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create_mesh.py
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create_mesh.py
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# Standard library
import os
from argparse import ArgumentParser
# Third-party
import matplotlib
import matplotlib.pyplot as plt
import networkx
import numpy as np
import scipy.spatial
import torch
import torch_geometric as pyg
from torch_geometric.utils.convert import from_networkx
# First-party
from neural_lam import constants
def plot_graph(graph, title=None):
fig, axis = plt.subplots(figsize=(8, 8), dpi=200) # W,H
edge_index = graph.edge_index
pos = graph.pos
# Fix for re-indexed edge indices only containing mesh nodes at
# higher levels in hierarchy
edge_index = edge_index - edge_index.min()
if pyg.utils.is_undirected(edge_index):
# Keep only 1 direction of edge_index
edge_index = edge_index[:, edge_index[0] < edge_index[1]] # (2, M/2)
# TODO: indicate direction of directed edges
# Move all to cpu and numpy, compute (in)-degrees
degrees = (
pyg.utils.degree(edge_index[1], num_nodes=pos.shape[0]).cpu().numpy()
)
edge_index = edge_index.cpu().numpy()
pos = pos.cpu().numpy()
# Plot edges
from_pos = pos[edge_index[0]] # (M/2, 2)
to_pos = pos[edge_index[1]] # (M/2, 2)
edge_lines = np.stack((from_pos, to_pos), axis=1)
axis.add_collection(
matplotlib.collections.LineCollection(
edge_lines, lw=0.4, colors="black", zorder=1
)
)
# Plot nodes
node_scatter = axis.scatter(
pos[:, 0],
pos[:, 1],
c=degrees,
s=3,
marker="o",
zorder=2,
cmap="viridis",
clim=None,
)
plt.colorbar(node_scatter, aspect=50)
margin = 0.5
axis.set_xlim(left=0 - margin, right=constants.GRID_SHAPE[0] + margin)
axis.set_ylim(bottom=0 - margin, top=constants.GRID_SHAPE[1] + margin)
if title is not None:
axis.set_title(title)
return fig, axis
def sort_nodes_internally(nx_graph):
# For some reason the networkx .nodes() return list can not be sorted,
# but this is the ordering used by pyg when converting.
# This function fixes this.
H = networkx.DiGraph()
H.add_nodes_from(sorted(nx_graph.nodes(data=True)))
H.add_edges_from(nx_graph.edges(data=True))
return H
def save_edges(graph, name, base_path):
torch.save(
graph.edge_index, os.path.join(base_path, f"{name}_edge_index.pt")
)
edge_features = torch.cat((graph.len.unsqueeze(1), graph.vdiff), dim=1).to(
torch.float32
) # Save as float32
torch.save(edge_features, os.path.join(base_path, f"{name}_features.pt"))
def save_edges_list(graphs, name, base_path):
torch.save(
[graph.edge_index for graph in graphs],
os.path.join(base_path, f"{name}_edge_index.pt"),
)
edge_features = [
torch.cat((graph.len.unsqueeze(1), graph.vdiff), dim=1).to(
torch.float32
)
for graph in graphs
] # Save as float32
torch.save(edge_features, os.path.join(base_path, f"{name}_features.pt"))
def from_networkx_with_start_index(nx_graph, start_index):
pyg_graph = from_networkx(nx_graph)
pyg_graph.edge_index += start_index
return pyg_graph
def mk_2d_graph(xy, nx, ny):
xm, xM = np.amin(xy[0][0, :]), np.amax(xy[0][0, :])
ym, yM = np.amin(xy[1][:, 0]), np.amax(xy[1][:, 0])
# avoid nodes on border
dx = (xM - xm) / nx
dy = (yM - ym) / ny
lx = np.linspace(xm + dx / 2, xM - dx / 2, nx)
ly = np.linspace(ym + dy / 2, yM - dy / 2, ny)
mg = np.meshgrid(lx, ly)
