", - "tensor([[-2.4196e-04],\n", - " [-2.5080e-04],\n", - " [ 6.9212e-02],\n", - " [ 4.4125e-03],\n", - " [-1.0030e+00],\n", - " [ 6.0636e-02],\n", - " [-2.6651e-04],\n", - " [-1.4484e-06],\n", - " [ 1.9089e-04]], requires_grad=True)\n", - "19500 1.8E-03 1.8E-03 4.9E-05 1.5E-05\n", - "tensor([[ 3.5155e-05],\n", - " [-4.6054e-05],\n", - " [ 6.9205e-02],\n", - " [ 4.5466e-03],\n", - " [-1.0036e+00],\n", - " [ 6.1074e-02],\n", - " [-4.0332e-05],\n", - " [-4.5013e-04],\n", - " [-1.3871e-04]], requires_grad=True)\n" - ] - } - ], - "source": [ - "network, coeff_vector_list, sparsity_mask_list = deepmod_init(network_config, library_config)\n", - "time_deriv_list, theta, coeff_vector_list = train(X_train, y_train, network, coeff_vector_list, sparsity_mask_list, library_config, optim_config)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "c_inferred_deepmod = network(torch.tensor(X, dtype=torch.float32)).reshape(data['x'].shape).detach().cpu().numpy()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "now let's try it with a normal network:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "network_MSE = deepmod_init(network_config, library_config)[0]\n", - "optimizer = torch.optim.Adam([{'params': network_MSE.parameters(), 'lr': 0.002}])\n", - "max_iterations = 20000" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0 0.04426572471857071\n", - "1000 0.001981872832402587\n", - "2000 0.0019115458708256483\n", - "3000 0.001889391103759408\n", - "4000 0.0018731887685135007\n", - "5000 0.0018576805014163256\n", - "6000 0.001846631639637053\n", - "7000 0.001837736228480935\n", - "8000 0.0018300212686881423\n", - "9000 0.001820864505134523\n", - "10000 0.001800038036890328\n", - "11000 0.0017825120594352484\n", - "12000 0.0017624474130570889\n", - "13000 0.0017337758326902986\n", - "14000 0.001695124665275216\n", - "15000 0.0016437311423942447\n", - "16000 0.0015969846863299608\n", - "17000 0.0015697209164500237\n", - "18000 0.0014671818353235722\n", - "19000 0.001410367782227695\n" - ] - } - ], - "source": [ - "for iteration in np.arange(max_iterations):\n", - " prediction = network_MSE(X_train)\n", - " loss = torch.mean((prediction - y_train)**2)\n", - " loss.backward()\n", - " \n", - " optimizer.step()\n", - " optimizer.zero_grad()\n", - " \n", - " if iteration % 1000 == 0:\n", - " print(iteration, loss.item())" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "c_inferred_MSE = network_MSE(torch.tensor(X, dtype=torch.float32)).reshape(data['x'].shape).detach().cpu().numpy()" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "plt.style.use('seaborn-paper')" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "frame = 50\n", - "factor = 1\n", - "\n", - "plt.figure(figsize=(7*factor, 3*factor))\n", - "plt.scatter(data['x'][:, frame], y_noisy.reshape(data['u'].shape)[:, frame], marker='x', c='grey', s=10, linewidths=0.1 ,label='Noisy data')\n", - "plt.plot(data['x'][:, frame], c_inferred_deepmod[:, frame], 'b', label='DeepMoD')\n", - "plt.plot(data['x'][:, frame], c_inferred_MSE[:, frame], 'r', label='No regularization')\n", - "plt.plot(data['x'][:, frame], np.real(data['u'])[:, frame], 'k--', label='Truth')\n", - "\n", - "plt.legend()\n", - "\n", - "plt.xlabel('space')\n", - "plt.ylabel('concentration')\n", - "\n", - "plt.tight_layout()\n", - "plt.savefig('DeepMoD_vs_MSE.pdf', bbox_inches='tight')" - ] - }, - { - "cell_type": "code", - "execution_count": 98, - "metadata": {}, - "outputs": [], - "source": [ - "used_idx = np.where(X[idx, 0][:number_of_samples] ==data['t'][0, frame])[0]" - ] - }, - { - "cell_type": "code", - "execution_count": 101, - "metadata": {}, - "outputs": [], - "source": [ - "c_used = y_noisy[idx][:number_of_samples][used_idx]\n", - "x_used = X[idx, 1][:number_of_samples][used_idx]" - ] - }, - { - "cell_type": "code", - "execution_count": 114, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 114, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "frame = 50\n", - "factor = 5\n", - "\n", - "used_idx = np.where(X[idx, 0][:number_of_samples] ==data['t'][0, frame])[0]\n", - "c_used = y_noisy[idx][:number_of_samples][used_idx]\n", - "x_used = X[idx, 1][:number_of_samples][used_idx]\n", - "\n", - "sort_idx = np.argsort(x_used)\n", - "c_used = c_used[sort_idx]\n", - "x_used = x_used[sort_idx]\n", - "\n", - "plt.figure(figsize=(7*factor, 3*factor))\n", - "\n", - "plt.subplot(121)\n", - "plt.scatter(x_used, c_used)\n", - "plt.plot(data['x'][:, 50], c_inferred_deepmod[:, frame])\n", - "plt.plot(data['x'][:, 50], c_inferred_MSE[:, frame])\n", - "plt.plot(data['x'][:, 50], np.real(data['u'])[:, frame], 'k--')\n" - ] - }, - { - "cell_type": "code", - "execution_count": 109, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 8, 1, 6, 0, 4, 10, 9, 7, 2, 5, 3])" - ] - }, - "execution_count": 109, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/examples/Example.ipynb b/examples/Example.ipynb new file mode 100644 index 0000000..9e4809b --- /dev/null +++ b/examples/Example.ipynb @@ -0,0 +1,459 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example Burgers' equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook we provide a simple example of the DeepMoD algorithm by applying it on the Burgers' equation. \n", + "\n", + "We start by importing the required libraries and setting the plotting style:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "import torch\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('seaborn-notebook')\n", + "\n", + "# DeepMoD stuff\n", + "from deepymod_torch.DeepMod import DeepMod\n", + "from deepymod_torch.library_functions import library_basic\n", + "from deepymod_torch.utilities import create_deriv_data\n", + "\n", + "# Setting cuda if GPU is available\n", + "if torch.cuda.is_available():\n", + " torch.set_default_tensor_type('torch.cuda.FloatTensor')\n", + "\n", + "# Settings for reproducibility\n", + "np.random.seed(42)\n", + "torch.manual_seed(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we prepare the dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shape of grid: (256, 101)\n" + ] + } + ], + "source": [ + "data = np.load('data/burgers.npy', allow_pickle=True).item()\n", + "print('Shape of