SKFSR: SKip-connected Feature-reuse Super-Resolution

A deep-learning model combines guidance of physics and data to learn observation functions accurately and efficiently, which conducts a linearization and preidiction of high-dimensional nonlinear dynamical systems.

Introduction

• This repo provides code for the paper ["Fractal-constrained Deep Learning for Super-resolution of Turbulence with Zero or Few Label Data"](under review) by Jiaxin Wu, Min Luo, Boo Cheong Khoo and Pengzhi Lin.
• This study proposes a deep-learning model that constrained by fractal physics and utilizes zero / few data, for the high-resolution reconstruction of turbulent flows.

Structure

│  LICENSE
│  README.md
├─ Fractal_script              
│  │  SKFSR_main.py  (main program)
│  └─ ML_SKFSR_TorchModel.py  (main network)
├─ data         
└─ utils
    │  loadSnapshotsObjects(...).py  (visualization tools)
    │  ML_plot.py  (visualization utilities)
    │  generator.py  (tool for generating sierpinski foam)
    │  fdgpu.py  (tensorized differential computation for fractal dimensions)
    └─ ML_utils.py  (general utilities)

Common usage

• Runing SKFSR_main.py with arguments

• e.g., python SKFSR_main.py -m DB_unsp_single -c Channel -b 32 -s 4 -e 1000

• Some basic denotes have been made in SKFSR_main.py, refer to python SKFSR_main.py --help

  parser.add_argument('-m', dest='method', type=str, default='SKFSR_DB_unsp_single', help=' arguments: binarization + training strategy + snapshot quantity'
  'DB/ TB + unsp/ semi/ sup + single/ few/ standard' ' eg. SKFSR_DB_unsp_single')

  parser.add_argument('-c', dest='case', type=str, default='Channel', help= 'Name of Dataset: Channel/ Iso/ Koch126/' ' eye/ Koch15/ Koch146/ Sire189/ ')

  parser.add_argument('-b', dest='batch_size', type=int, default=32, help="Batch Size")

  parser.add_argument('-s', dest='scaler', type=int, default=1, help="s x 2 = Super Resolution Ratio")

  parser.add_argument('-e',dest='epochs', type=int, default=1000, help="Number of Epochs")

  parser.add_argument('--load', dest='load', default=False, action='store_true')

General hyperparameters

• "case" for selecting numerical cases eye/ Koch126/ Koch15/ Koch146/ Sire189 Channel/ Iso/
• "method" for defining numerical approaches template: (1) binarization scheme + (2) training strategy + (3) snapshot quantity, (1) binarization scheme: TB (truncated binarinzation) / DB (differential binarization) (2) upscaling ratio: 2X / 4X / 8X (can either be input in argument "-s") (3) training strategy: unsp / semi / sup (4) snapshot quantity: single (1) / few (30) / standard (120) Notice that Cases C1a-e can only use the argument "single" e.g., DB_2X_unsp_single, TB_8X_semi_few,...

Datasets

Cases C1a-e are generated by IFS are studied including:

• C1a: Please use "np.eye" function instead
• C1b: koch126_512_9.npy
• C1c: koch146_512_9.npy
• C1d: koch15_512_7.npy
• C1e: sier_512_7.npy

Cases C2a&b are downloaded from Johns Hopkins Turbulence Databases (https://turbulence.pha.jhu.edu/) including:

• C2a: channel turbulence channel_u_512X128p_4to24s_dt0.13.npy
• C2b: isotropic turbulence iso_velocity_pressure_256x256_2to8.npy

Please download turbulence data from (https://osf.io/5whfj/) and put them into the "data" folder

Requirements

The model is built in Python environment using TensorFlow v2 backend, basically using packages of:

• Python 3.x
• torch
• sklearn
• numpy