g = networkx.grid_2d_graph(len(ly), len(lx))
for node in g.nodes:
g.nodes[node]["pos"] = np.array([mg[0][node], mg[1][node]])
# add diagonal edges
g.add_edges_from(
[((x, y), (x + 1, y + 1)) for x in range(nx - 1) for y in range(ny - 1)]
+ [
((x + 1, y), (x, y + 1))
for x in range(nx - 1)
for y in range(ny - 1)
]
)
# turn into directed graph
dg = networkx.DiGraph(g)
for u, v in g.edges():
d = np.sqrt(np.sum((g.nodes[u]["pos"] - g.nodes[v]["pos"]) ** 2))
dg.edges[u, v]["len"] = d
dg.edges[u, v]["vdiff"] = g.nodes[u]["pos"] - g.nodes[v]["pos"]
dg.add_edge(v, u)
dg.edges[v, u]["len"] = d
dg.edges[v, u]["vdiff"] = g.nodes[v]["pos"] - g.nodes[u]["pos"]
return dg
def prepend_node_index(graph, new_index):
# Relabel node indices in graph, insert (graph_level, i, j)
ijk = [tuple((new_index,) + x) for x in graph.nodes]
to_mapping = dict(zip(graph.nodes, ijk))
return networkx.relabel_nodes(graph, to_mapping, copy=True)
def main():
parser = ArgumentParser(description="Graph generation arguments")
parser.add_argument(
"--dataset",
type=str,
default="meps_example",
help="Dataset to load grid point coordinates from "
"(default: meps_example)",
)
parser.add_argument(
"--graph",
type=str,
default="multiscale",
help="Name to save graph as (default: multiscale)",
)
parser.add_argument(
"--plot",
type=int,
default=0,
help="If graphs should be plotted during generation "
"(default: 0 (false))",
)
parser.add_argument(
"--levels",
type=int,
help="Limit multi-scale mesh to given number of levels, "
"from bottom up (default: None (no limit))",
)
parser.add_argument(
"--hierarchical",
type=int,
default=0,
help="Generate hierarchical mesh graph (default: 0, no)",
)
args = parser.parse_args()
# Load grid positions
static_dir_path = os.path.join("data", args.dataset, "static")
graph_dir_path = os.path.join("graphs", args.graph)
os.makedirs(graph_dir_path, exist_ok=True)
xy = np.load(os.path.join(static_dir_path, "nwp_xy.npy"))
grid_xy = torch.tensor(xy)
pos_max = torch.max(torch.abs(grid_xy))
#
# Mesh
#
# graph geometry
nx = constants.GRAPH_NUM_CHILDREN # number of children = nx**2
nlev = int(np.log(max(xy.shape)) / np.log(nx))
nleaf = nx**nlev # leaves at the bottom = nleaf**2
mesh_levels = nlev - 1
if args.levels:
# Limit the levels in mesh graph
mesh_levels = min(mesh_levels, args.levels)
print(f"nlev: {nlev}, nleaf: {nleaf}, mesh_levels: {mesh_levels}")
# multi resolution tree levels
G = []
for lev in range(1, mesh_levels + 1):
n = int(nleaf / (nx**lev))
g = mk_2d_graph(xy, n, n)
if args.plot:
plot_graph(from_networkx(g), title=f"Mesh graph, level {lev}")
# save figure
plt.savefig(os.path.join(graph_dir_path, f"mesh_graph_{lev}.png"))
G.append(g)
if args.hierarchical:
# Relabel nodes of each level with level index first
G = [
prepend_node_index(graph, level_i)
for level_i, graph in enumerate(G)
]
num_nodes_level = np.array([len(g_level.nodes) for g_level in G])
# First node index in each level in the hierarchical graph
first_index_level = np.concatenate(
(np.zeros(1, dtype=int), np.cumsum(num_nodes_level[:-1]))
)
# Create inter-level mesh edges
up_graphs = []
down_graphs = []
for from_level, to_level, G_from, G_to, start_index in zip(
range(1, mesh_levels),
range(0, mesh_levels - 1),
G[1:],
G[:-1],
first_index_level[: mesh_levels - 1],