grid:', data['x'].shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot it to get an idea of the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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p3wTomlRK2tzwApheRByyfal6XdgrJF0dEbtsX5K9vnWZ4SdK2patqFdK+lxE3DDtnPgoFQBg5kXEDkk7Bp4bGsoR8Za+7/dJOq3s+XAICTqJk8FGY78ZSB/hDBSUSkl7Oew3A+1GOAMAkBjCGQCAxBDO6Jwq95tTKmlP0qnNfjPQDoQzAACJIZxRmzqP7qxCSqvm5dAMBrQf4QwAQGIIZ2BGsN8MtAfhjE6pqhkstZI2x3YC3UY4Ax3CfjPQDYQzMAMoaQPtQjgDY6RW0gbQfYQzOoObXQDoCsIZaJlRzWDsN7fP3J6FpqeARBHOwDK6UNJmvzldS6eubXoKSBThDABAYghnAAASQzijFlWfq11FM1gXStoA2olwBjpgVDMY+81AOxHOQItwbCcwGxoLZ9srbH/b9leamgMwCiVtAE1qcuX8bkm7G3x/AACS1Eg4214r6dWSrmri/dEts34yGPvNQPc0tXL+uKTfl/R4nottz9sO2/Ho0sFqZ4aZR0kbKeD0sNlWezjbfo2kAxFxV94xETEfEY4IHzG3qsLZAemiGQyYHU2snM+R9Frb90u6VtLLbf+3BuYBAMniaM/ZVns4R8T7ImJtRJwk6UJJX4uIN9Y9D3RD2fvNbStps98MdBOfcwaABLHnXC/bm2zfZ3uv7S1DXt9s+27bO23fafuf5x07iUbDOSK+HhGvaXIOQBuw3zx7KGvXx/YKSVdKukDSBkkX2d4wcNktkk6LiNMlvU3Zp41yji2MlTMqV/W52mVpW0l7FEraQGEbJe2NiH0RsaReP9Tm/gsi4u8j4vA+0tGSIu/YSRDOQEuN2m8GIElaffgjuNnX/DLXrpG0v+/xQvbcE9h+ve09kr6q3uo599iiVk77A4CmtOnwkZPW/ugJj+9feGZDMwHaY8XSVL+ELkbE6pzXDvvH5ElvHBHbJG2z/euSPiTpFXnHFsXKGVC1Je3BYB71HIDGLEha1/d4raTFURdHxK2STrF9fNGxeRHOQIXKCOEizWDsNwMTuUPSetsn255T72O+2/svsP2PbDv7/gxJc5L+T56xk6CsDVSkytUx+81AeSLikO1LJd0oaYWkqyNil+1Lste3SvrXkt5s+5eS/q+kf5s1iA0dO+2cCGfMvCpK2pStMa25PQt8nKpGEbFD0o6B57b2ff8RSR/JO3ZalLXRSm1qBqsLJW2gOwhnoGSsmlEGVs2zjXDGTCu7pF12MA9rBmO/Geg+whkAgMQQzmidVPebmyxns98MdAvhjEqlfK52mSVt9plnW/8dpIrcTarucWgPwhlIFPvN7dHfvEUjF8pAOGMmsWoGkDLCGWg59puB7iGc0SqpNYPVuWqmpA3MDsIZM6fKO1CVpcjNLtBek+5Vs8fdfYQzMKEU9popaQPdRDgDAJAYwhkzpaySdt2rZvabgdlCOKM1UmkGS6GcLVHSBrqMcAYSQzPY7OGULwwinDEzyihpp7JqRrfQcY1BhDPQgPsXnpn7Wvabu4uztTEK4YzKpHzTi0mktGpmvzkthCXKRjijFaZtBmvDwSMS+80AeghnIIemVs2UtNuBE7tQNsIZaBlK2kD3Ec7ovGlL2intNaNbOFsboxDOSF4qh49Ujf3m2TRpAxmNZ91GOAPLqGLVnPdjVMP2mylpd0//yrdI4E46Du1AOKPT2tKlje6qI3ApbXcP4QyMUOdeMyXtbukP1iLBWcY4dAPhDCSIj1C1W92BzMq5ewhnJG2aZrBpStopdmiz39xNkwYrgVwu25ts32d7r+0tQ14/1fY3bT9q+/cGXrvf9j22d9q+s4z5EM5AjYqcqY32qPuMbI4LLZftFZKulHSBpA2SLrK9YeCyhyT9jqSPjfgx50bE6RFxZhlzIpyBAXWvmtlvRl0I8pE2StobEfsiYknStZI2918QEQci4g5Jv6xjQoQzKtH0TS/a3KXNR6iA2q2RtL/v8UL2XF4h6Sbbd9l+RxkTWlnGDwG6IsW9ZqAKc3sWkt+3XvFITPOL6Wrb/b/pXhYR8yOuHdbcUqQr85yIWLR9gqSbbe+JiFsLjH8SwhnJmpWTwQBUYjEiVue8dkHSur7HayUt5n2jiFjM/jxge5t6ZfKpwpmyNjpn0pJ21avmYc1gg/vNlLSBRtwhab3tk23PSbpQ0vY8A20fbfuYw99LeqWke6edECtnAJhBqZe06xQRh2xfKulGSSskXR0Ru2xfkr2+1fazJN0paZWkx22/R73O7uMlbbMt9TL1cxFxw7RzIpwBsdcMzLqI2CFpx8BzW/u+/4F65e5BByWdVvZ8KGujU9rcpT0MJe12qPvWj2WMQ9oIZyRpFprB8uw3o13qvv0jn1vuLsIZM6+OkjYng82Guo/iZCXcXYQzOoOSNlLHChl5Ec6YaU01glHSnk1l3K+ZoJ4NhDMANIBSNpZTezjbXmf7r2zvtr3L9rvrngPSNkkz2CQl7bpWzew3Ayiqic85H5L0uxHxrexUlbts3xwR32lgLkDjOBUMwKDaV84R8WBEfCv7/meSdqvY3T+QuKbvSJVHk4eOcItIAOM0uuds+yRJL5Z0e5PzQLt1rUsb6WvL55lpHmuvxsLZ9q9Iul7SeyLi4Jhr522H7Xh0adlL0XJ1HD5S56p53H4zJe12asvnmWkea69Gwtn2U9UL5s9GxBfHXR8R8xHhiPARc6uqnyBQEUra3cbKGGVpolvbkj4laXdE/HHd749uKVrS5gYXqBIrY5SliZXzOZLeJOnltndmX69qYB5Aoyhpp6d/JcqqFE2q/aNUEfHXkrp/VwMkp+5V8+B+MyVtAHlxQhiSUbQZjC5tNC3F1XWKc0JxTRxCAtRu2lXz+c/a84THN//g1Kl+HiXtbkhxzzfFOaE4Vs7AGIPBPAlK2rOJVSwmRTijlYqUtKdZNY8K5nGBzXna7dS/6ixjBcoqFpMinIERylgxD0NJG8A4hDOSUMfJYEVUFczoHg4eQRUIZ7RO1SXtaYOZj1DNFg4eQRUIZ6BP1StmStoA8iCc0VlFV82UsgGkgnBGq7Tt4BFK2u3Slv1j9p27j3BGqR4+5YjCY6poBqt61TzqEJLlPkJFSTt9RfZz+wOyLePQHoQzZh7lbEyiLY1gNJC1E+GM1shb0k7ltpCUtAFMinDGTCtz1UxJux0mvS0k41AnwhmdUmTVTDkbmF5Xgtz2Jtv32d5re8uQ1237T7PX77Z9Rt6xkyCc0ai8zWBld2lXHcyUtNuB/djhivx36cJ/Q9srJF0p6QJJGyRdZHvDwGUXSFqffb1D0icKjC2McEZn1LXXPKxTm5J2e5TRWDVpeLVl3AzaKGlvROyLiCVJ10raPHDNZkmfiZ7bJB1r+9k5xxbG/ZwxcyhnoypzexYmCrm2jKubH1mapmy+2nb/b8aXRcT8iGvXSNrf93hB0tk5rlmTc2xhrJyRvDJL2nUEMyVtSPUcMMLHq5a1GBHu+5pf5tph+2uDJa9R1+QZWxgrZ3RCkx+foqSNw+ouRaM0C5LW9T1eK2kx5zVzOcYWxsoZM4NyNsrSluM6u9JJXYM7JK23fbLtOUkXSto+cM12SW/OurZfIunhiHgw59jCCGc0pqxjO+tcNY86tvMwStrd1ZbjOlFcRBySdKmkGyXtlvSFiNhl+xLbl2SX7ZC0T9JeSX8h6beXGzvtnChrI2ll7TdXtWqmpD07Uj52c1SDF6GeX0TsUC+A+5/b2vd9SHpn3rHTYuWMVsuzaq6rnM2qGU0hhLuHcAZyGlfSRre0ZX+YfeVuIpyRrHEl7aZXzZS022fSjyl1cdw4hH6zCGc0oop7OA+qszubknY7tCU4UwhqSuXNIpzRSqncFjIvVs3pSbnBq8lxSEPrw5nSSzdN26Vd9qp5cL+5aEkb6WjLrRjbOA7laX04Y/aMWzXXfdgIJW0AZWt9OFO6QUpYNaevLeXlJsvZ/LvavNaHM9pnXDPYNCXtKlbNy5W086ya2W9OV1satqoaV8bpZagG4YxWaVsjGJqVQgCmPI5ms3QRzuiMOvaaaQRrl7aUlNsyruqfhf+vdeHsR8q7ty/K9fApR0z9M5YraS+3aq4qmJc7FYySdrra2OncxXGYXOvCGQCAriOc0QoprJopabdTW0rGKY+jdF0/bhmJWi3XqT1Jl3aRYH7Dqm894fF1B88o/H6HUdJOW8pB18Zxo37GqFtVYnqtC+c4kgMfZs20HdqDoTyJ5VbNwKwimKtDWRutlWfVPGkwF2kEo6SNWUaDWDVaH850EXbDqJL2NKvmMlbMk6KkXb22dCx3fRyq0fpwxmwat2qeJpiLNIIBQBUIZyRr1Kq5ymAeh5I2gDrMbDhTwqnfqE7taW8P2a/sYJ5k1UxJG8C0Zjac0U7LrZrLCGYawQCkgHBGkoaVtMsM5mk+4wwAVSOc0XpllbJpBAOQCsIZjRq231x01VyHvCVt9psBlKFT4TzpWbGcctNek6yah5W0WTW3W1uOwez6OJSnleHc313NX6J2WO5M7X5FVs11HTKS5xxt1K/I//uT/pvBuPHjUI1WhjOB3A15PkLVRDCPWzVT0m6ftqw8uz4O+TUSzrY32b7P9l7bW5qYA9KT96jOaYI5T0kbQH5dD2rbz7B9s+3vZn8eN+K6q20fsH3vwPPztr9ve2f29ao871t7ONteIelKSRdI2iDpItsb6p4H0jds1Vx1KXtw1UxJO21llFdHHUg07qCiUe9dZNyk75fKuBmxRdItEbFe0i3Z42GukbRpxGt/EhGnZ1878rxpEyvnjZL2RsS+iFiSdK2kzQ3MAw2a5FSwaYO5jFUzB4+kZdJV29yehaEhk+fnTRJOkwbaqHlWOQ5PslnSp7PvPy3pdcMuiohbJT1U1ps6ot5/bGy/QdKmiPit7PGbJJ0dEZcuM2Ze0gezh7+UdHfV8yzZakmLTU+iIOZcD+ZcvbbNV2rfnJ8bEaV/xMH2DZKOn3D4sZJO6Xt8WUTMTzCHn0bEsX2PfxIRo0rbJ0n6SkS8sO+5eUlvkXRQ0p2SfjcifjLufVcWnWgJhrXtLvsbQvYfdF6SbEdEnFn+tKqTzXl10/MogjnXgzlXr23zldo55ypExKgycals/w9Jzxry0gdK+PGfkPQh9XLuQ5L+SNLbxg1qIpwXJK3re7xW7foNEQDQIRHxilGv2f6h7WdHxIO2ny3pQMGf/cO+n/UXkr6SZ1wTe853SFpv+2Tbc5IulLS9gXkAADDOdkkXZ99fLOnLRQZngX7Y6yXdO+rafrWHc0QcknSppBsl7Zb0hYjYVeBHXFbJxKrFnOvBnOvRtjm3bb5SO+fcVR+WdL7t70o6P3ss26tt/0Pnte3PS/qmpBfYXrD99uylj9q+x/bdks6V9N48b1p7QxgAAFheK08IAwCgywhnAAASQzgDAJAYwhkAgMQQzgAAJIZwBgAgMa0MZ9un274tu/3WnbY3Nj2nPGy/K7tV5i7bH216PnnZ/j3bYXvSM25rY/ty23ts3217m+1jx4+qX9tum2p7ne2/sr07+/v77qbnlJftFba/bTvXyUxNs32s7euyv8e7bf/TpueE+rUynCV9VL1DzE+X9J+zx0mzfa56dzd5UUT8mqSPNTylXGyvU++D9w80PZecbpb0woh4kaT/Lel9Dc/nSVp629RD6h3Y/6uSXiLpnS2Y82HvVu/Ao7a4QtINEXGqpNPUrrmjJG0N55C0Kvv+6WrH2dz/QdKHI+JRSYqIQuezNuhPJP2+xtycJBURcVN2Cp0k3abe2e2pad1tUyPiwYj4Vvb9z9QLjDXNzmo822slvVrSVU3PJQ/bqyT9uqRPSVJELEXET5udFZrQ1nB+j6TLbe9XbwWa3OpoiOdLeqnt221/w/ZZTU9oHNuvlfT9iPibpucyobdJ+u9NT2KINZL29z1eUAuC7rDstngvlnR7szPJ5ePq/XL5eNMTyel5kn4k6S+zUvxVto9uelKoXxN3pcplzC28zpP03oi43vZvqvdb5si7itRlzJxXSjpOvZLgWZK+YPt50fD5qWPm/H5Jr6x3RuMtN+eI+HJ2zQfUK8V+ts655VT4tqmpsP0rkq6X9J6IONj0fJZj+zWSDkTEXbZf1vR8clop6QxJ74qI210Tg9IAAAJXSURBVG1fIWmLpP/U7LRQt1aerW37YUnHRkTYtqSHI2LVuHFNym4a/uGI+Hr2+HuSXhIRP2p0YiPY/seSbpH0i+ypw7f23BgRP2hsYjnYvljSJZLOi4hfjLu+blmDz3xE/Ivs8fskKSL+sNGJjWH7qerd7u7GiPjjpuczju0/lPQm9X5JO1K9rbAvRsQbG53YMmw/S9JtEXFS9vilkrZExKsbnRhq19ay9qKk38i+f7mk7zY4l7y+pN5cZfv5kuYk/bjRGS0jIu6JiBMi4qTsH4oFSWe0IJg3SfoDSa9NMZgzrbttavZL8Kck7W5DMEtSRLwvItZmf38vlPS1lINZkrL/v/bbfkH21HmSvtPglNCQZMvaY/x7SVfYXinpEUnvaHg+eVwt6Wrb90paknRx0yXtjvovko6QdHMvT3RbRFzS7JSeKCIO2T5829QVkq4ueNvUJpyj3ir0Hts7s+feHxE7lhmDybxL0mezX9z2SXprw/NBA1pZ1gYAoMvaWtYGAKCzCGcAABJDOAMAkBjCGQCAxBDOAAAkhnAGACAxhDMAAIkhnIEa2T7V9n7bz80ez9u+tul5AUgLh5AANbP9JknvVO9e5H8m6azUbyIBoF6EM9AA29dI+k1JL42IuxqeDoDEUNYGapadmfxrkn4q6cSGpwMgQYQzUL/LJd0l6XxJW22vbXg+ABLT1rtSAa1k+3WSXibp7Ih4xPZlkj5v+9yIONTs7ACkgj1nAAASQ1kbAIDEEM4AACSGcAYAIDGEMwAAiSGcAQBIDOEMAEBiCGcAABLz/wANnP60hf1+DgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "im = ax.contourf(data['x'], data['t'], np.real(data['u']))\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('t')\n", + "fig.colorbar(mappable=im)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(25856, 2) (25856, 1)\n" + ] + } + ], + "source": [ + "X = np.transpose((data['t'].flatten(), data['x'].flatten()))\n", + "y = np.real(data['u']).reshape((data['u'].size, 1))\n", + "\n", + "print(X.shape, y.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0. , -8. ],\n", + " [ 0.1 , -8. ],\n", + " [ 0.2 , -8. ],\n", + " ...,\n", + " [ 9.8 , 7.9375],\n", + " [ 9.9 , 7.9375],\n", + " [10. , 7.9375]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see, $X$ has 2 dimensions, $\\{x, t\\}$, while $y$ has only one, $\\{u\\}$. Always explicity set the shape (i.e. $N\\times 1$, not $N$) or you'll get errors. This dataset is noiseless, so let's add $5\\%$ noise:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "noise_level = 0.05\n", + "y_noisy = y + noise_level * np.std(y) * np.random.randn(y.size, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dataset is also much larger than needed, so let's hussle it and pick out a 1000 samples:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "number_of_samples = 1000\n", + "\n", + "idx = np.random.permutation(y.shape[0])\n", + "X_train = torch.tensor(X[idx, :][:number_of_samples], dtype=torch.float32, requires_grad=True)\n", + "y_train = torch.tensor(y_noisy[idx, :][:number_of_samples], dtype=torch.float32)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([1000, 2]) torch.Size([1000, 1])\n" + ] + } + ], + "source": [ + "print(X_train.shape, y_train.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have a dataset which we can use. Let's plot, for a final time, the original dataset, the noisy set and the samples points:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(ncols=3, figsize=(15, 4))\n", + "\n", + "im0 = axes[0].contourf(data['x'], data['t'], np.real(data['u']), cmap='coolwarm')\n", + "axes[0].set_xlabel('x')\n", + "axes[0].set_ylabel('t')\n", + "axes[0].set_title('Ground truth')\n", + "\n", + "im1 = axes[1].contourf(data['x'], data['t'], y_noisy.reshape(data['x'].shape), cmap='coolwarm')\n", + "axes[1].set_xlabel('x')\n", + "axes[1].set_title('Noisy')\n", + "\n", + "sampled = np.array([y_noisy[index, 0] if index in idx[:number_of_samples] else np.nan for index in np.arange(data['x'].size)])\n", + "sampled = np.rot90(sampled.reshape(data['x'].shape)) #array needs to be rotated because of imshow\n", + "\n", + "im2 = axes[2].imshow(sampled, aspect='auto', cmap='coolwarm')\n", + "axes[2].set_xlabel('x')\n", + "axes[2].set_title('Sampled')\n", + "\n", + "fig.colorbar(im1, ax=axes.ravel().tolist())\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Configuring DeepMoD" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now setup the options for DeepMoD. The setup requires the dimensions of the neural network, a library function and some args for the library function:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "config = {'input_dim': 2, 'hidden_dim': 20, 'layers': 5, 'output_dim': 1, 'library_function': library_basic, 'library_args':{'poly_order': 2, 'diff_order': 2}}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we instantiate the model:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "model = DeepMod(config)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run DeepMoD " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now run DeepMoD using all the options we have set and the training data. We need to slightly preprocess the input data for the derivatives:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "optimizer = torch.optim.Adam(model.parameters(), lr=0.002)\n", + "X_input = create_deriv_data(X_train, config['library_args']['diff_order'])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "| Iteration | Progress | Time remaining | Cost | MSE | Reg | L1 |\n", + " 5000 100.00% 0s 9.38e-05 7.68e-05 2.42e-06 1.46e-05 \n", + "[Parameter containing:\n", + "tensor([[ 0.0952],\n", + " [-0.9262]], requires_grad=True)]\n", + "[tensor([2, 4])]\n", + "\n", + "| Iteration | Progress | Time remaining | Cost | MSE | Reg | L1 |\n", + " 5000 100.00% 0s 1.13e-04 7.68e-05 3.57e-05 0.00e+00 " + ] + } + ], + "source": [ + "model.train(X_input, y_train, optimizer, 5000, type='deepmod')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that DeepMoD has converged, it has found the following equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final result:\n", + "Parameter containing:\n", + "tensor([[ 0.0952],\n", + " [-0.9262]], requires_grad=True) [tensor([2, 4])]\n" + ] + } + ], + "source": [ + "print('Final result:')\n", + "print(model.coeff_vector_list[0], model.sparsity_mask_list)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Other options" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have a few other options, most notably training the mse or a single deepmod cycle (i.e. mse + reg + l1, but not thresholding):" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "| Iteration | Progress | Time remaining | Cost | MSE | Reg | L1 |\n", + " 1000 100.00% 0s 7.68e-05 7.68e-05 0.00e+00 0.00e+00 " + ] + } + ], + "source": [ + "model.train(X_input, y_train, optimizer, 