):
# start out from graph at from level
G_down = G_from.copy()
G_down.clear_edges()
G_down = networkx.DiGraph(G_down)
# Add nodes of to level
G_down.add_nodes_from(G_to.nodes(data=True))
# build kd tree for mesh point pos
# order in vm should be same as in vm_xy
v_to_list = list(G_to.nodes)
v_from_list = list(G_from.nodes)
v_from_xy = np.array([xy for _, xy in G_from.nodes.data("pos")])
kdt_m = scipy.spatial.KDTree(v_from_xy)
# add edges from mesh to grid
for v in v_to_list:
# find 1(?) nearest neighbours (index to vm_xy)
neigh_idx = kdt_m.query(G_down.nodes[v]["pos"], 1)[1]
u = v_from_list[neigh_idx]
# add edge from mesh to grid
G_down.add_edge(u, v)
d = np.sqrt(
np.sum(
(G_down.nodes[u]["pos"] - G_down.nodes[v]["pos"]) ** 2
)
)
G_down.edges[u, v]["len"] = d
G_down.edges[u, v]["vdiff"] = (
G_down.nodes[u]["pos"] - G_down.nodes[v]["pos"]
)
# relabel nodes to integers (sorted)
G_down_int = networkx.convert_node_labels_to_integers(
G_down, first_label=start_index, ordering="sorted"
) # Issue with sorting here
G_down_int = sort_nodes_internally(G_down_int)
pyg_down = from_networkx_with_start_index(G_down_int, start_index)
# Create up graph, invert downwards edges
up_edges = torch.stack(
(pyg_down.edge_index[1], pyg_down.edge_index[0]), dim=0
)
pyg_up = pyg_down.clone()
pyg_up.edge_index = up_edges
up_graphs.append(pyg_up)
down_graphs.append(pyg_down)
if args.plot:
plot_graph(
pyg_down, title=f"Down graph, {from_level} -> {to_level}"
)
plt.savefig(
os.path.join(
graph_dir_path, f"mesh_down_graph_{from_level}.png"
)
)
plot_graph(
pyg_down, title=f"Up graph, {to_level} -> {from_level}"
)
plt.savefig(
os.path.join(
graph_dir_path, f"mesh_up_graph_{to_level}.png"
)
)
# Save up and down edges
save_edges_list(up_graphs, "mesh_up", graph_dir_path)
save_edges_list(down_graphs, "mesh_down", graph_dir_path)
# Extract intra-level edges for m2m
m2m_graphs = [
from_networkx_with_start_index(
networkx.convert_node_labels_to_integers(
level_graph, first_label=start_index, ordering="sorted"
),
start_index,
)
for level_graph, start_index in zip(G, first_index_level)
]
mesh_pos = [graph.pos.to(torch.float32) for graph in m2m_graphs]
# For use in g2m and m2g
G_bottom_mesh = G[0]
joint_mesh_graph = networkx.union_all([graph for graph in G])
all_mesh_nodes = joint_mesh_graph.nodes(data=True)
else:
# combine all levels to one graph
G_tot = G[0]
for lev in range(1, len(G)):
nodes = list(G[lev - 1].nodes)
n = int(np.sqrt(len(nodes)))
ij = (
np.array(nodes)
.reshape((n, n, 2))[1::nx, 1::nx, :]
.reshape(int(n / nx) ** 2, 2)
)
ij = [tuple(x) for x in ij]
G[lev] = networkx.relabel_nodes(G[lev], dict(zip(G[lev].nodes, ij)))
G_tot = networkx.compose(G_tot, G[lev])
# Relabel mesh nodes to start with 0
G_tot = prepend_node_index(G_tot, 0)
# relabel nodes to integers (sorted)
G_int = networkx.convert_node_labels_to_integers(
G_tot, first_label=0, ordering="sorted"
)
# Graph to use in g2m and m2g
G_bottom_mesh = G_tot
all_mesh_nodes = G_tot.nodes(data=True)
# export the nx graph to PyTorch geometric
pyg_m2m = from_networkx(G_int)
m2m_graphs = [pyg_m2m]
mesh_pos = [pyg_m2m.pos.to(torch.float32)]
if args.plot:
plot_graph(pyg_m2m, title="Mesh-to-mesh")
plt.savefig(os.path.join(graph_dir_path, "mesh_graph.png"))
# Save m2m edges
save_edges_list(m2m_graphs, "m2m", graph_dir_path)