1000, type='mse')" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "| Iteration | Progress | Time remaining | Cost | MSE | Reg | L1 |\n", + " 1000 100.00% 0s 1.26e-04 7.68e-05 3.57e-05 1.35e-05 " + ] + } + ], + "source": [ + "model.train(X_input, y_train, optimizer, 1000, type='single_cycle')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/examples/Example_Advection_Diffusion.ipynb b/examples/Example_Advection_Diffusion.ipynb deleted file mode 100644 index 0dbfa5a..0000000 --- a/examples/Example_Advection_Diffusion.ipynb +++ /dev/null @@ -1,352 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example Burgers' equation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this notebook we provide a simple example of the DeepMoD algorithm by applying it on the Burgers' equation. \n", - "\n", - "We start by importing the required libraries and setting the plotting style:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import torch\n", - "from scipy.io import loadmat\n", - "from deepymod_torch.library_function import *\n", - "from deepymod_torch.DeepMod import DeepMoD\n", - "\n", - "import matplotlib.pyplot as plt\n", - "plt.style.use('seaborn-notebook')\n", - "\n", - "np.random.seed(40)\n", - "\n", - "#torch.set_default_tensor_type('torch.cuda.FloatTensor') # enable for gpu." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we prepare the dataset." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "data = loadmat('../data/processed/Advection_diffusion.mat')\n", - "usol = np.real(data['Expression1'])\n", - "usol= usol.reshape((51,51,61,4))\n", - "\n", - "x_v= usol[:,:,:,0]\n", - "y_v = usol[:,:,:,1]\n", - "t_v = usol[:,:,:,2]\n", - "u_v = usol[:,:,:,3]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's plot it to get an idea of the data:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, axes = plt.subplots(ncols=3, figsize=(15, 4))\n", - "\n", - "im0 = axes[0].contourf(x_v[:,:,0], y_v[:,:,0], u_v[:,:,0], cmap='coolwarm')\n", - "axes[0].set_xlabel('x')\n", - "axes[0].set_ylabel('y')\n", - "axes[0].set_title('t = 0')\n", - "\n", - "im1 = axes[1].contourf(x_v[:,:,10], y_v[:,:,10], u_v[:,:,10], cmap='coolwarm')\n", - "axes[1].set_xlabel('x')\n", - "axes[1].set_title('t = 10')\n", - "\n", - "im2 = axes[2].contourf(x_v[:,:,20], y_v[:,:,20], u_v[:,:,20], cmap='coolwarm')\n", - "axes[2].set_xlabel('x')\n", - "axes[2].set_title('t= 20')\n", - "\n", - "fig.colorbar(im1, ax=axes.ravel().tolist())\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(158661, 3) (158661, 1)\n" - ] - } - ], - "source": [ - "X = np.transpose((t_v.flatten(),x_v.flatten(), y_v.flatten()))\n", - "y = u_v.reshape((u_v.size, 1))\n", - "\n", - "print(X.shape, y.shape)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As we can see, $X$ has 2 dimensions, $\\{x, t\\}$, while $y$ has only one, $\\{u\\}$. Always explicity set the shape (i.e. $N\\times 1$, not $N$) or you'll get errors. This dataset is noiseless, so let's add $5\\%$ noise:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "noise_level = 0.05\n", - "y_noisy = y + noise_level * np.std(y) * np.random.randn(y.size, 1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The dataset is also much larger than needed, so let's hussle it and pick out a 1000 samples:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "number_of_samples = 1000\n", - "\n", - "idx = np.random.permutation(y.size)\n", - "X_train = torch.tensor(X[idx, :][:number_of_samples], dtype=torch.float32, requires_grad=True)\n", - "y_train = torch.tensor(y_noisy[idx, :][:number_of_samples], dtype=torch.float32)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "torch.Size([1000, 3]) torch.Size([1000, 1])\n" - ] - } - ], - "source": [ - "print(X_train.shape, y_train.shape)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Configure the neural network" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We now setup the options for DeepMoD. There's as few dictionaries to fill, starting with the 'optim config', which sets the maximal number of iterations and the amplitude of the $L_1$ penalty" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "optim_config = {'lambda': 10**-5, 'max_iterations': 10000}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we choose the size of the neural network " - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "network_config = {'input_dim': 3, 'hidden_dim': 20, 'layers': 5, 'output_dim': 1}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "DeepMoD accepts any arbitrary library function and any options for it can be given through *the library_config*. The library function for the burgers case accepts a maximum order for the polynomial and derivative terms." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "lib_config = {'type': library_2Din_1Dout, 'poly_order': 1, 'diff_order': 3}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Run DeepMoD " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now run DeepMoD using all the options we have set and the training data. We also need to specify which library function we wish to use. You can build any library you want and just pass is through this command:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch | Total loss | MSE | PI | L1 \n", - "0 3.9E-01 3.8E-01 1.4E-02 1.9E-03\n", - "tensor([[ 0.1821],\n", - " [-1.1177],\n", - " [-0.0823],\n", - " [ 0.7238],\n", - " [ 1.3714],\n", - " [ 0.4207],\n", - " [-0.8091],\n", - " [ 1.3054],\n", - " [-1.0528],\n", - " [ 1.5336],\n", - " [-0.0356],\n", - " [-0.6693]], requires_grad=True)\n" - ] - }, - { - "ename": "KeyboardInterrupt", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m 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network = DeepMoD(X_train, y_train, network_config, lib_config, optim_config)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now that DeepMoD has converged, it has found the following equation:" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Final result:\n", - "(tensor([[ 0.0994],\n", - " [-1.0001]], requires_grad=True),) (tensor([2, 5]),)\n" - ] - } - ], - "source": [ - "print('Final result:')\n", - "print(sparse_coeff_vector, sparsity_mask)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/examples/Example_Burgers.ipynb b/examples/Example_Burgers.ipynb deleted file mode 100644 index d511367..0000000 --- a/examples/Example_Burgers.ipynb +++ /dev/null @@ -1,1044 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example Burgers' equation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this notebook we provide a simple example of the DeepMoD algorithm by applying it on the Burgers' equation. \n", - "\n", - "We start by importing the required libraries and setting the plotting style:" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import torch\n", - "from deepymod_torch.library_function import library_1D_in\n", - "from deepymod_torch.DeepMod import DeepMoD\n", - "\n", - "import matplotlib.pyplot as plt\n", - "plt.style.use('seaborn-notebook')\n", - "\n", - "np.random.seed(40)\n", - "\n", - "#torch.set_default_tensor_type('torch.cuda.FloatTensor') # enable for gpu." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we prepare the dataset." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Shape of grid: (256, 101)\n" - ] - } - ], - "source": [ - "data = np.load('../data/processed/burgers.npy', allow_pickle=True).item()\n", - "print('Shape of grid:', data['x'].shape)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's plot it to get an idea of the data:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots()\n", - "im = ax.contourf(data['x'], data['t'], np.real(data['u']))\n", - "ax.set_xlabel('x')\n", - "ax.set_ylabel('t')\n", - "fig.colorbar(mappable=im)\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(25856, 2) (25856, 1)\n" - ] - } - ], - "source": [ - "X = np.transpose((data['t'].flatten(), data['x'].flatten()))\n", - "y = np.real(data['u']).reshape((data['u'].size, 1))\n", - "\n", - "print(X.shape, y.shape)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 0. , -8. ],\n", - " [ 0.1 , -8. ],\n", - " [ 0.2 , -8. ],\n", - " ...,\n", - " [ 9.8 , 7.9375],\n", - " [ 9.9 , 7.9375],\n", - " [10. , 7.9375]])" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "X" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As we can see, $X$ has 2 dimensions, $\\{x, t\\}$, while $y$ has only one, $\\{u\\}$. Always explicity set the shape (i.e. $N\\times 1$, not $N$) or you'll get errors. This dataset is noiseless, so let's add $5\\%$ noise:" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [], - "source": [ - "noise_level = 0.05\n", - "y_noisy = y + noise_level * np.std(y) * np.random.randn(y.size, 1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The dataset is also much larger than needed, so let's hussle it and pick out a 1000 samples:" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [], - "source": [ - "number_of_samples = 1000\n", - "\n", - "idx = np.random.permutation(y.size)\n", - "X_train = torch.tensor(X[idx, :][:number_of_samples], dtype=torch.float32, requires_grad=True)\n", - "y_train = torch.tensor(y_noisy[idx, :][:number_of_samples], dtype=torch.float32)" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "torch.Size([1000, 2]) torch.Size([1000, 1])\n" - ] - } - ], - "source": [ - "print(X_train.shape, y_train.shape)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We now have a dataset which we can use. Let's plot, for a final time, the original dataset, the noisy set and the samples points:" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, axes = plt.subplots(ncols=3, figsize=(15, 4))\n", - "\n", - "im0 = axes[0].contourf(data['x'], data['t'], np.real(data['u']), cmap='coolwarm')\n", - "axes[0].set_xlabel('x')\n", - "axes[0].set_ylabel('t')\n", - "axes[0].set_title('Ground truth')\n", - "\n", - "im1 = axes[1].contourf(data['x'], data['t'], y_noisy.reshape(data['x'].shape), cmap='coolwarm')\n", - "axes[1].set_xlabel('x')\n", - "axes[1].set_title('Noisy')\n", - "\n", - "sampled = np.array([y_noisy[index, 0] if index in idx[:number_of_samples] else np.nan for index in np.arange(data['x'].size)])\n", - "sampled = np.rot90(sampled.reshape(data['x'].shape)) #array needs to be rotated because of imshow\n", - "\n", - "im2 = axes[2].imshow(sampled, aspect='auto', cmap='coolwarm')\n", - "axes[2].set_xlabel('x')\n", - "axes[2].set_title('Sampled')\n", - "\n", - "fig.colorbar(im1, ax=axes.ravel().tolist())\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Configure the neural network" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We now setup the options for DeepMoD. There's as few dictionaries to fill, starting with the 'optim config', which sets the maximal number of iterations and the amplitude of the $L_1$ penalty" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [], - "source": [ - "optim_config = {'lambda': 10**-5, 'max_iterations': 20000}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we choose the size of the neural network " - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [], - "source": [ - "network_config = {'input_dim': 2, 'hidden_dim': 20, 'layers': 5, 'output_dim': 1}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "DeepMoD accepts any arbitrary library function and any options for it can be given through *the library_config*. The library function for the burgers case accepts a maximum order for the polynomial and derivative terms." - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "lib_config = {'type': library_1D_in, 'poly_order': 2, 'diff_order': 3}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Run DeepMoD " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now run DeepMoD using all the options we have set and the training data. We also need to specify which library function we wish to use. You can build any library you want and just pass is through this command:" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Epoch | Total loss | MSE | PI | L1 \n", - "0 5.1E-01 4.6E-02 4.6E-01 2.3E-03\n", - "tensor([[-0.6836],\n", - " [ 0.2441],\n", - " [-1.0590],\n", - " [ 1.6611],\n", - " [ 0.1850],\n", - " [-0.7019],\n", - " [ 0.4375],\n", - " [ 1.6637],\n", - " [-0.0451],\n", - " [ 0.6706],\n", - " [-0.1395],\n", - " [-1.6934]], requires_grad=True)\n", - "500 2.2E-02 1.4E-02 7.9E-03 1.1E-04\n", - "tensor([[-0.1976],\n", - " [ 0.7616],\n", - " [-0.2542],\n", - " [ 1.5396],\n", - " [ 0.6154],\n", - " [-0.4006],\n", - " [ 