# Divide mesh node pos by max coordinate of grid cell
mesh_pos = [pos / pos_max for pos in mesh_pos]
# Save mesh positions
torch.save(
mesh_pos, os.path.join(graph_dir_path, "mesh_features.pt")
) # mesh pos, in float32
#
# Grid2Mesh
#
# radius within which grid nodes are associated with a mesh node
# (in terms of mesh distance)
DM_SCALE = 0.67
# mesh nodes on lowest level
vm = G_bottom_mesh.nodes
vm_xy = np.array([xy for _, xy in vm.data("pos")])
# distance between mesh nodes
dm = np.sqrt(
np.sum((vm.data("pos")[(0, 1, 0)] - vm.data("pos")[(0, 0, 0)]) ** 2)
)
# grid nodes
Ny, Nx = xy.shape[1:]
G_grid = networkx.grid_2d_graph(Ny, Nx)
G_grid.clear_edges()
# vg features (only pos introduced here)
for node in G_grid.nodes:
# pos is in feature but here explicit for convenience
G_grid.nodes[node]["pos"] = np.array([xy[0][node], xy[1][node]])
# add 1000 to node key to separate grid nodes (1000,i,j) from mesh nodes
# (i,j) and impose sorting order such that vm are the first nodes
G_grid = prepend_node_index(G_grid, 1000)
# build kd tree for grid point pos
# order in vg_list should be same as in vg_xy
vg_list = list(G_grid.nodes)
vg_xy = np.array([[xy[0][node[1:]], xy[1][node[1:]]] for node in vg_list])
kdt_g = scipy.spatial.KDTree(vg_xy)
# now add (all) mesh nodes, include features (pos)
G_grid.add_nodes_from(all_mesh_nodes)
# Re-create graph with sorted node indices
# Need to do sorting of nodes this way for indices to map correctly to pyg
G_g2m = networkx.Graph()
G_g2m.add_nodes_from(sorted(G_grid.nodes(data=True)))
# turn into directed graph
G_g2m = networkx.DiGraph(G_g2m)
# add edges
for v in vm:
# find neighbours (index to vg_xy)
neigh_idxs = kdt_g.query_ball_point(vm[v]["pos"], dm * DM_SCALE)
for i in neigh_idxs:
u = vg_list[i]
# add edge from grid to mesh
G_g2m.add_edge(u, v)
d = np.sqrt(
np.sum((G_g2m.nodes[u]["pos"] - G_g2m.nodes[v]["pos"]) ** 2)
)
G_g2m.edges[u, v]["len"] = d
G_g2m.edges[u, v]["vdiff"] = (
G_g2m.nodes[u]["pos"] - G_g2m.nodes[v]["pos"]
)
pyg_g2m = from_networkx(G_g2m)
if args.plot:
plot_graph(pyg_g2m, title="Grid-to-mesh")
plt.savefig(os.path.join(graph_dir_path, "grid_to_mesh.png"))
#
# Mesh2Grid
#
# start out from Grid2Mesh and then replace edges
G_m2g = G_g2m.copy()
G_m2g.clear_edges()
# build kd tree for mesh point pos
# order in vm should be same as in vm_xy
vm_list = list(vm)
kdt_m = scipy.spatial.KDTree(vm_xy)
# add edges from mesh to grid
for v in vg_list:
# find 4 nearest neighbours (index to vm_xy)
neigh_idxs = kdt_m.query(G_m2g.nodes[v]["pos"], 4)[1]
for i in neigh_idxs:
u = vm_list[i]
# add edge from mesh to grid
G_m2g.add_edge(u, v)
d = np.sqrt(
np.sum((G_m2g.nodes[u]["pos"] - G_m2g.nodes[v]["pos"]) ** 2)
)
G_m2g.edges[u, v]["len"] = d
G_m2g.edges[u, v]["vdiff"] = (
G_m2g.nodes[u]["pos"] - G_m2g.nodes[v]["pos"]
)
# relabel nodes to integers (sorted)
G_m2g_int = networkx.convert_node_labels_to_integers(
G_m2g, first_label=0, ordering="sorted"
)
pyg_m2g = from_networkx(G_m2g_int)
if args.plot:
plot_graph(pyg_m2g, title="Mesh-to-grid")
plt.savefig(os.path.join(graph_dir_path, "mesh_to_grid.png"))
# Save g2m and m2g everything
# g2m
save_edges(pyg_g2m, "g2m", graph_dir_path)
# m2g
save_edges(pyg_m2g, "m2g", graph_dir_path)
if __name__ == "__main__":
main()