0.3261],\n", - " [ 1.5048],\n", - " [ 0.3577],\n", - " [ 1.0663],\n", - " [-0.4060],\n", - " [-1.8981]], requires_grad=True)\n", - "1000 6.7E-03 3.9E-03 2.6E-03 1.6E-04\n", - "tensor([[-0.0835],\n", - " [ 0.4111],\n", - " [ 0.6960],\n", - " [ 0.6732],\n", - " [ 0.5493],\n", - " [-0.6961],\n", - " [ 1.2284],\n", - " [ 1.0464],\n", - " [ 0.2509],\n", - " [ 1.0777],\n", - " [ 0.3777],\n", - " [-2.7498]], requires_grad=True)\n", - "1500 3.6E-03 1.9E-03 1.6E-03 9.8E-05\n", - "tensor([[-0.0462],\n", - " [ 0.0971],\n", - " [ 0.3274],\n", - " [ 0.1028],\n", - " [ 0.4244],\n", - " [-1.3105],\n", - " [ 1.1725],\n", - " [ 1.1466],\n", - " [ 0.1403],\n", - " [ 0.2518],\n", - " [ 0.2611],\n", - " [-2.9867]], requires_grad=True)\n", - "2000 1.7E-03 1.2E-03 4.0E-04 7.8E-05\n", - "tensor([[-1.8484e-02],\n", - " [-4.9587e-02],\n", - " [ 4.3971e-02],\n", - " [-7.5622e-02],\n", - " [ 2.9072e-01],\n", - " [-2.0497e+00],\n", - " [ 1.2226e+00],\n", - " [ 1.9819e-01],\n", - " [-2.7124e-04],\n", - " [-6.7962e-01],\n", - " [ 1.0438e-01],\n", - " [-1.3692e+00]], requires_grad=True)\n", - "2500 5.5E-04 3.2E-04 1.5E-04 7.8E-05\n", - "tensor([[-0.0075],\n", - " [-0.0088],\n", - " [-0.0150],\n", - " [-0.0365],\n", - " [ 0.2141],\n", - " [-2.0969],\n", - " [ 1.1485],\n", - " [ 0.0657],\n", - " [-0.0680],\n", - " [-0.4016],\n", - " [-0.2894],\n", - " [-0.8153]], requires_grad=True)\n", - "3000 3.2E-04 1.8E-04 6.7E-05 7.2E-05\n", - "tensor([[-0.0042],\n", - " [ 0.0207],\n", - " [ 0.0026],\n", - " [-0.0170],\n", - " [ 0.1566],\n", - " [-1.9108],\n", - " [ 0.9961],\n", - " [ 0.0411],\n", - " [-0.1067],\n", - " [ 0.0281],\n", - " [-0.6301],\n", - " [-0.4788]], requires_grad=True)\n", - "3500 2.3E-04 1.3E-04 3.3E-05 6.4E-05\n", - "tensor([[-0.0017],\n", - " [ 0.0127],\n", - " [ 0.0079],\n", - " [-0.0094],\n", - " [ 0.1174],\n", - " [-1.7087],\n", - " [ 0.8591],\n", - " [ 0.0146],\n", - " [-0.1248],\n", - " [ 0.2440],\n", - " [-0.7161],\n", - " [-0.2654]], requires_grad=True)\n", - "4000 1.9E-04 1.1E-04 2.3E-05 5.5E-05\n", - "tensor([[-4.7823e-04],\n", - " [-8.6400e-06],\n", - " [ 1.1794e-02],\n", - " [-5.7139e-03],\n", - " [ 9.5278e-02],\n", - " [-1.5539e+00],\n", - " [ 7.2357e-01],\n", - " [ 3.9211e-05],\n", - " [-1.2285e-01],\n", - " [ 3.6273e-01],\n", - " [-6.5619e-01],\n", - " [-1.3687e-01]], requires_grad=True)\n", - "4500 4.9E-04 4.1E-04 3.2E-05 5.0E-05\n", - "tensor([[-1.1595e-04],\n", - " [-1.1608e-03],\n", - " [ 2.2045e-02],\n", - " [-3.9343e-03],\n", - " [ 7.7913e-02],\n", - " [-1.4459e+00],\n", - " [ 5.7067e-01],\n", - " [-6.1506e-04],\n", - " [-1.1263e-01],\n", - " [ 4.2091e-01],\n", - " [-5.3391e-01],\n", - " [-7.4888e-02]], requires_grad=True)\n", - "5000 1.4E-04 8.7E-05 1.2E-05 4.0E-05\n", - "tensor([[ 6.8457e-07],\n", - " [-3.6631e-03],\n", - " [ 3.8922e-02],\n", - " [-3.0871e-03],\n", - " [ 6.0962e-02],\n", - " [-1.3428e+00],\n", - " [ 4.0905e-01],\n", - " [ 2.8657e-05],\n", - " [-9.9380e-02],\n", - " [ 4.3375e-01],\n", - " [-4.0279e-01],\n", - " [-3.2518e-02]], requires_grad=True)\n", - "5500 1.2E-04 8.3E-05 8.6E-06 3.3E-05\n", - "tensor([[-9.0940e-07],\n", - " [-5.5522e-03],\n", - " [ 5.8044e-02],\n", - " [-1.6781e-03],\n", - " [ 4.5063e-02],\n", - " [-1.2482e+00],\n", - " [ 2.6122e-01],\n", - " [-4.5029e-05],\n", - " [-8.5159e-02],\n", - " [ 4.0829e-01],\n", - " [-2.7329e-01],\n", - " [-1.2851e-02]], requires_grad=True)\n", - "6000 1.1E-04 8.0E-05 7.5E-06 2.7E-05\n", - "tensor([[-3.5338e-07],\n", - " [-6.0765e-03],\n", - " [ 7.6158e-02],\n", - " [-2.7715e-05],\n", - " [ 3.0875e-02],\n", - " [-1.1634e+00],\n", - " [ 1.3547e-01],\n", - " [ 1.0477e-05],\n", - " [-6.9292e-02],\n", - " [ 3.4284e-01],\n", - " [-1.5644e-01],\n", - " [-5.5317e-03]], requires_grad=True)\n", - "6500 1.1E-04 7.8E-05 7.1E-06 2.2E-05\n", - "tensor([[-9.8471e-07],\n", - " [-6.8820e-03],\n", - " [ 8.9038e-02],\n", - " [ 7.0355e-04],\n", - " [ 1.9135e-02],\n", - " [-1.0957e+00],\n", - " [ 4.9972e-02],\n", - " [ 1.1611e-05],\n", - " [-5.1117e-02],\n", - " [ 2.5867e-01],\n", - " [-7.1343e-02],\n", - " [-2.1375e-03]], requires_grad=True)\n", - "7000 1.0E-04 7.7E-05 6.4E-06 1.8E-05\n", - "tensor([[ 2.8075e-06],\n", - " [-7.2803e-03],\n", - " [ 9.7136e-02],\n", - " [ 1.8101e-03],\n", - " [ 8.7523e-03],\n", - " [-1.0364e+00],\n", - " [ 1.3589e-04],\n", - " [-2.6864e-05],\n", - " [-3.1054e-02],\n", - " [ 1.6087e-01],\n", - " [-1.6613e-02],\n", - " [-3.4703e-03]], requires_grad=True)\n", - "7500 9.8E-05 7.7E-05 5.3E-06 1.6E-05\n", - "tensor([[ 7.0111e-05],\n", - " [-9.7974e-03],\n", - " [ 9.7597e-02],\n", - " [ 1.8542e-03],\n", - " [ 3.6692e-04],\n", - " [-9.8941e-01],\n", - " [-4.3295e-05],\n", - " [-1.5453e-05],\n", - " [-7.9267e-03],\n", - " [ 5.4461e-02],\n", - " [-3.5239e-03],\n", - " [-5.7182e-03]], requires_grad=True)\n", - "8000 9.5E-05 7.6E-05 4.3E-06 1.5E-05\n", - "tensor([[ 4.7070e-06],\n", - " [-1.4333e-02],\n", - " [ 9.7336e-02],\n", - " [ 1.4981e-03],\n", - " [-1.4519e-06],\n", - " [-9.5404e-01],\n", - " [ 5.6878e-05],\n", - " [-6.0121e-06],\n", - " [-4.5131e-03],\n", - " [-8.5465e-05],\n", - " [-1.4539e-04],\n", - " [-4.8250e-03]], requires_grad=True)\n", - "8500 1.0E-04 8.2E-05 3.9E-06 1.5E-05\n", - "tensor([[ 1.1069e-04],\n", - " [-1.6273e-02],\n", - " [ 9.6130e-02],\n", - " [ 8.4822e-04],\n", - " [-2.2806e-05],\n", - " [-9.4983e-01],\n", - " [ 1.8668e-04],\n", - " [ 5.1667e-05],\n", - " [-5.7211e-03],\n", - " [ 1.3703e-04],\n", - " [-6.4786e-05],\n", - " [-1.6859e-03]], requires_grad=True)\n", - "9000 9.3E-05 7.6E-05 3.1E-06 1.5E-05\n", - "tensor([[ 3.0162e-05],\n", - " [-1.4593e-02],\n", - " [ 9.5803e-02],\n", - " [ 5.1464e-04],\n", - " [-3.7405e-06],\n", - " [-9.5333e-01],\n", - " [ 9.1416e-05],\n", - " [-8.3540e-07],\n", - " [-5.0855e-03],\n", - " [-2.6978e-04],\n", - " [-1.0875e-04],\n", - " [ 5.1053e-06]], requires_grad=True)\n", - "9500 9.3E-05 7.5E-05 2.6E-06 1.5E-05\n", - "tensor([[ 1.6432e-05],\n", - " [-1.2351e-02],\n", - " [ 9.6170e-02],\n", - " [ 3.9166e-04],\n", - " [-6.3330e-07],\n", - " [-9.5960e-01],\n", - " [ 1.7061e-05],\n", - " [ 9.1258e-05],\n", - " [-4.6063e-03],\n", - " [-1.5472e-03],\n", - " [ 1.6086e-05],\n", - " [-1.2202e-05]], requires_grad=True)\n", - "10000 9.2E-05 7.5E-05 2.3E-06 1.5E-05\n", - "tensor([[ 1.5544e-05],\n", - " [-1.0634e-02],\n", - " [ 9.6434e-02],\n", - " [ 2.8442e-04],\n", - " [-5.2577e-05],\n", - " [-9.6482e-01],\n", - " [ 2.4199e-05],\n", - " [ 7.3105e-05],\n", - " [-4.3988e-03],\n", - " [-1.4554e-03],\n", - " [ 1.1958e-05],\n", - " [ 5.5556e-05]], requires_grad=True)\n", - "10500 9.2E-05 7.5E-05 2.1E-06 1.5E-05\n", - "tensor([[ 4.5583e-05],\n", - " [-9.3972e-03],\n", - " [ 9.6696e-02],\n", - " [ 1.8867e-04],\n", - " [-3.1869e-05],\n", - " [-9.6835e-01],\n", - " [ 2.2913e-04],\n", - " [ 2.0867e-04],\n", - " [-4.1514e-03],\n", - " [-1.6383e-03],\n", - " [-9.8773e-06],\n", - " [ 5.0898e-06]], requires_grad=True)\n", - "11000 1.2E-04 1.0E-04 3.2E-06 1.4E-05\n", - "tensor([[-2.4451e-05],\n", - " [-8.8835e-03],\n", - " [ 9.5219e-02],\n", - " [ 4.5232e-05],\n", - " [-7.8536e-05],\n", - " [-9.6974e-01],\n", - " [ 4.7846e-04],\n", - " [ 4.2764e-04],\n", - " [-4.7288e-03],\n", - " [ 2.2531e-04],\n", - " [ 2.2433e-04],\n", - " [ 3.2979e-04]], requires_grad=True)\n", - "11500 9.1E-05 7.5E-05 1.8E-06 1.5E-05\n", - "tensor([[-2.3673e-05],\n", - " [-8.4207e-03],\n", - " [ 9.6668e-02],\n", - " [ 3.4632e-05],\n", - " [-1.8702e-05],\n", - " [-9.7096e-01],\n", - " [ 8.8132e-05],\n", - " [ 2.8518e-04],\n", - " [-4.0621e-03],\n", - " [-2.0245e-03],\n", - " [ 1.4232e-04],\n", - " [ 5.1765e-04]], requires_grad=True)\n", - "12000 9.1E-05 7.5E-05 1.7E-06 1.5E-05\n", - "tensor([[ 1.9042e-05],\n", - " [-7.7603e-03],\n", - " [ 9.6760e-02],\n", - " [ 2.0320e-05],\n", - " [-2.5006e-05],\n", - " [-9.7228e-01],\n", - " [ 3.4245e-04],\n", - " [ 1.5372e-04],\n", - " [-3.8800e-03],\n", - " [-2.8246e-03],\n", - " [ 9.6894e-05],\n", - " [ 8.0552e-04]], requires_grad=True)\n", - "12500 9.1E-05 7.5E-05 1.6E-06 1.5E-05\n", - "tensor([[ 1.1784e-05],\n", - " [-7.1111e-03],\n", - " [ 9.6946e-02],\n", - " [ 8.3534e-05],\n", - " [-6.4382e-05],\n", - " [-9.7390e-01],\n", - " [ 5.8895e-06],\n", - " [ 1.1787e-04],\n", - " [-3.5943e-03],\n", - " [-2.7854e-03],\n", - " [ 1.8555e-04],\n", - " [ 9.1652e-04]], requires_grad=True)\n", - "13000 9.1E-05 7.5E-05 1.6E-06 1.5E-05\n", - "tensor([[-2.2073e-05],\n", - " [-6.8721e-03],\n", - " [ 9.6826e-02],\n", - " [-7.0843e-06],\n", - " [ 2.3585e-05],\n", - " [-9.7457e-01],\n", - " [ 1.1586e-04],\n", - " [ 9.4982e-05],\n", - " [-3.5977e-03],\n", - " [-2.2540e-03],\n", - " [ 1.4519e-04],\n", - " [ 1.0219e-03]], requires_grad=True)\n", - "13500 9.1E-05 7.5E-05 1.5E-06 1.5E-05\n", - "tensor([[ 1.7223e-05],\n", - " [-6.5965e-03],\n", - " [ 9.6846e-02],\n", - " [ 3.4718e-05],\n", - " [-1.2007e-04],\n", - " [-9.7520e-01],\n", - " [ 1.1764e-04],\n", - " [ 1.3544e-04],\n", - " [-3.3121e-03],\n", - " [-1.9919e-03],\n", - " [ 3.0227e-04],\n", - " [ 1.2474e-03]], requires_grad=True)\n", - "14000 9.0E-05 7.4E-05 1.4E-06 1.5E-05\n", - "tensor([[ 6.1773e-05],\n", - " [-6.4211e-03],\n", - " [ 9.6877e-02],\n", - " [ 1.4509e-05],\n", - " [-2.1241e-04],\n", - " [-9.7560e-01],\n", - " [-8.5203e-05],\n", - " [ 1.0859e-04],\n", - " [-2.9373e-03],\n", - " [-1.7240e-03],\n", - " [ 1.0743e-04],\n", - " [ 1.2831e-03]], requires_grad=True)\n", - "14500 9.1E-05 7.5E-05 1.4E-06 1.5E-05\n", - "tensor([[-3.4434e-06],\n", - " [-6.3044e-03],\n", - " [ 9.6667e-02],\n", - " [ 2.7953e-05],\n", - " [-1.1515e-04],\n", - " [-9.7577e-01],\n", - " [ 1.7910e-04],\n", - " [ 1.0602e-04],\n", - " [-3.5216e-03],\n", - " [-1.2731e-03],\n", - " [ 6.3793e-05],\n", - " [ 1.3837e-03]], requires_grad=True)\n", - "15000 9.0E-05 7.4E-05 1.4E-06 1.5E-05\n", - "tensor([[-2.9708e-05],\n", - " [-6.0253e-03],\n", - " [ 9.6795e-02],\n", - " [ 5.2956e-05],\n", - " [-2.2970e-04],\n", - " [-9.7683e-01],\n", - " [ 2.4145e-05],\n", - " [ 5.1910e-05],\n", - " [-2.7994e-03],\n", - " [-1.1817e-03],\n", - " [ 2.1452e-04],\n", - " [ 1.3203e-03]], requires_grad=True)\n", - "15500 9.1E-05 7.5E-05 1.4E-06 1.5E-05\n", - "tensor([[-7.1294e-05],\n", - " [-6.1377e-03],\n", - " [ 9.6517e-02],\n", - " [ 4.7321e-05],\n", - " [-2.3139e-04],\n", - " [-9.7612e-01],\n", - " [ 2.8514e-04],\n", - " [ 7.4449e-05],\n", - " [-2.8955e-03],\n", - " [-1.9631e-03],\n", - " [ 1.8998e-04],\n", - " [ 1.2484e-03]], requires_grad=True)\n", - "16000 9.0E-05 7.4E-05 1.3E-06 1.5E-05\n", - "tensor([[ 3.8379e-05],\n", - " [-5.4854e-03],\n", - " [ 9.7052e-02],\n", - " [-7.8270e-06],\n", - " [-4.8451e-04],\n", - " [-9.7740e-01],\n", - " [ 8.0550e-05],\n", - " [ 7.7368e-05],\n", - " [-2.5758e-03],\n", - " [-1.9928e-03],\n", - " [ 3.7444e-04],\n", - " [ 1.2723e-03]], requires_grad=True)\n", - "16500 9.0E-05 7.4E-05 1.3E-06 1.5E-05\n", - "tensor([[ 2.5919e-05],\n", - " [-5.1977e-03],\n", - " [ 9.7246e-02],\n", - " [ 5.2604e-05],\n", - " [-1.2197e-04],\n", - " [-9.7825e-01],\n", - " [ 6.1921e-05],\n", - " [ 1.0753e-04],\n", - " [-2.6086e-03],\n", - " [-1.8846e-03],\n", - " [ 9.0801e-05],\n", - " [ 1.1911e-03]], requires_grad=True)\n", - "17000 9.0E-05 7.5E-05 1.3E-06 1.5E-05\n", - "tensor([[ 4.2591e-05],\n", - " [-5.3679e-03],\n", - " [ 9.7430e-02],\n", - " [ 3.8625e-05],\n", - " [-2.2096e-04],\n", - " [-9.7851e-01],\n", - " [ 1.3438e-04],\n", - " [ 5.2651e-05],\n", - " [-2.4212e-03],\n", - " [-7.1032e-04],\n", - " [ 2.5797e-04],\n", - " [ 1.3279e-03]], requires_grad=True)\n", - "17500 9.1E-05 7.5E-05 1.4E-06 1.5E-05\n", - "tensor([[ 1.8889e-04],\n", - " [-4.9239e-03],\n", - " [ 9.6710e-02],\n", - " [ 7.2894e-05],\n", - " [ 9.5753e-05],\n", - " [-9.7907e-01],\n", - " [ 1.5212e-04],\n", - " [ 1.4334e-04],\n", - " [-3.4503e-03],\n", - " [-2.1608e-04],\n", - " [ 3.9423e-04],\n", - " [ 8.8776e-04]], requires_grad=True)\n", - "18000 9.8E-05 8.2E-05 1.9E-06 1.5E-05\n", - "tensor([[ 4.6510e-05],\n", - " [-5.1039e-03],\n", - " [ 9.6900e-02],\n", - " [ 2.0054e-04],\n", - " [-6.3697e-06],\n", - " [-9.7941e-01],\n", - " [-8.1275e-05],\n", - " [ 2.5071e-04],\n", - " [-3.5234e-03],\n", - " [-5.4350e-04],\n", - " [ 1.4040e-04],\n", - " [ 7.5787e-04]], requires_grad=True)\n", - "18500 9.0E-05 7.4E-05 1.3E-06 1.5E-05\n", - "tensor([[ 8.9651e-05],\n", - " [-4.4939e-03],\n", - " [ 9.7467e-02],\n", - " [ 3.9326e-05],\n", - " [-8.9446e-05],\n", - " [-9.8039e-01],\n", - " [ 1.8153e-04],\n", - " [ 1.8662e-04],\n", - " [-2.2179e-03],\n", - " [-1.5731e-03],\n", - " [ 1.9069e-04],\n", - " [ 8.4430e-04]], requires_grad=True)\n", - "19000 9.0E-05 7.4E-05 1.3E-06 1.5E-05\n", - "tensor([[ 4.2422e-05],\n", - " [-4.7982e-03],\n", - " [ 9.7256e-02],\n", - " [ 3.3804e-05],\n", - " [-2.4490e-05],\n", - " [-9.8008e-01],\n", - " [ 3.3383e-04],\n", - " [ 2.0860e-04],\n", - " [-2.2191e-03],\n", - " [-7.7689e-04],\n", - " [ 1.3314e-04],\n", - " [ 7.3374e-04]], requires_grad=True)\n", - "19500 9.0E-05 7.4E-05 1.3E-06 1.5E-05\n", - "tensor([[-6.2405e-05],\n", - " [-4.3485e-03],\n", - " [ 9.7785e-02],\n", - " [ 3.3308e-05],\n", - " [-8.7264e-06],\n", - " [-9.8147e-01],\n", - " [ 1.1902e-04],\n", - " [ 1.7938e-04],\n", - " [-1.7373e-03],\n", - " [-1.5016e-03],\n", - " [ 2.7804e-04],\n", - " [ 6.3585e-04]], requires_grad=True)\n", - "[tensor([[-7.2637e-05],\n", - " [-4.3764e-03],\n", - " [ 9.7624e-02],\n", - " [ 1.1330e-04],\n", - " [-2.4394e-04],\n", - " [-9.8180e-01],\n", - " [ 3.8570e-05],\n", - " [ 7.8436e-05],\n", - " [-1.8393e-03],\n", - " [-2.0742e-03],\n", - " [ 4.7429e-04],\n", - " [ 3.1368e-04]], requires_grad=True)] (tensor([[ 0.0976],\n", - " [-0.9818]], requires_grad=True),) (tensor([2, 5]),)\n", - "Now running final cycle.\n", - "Epoch | Total loss | MSE | PI | L1 \n", - "0 7.6E-05 7.4E-05 2.5E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9838]], requires_grad=True)\n", - "500 7.5E-05 7.4E-05 1.3E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9973]], requires_grad=True)\n", - "1000 7.5E-05 7.4E-05 1.3E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9974]], requires_grad=True)\n", - "1500 7.5E-05 7.3E-05 1.3E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9976]], requires_grad=True)\n", - "2000 7.5E-05 7.3E-05 1.3E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9980]], requires_grad=True)\n", - "2500 7.7E-05 7.6E-05 1.4E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9983]], requires_grad=True)\n", - "3000 7.5E-05 7.3E-05 1.3E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9986]], requires_grad=True)\n", - "3500 7.5E-05 7.3E-05 1.4E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9987]], requires_grad=True)\n", - "4000 7.5E-05 7.3E-05 1.4E-06 0.0E+00\n", - "tensor([[ 0.0994],\n", - " [-0.9989]], requires_grad=True)\n", - "4500 7.5E-05 7.3E-05 1.4E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9989]], requires_grad=True)\n", - "5000 7.4E-05 7.3E-05 1.4E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9990]], requires_grad=True)\n", - "5500 7.4E-05 7.3E-05 1.4E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9990]], requires_grad=True)\n", - "6000 7.6E-05 7.5E-05 1.5E-06 0.0E+00\n", - "tensor([[ 0.0993],\n", - " [-0.9992]], requires_grad=True)\n", - "6500 8.0E-05 7.8E-05 1.8E-06 0.0E+00\n", - "tensor([[ 0.0990],\n", - " [-0.9992]], requires_grad=True)\n", - "7000 7.5E-05 7.3E-05 1.5E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9990]], requires_grad=True)\n", - "7500 7.6E-05 7.4E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9990]], requires_grad=True)\n", - "8000 7.7E-05 7.5E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9990]], requires_grad=True)\n", - "8500 7.4E-05 7.3E-05 1.5E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9989]], requires_grad=True)\n", - "9000 7.5E-05 7.3E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9989]], requires_grad=True)\n", - "9500 7.5E-05 7.4E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9990]], requires_grad=True)\n", - "10000 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9990]], requires_grad=True)\n", - "10500 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9991]], requires_grad=True)\n", - "11000 7.4E-05 7.3E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0997],\n", - " [-0.9990]], requires_grad=True)\n", - "11500 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9992]], requires_grad=True)\n", - "12000 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9994]], requires_grad=True)\n", - "12500 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9994]], requires_grad=True)\n", - "13000 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9995]], requires_grad=True)\n", - "13500 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9996]], requires_grad=True)\n", - "14000 7.7E-05 7.5E-05 1.8E-06 0.0E+00\n", - "tensor([[ 0.0994],\n", - " [-0.9997]], requires_grad=True)\n", - "14500 7.4E-05 7.2E-05 1.6E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9997]], requires_grad=True)\n", - "15000 7.5E-05 7.4E-05 1.8E-06 0.0E+00\n", - "tensor([[ 0.0996],\n", - " [-0.9997]], requires_grad=True)\n", - "15500 7.4E-05 7.2E-05 1.7E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9999]], requires_grad=True)\n", - "16000 7.5E-05 7.3E-05 1.7E-06 0.0E+00\n", - "tensor([[ 0.0994],\n", - " [-1.0000]], requires_grad=True)\n", - "16500 8.6E-05 8.4E-05 1.9E-06 0.0E+00\n", - "tensor([[ 0.0993],\n", - " [-1.0000]], requires_grad=True)\n", - "17000 7.4E-05 7.2E-05 1.7E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9999]], requires_grad=True)\n", - "17500 7.4E-05 7.2E-05 1.7E-06 0.0E+00\n", - "tensor([[ 0.0994],\n", - " [-1.0001]], requires_grad=True)\n", - "18000 7.4E-05 7.2E-05 1.7E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-1.0000]], requires_grad=True)\n", - "18500 7.3E-05 7.2E-05 1.7E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-1.0000]], requires_grad=True)\n", - "19000 7.4E-05 7.2E-05 1.8E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-1.0000]], requires_grad=True)\n", - "19500 7.4E-05 7.2E-05 1.8E-06 0.0E+00\n", - "tensor([[ 0.0995],\n", - " [-0.9999]], requires_grad=True)\n" - ] - } - ], - "source": [ - "sparse_coeff_vector, sparsity_mask, network = DeepMoD(X_train, y_train, network_config, lib_config, optim_config)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now that DeepMoD has converged, it has found the following equation:" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Final result:\n", - "(tensor([[ 0.0994],\n", - " [-1.0001]], requires_grad=True),) (tensor([2, 5]),)\n" - ] - } - ], - "source": [ - "print('Final result:')\n", - "print(sparse_coeff_vector, sparsity_mask)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.9" - } - }, - "nbformat": 4, - "nbformat_minor": 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