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17396 +34903 13695 17354 17421 +34904 17354 9234 17421 +$EndElements diff --git a/data/datasets/stokes_cylinder/test_data.h5 b/data/datasets/stokes_cylinder/test_data.h5 new file mode 100644 index 0000000..3e200da Binary files /dev/null and b/data/datasets/stokes_cylinder/test_data.h5 differ diff --git a/data/datasets/stokes_cylinder/train_data.h5 b/data/datasets/stokes_cylinder/train_data.h5 new file mode 100644 index 0000000..09748d7 Binary files /dev/null and b/data/datasets/stokes_cylinder/train_data.h5 differ diff --git a/physics_driven_ml/dataset_processing/__init__.py b/physics_driven_ml/dataset_processing/__init__.py index dd64eab..0134975 100644 --- a/physics_driven_ml/dataset_processing/__init__.py +++ b/physics_driven_ml/dataset_processing/__init__.py @@ -1,3 +1,3 @@ -from physics_driven_ml.dataset_processing.data_types import BatchedElement, BatchElement # noqa: F401 +from physics_driven_ml.dataset_processing.data_types import BatchedElement, BatchElement, GraphBatchedElement, GraphBatchElement # noqa: F401 from physics_driven_ml.dataset_processing.generate_data import random_field, generate_data # noqa: F401 -from physics_driven_ml.dataset_processing.pde_dataset import PDEDataset # noqa: F401 +from physics_driven_ml.dataset_processing.pde_dataset import PDEDataset, StokesDataset # noqa: F401 diff --git a/physics_driven_ml/dataset_processing/data_types.py b/physics_driven_ml/dataset_processing/data_types.py index 9c24f48..e4e2672 100644 --- a/physics_driven_ml/dataset_processing/data_types.py +++ b/physics_driven_ml/dataset_processing/data_types.py @@ -18,3 +18,22 @@ class BatchedElement(NamedTuple): u_obs_fd: List[Function] target_fd: List[Function] batch_elements: Optional[List[BatchElement]] = None + + +class GraphBatchElement(NamedTuple): + """Batch element for PDE-based datasets as a tuple of PyTorch and Firedrake tensors.""" + edge_index: Tensor # shape = (2, num_edges) + u: Tensor # shape = (n,) + f: Tensor # shape = (m,) + u_fd: Function + f_fd: Function + + +class GraphBatchedElement(NamedTuple): + """Represent tensors for a list/batch of `BatchElement` that have been collated.""" + edge_index: Tensor # shape = (2, num_edges) + u: Tensor # shape = (batch_size, n) + f: Tensor # shape = (batch_size, m) + u_fd: List[Function] + f_fd: List[Function] + batch_elements: Optional[List[BatchElement]] = None diff --git a/physics_driven_ml/dataset_processing/generate_data_stokes_tutorial.py b/physics_driven_ml/dataset_processing/generate_data_stokes_tutorial.py new file mode 100644 index 0000000..735b6c1 --- /dev/null +++ b/physics_driven_ml/dataset_processing/generate_data_stokes_tutorial.py @@ -0,0 +1,189 @@ +import os +import argparse +import numpy as np +from typing import Union, Callable +from tqdm.auto import tqdm, trange +from numpy.random import default_rng +from physics_driven_ml.utils.graph.mesh_to_graph import build_adjacency + +from firedrake import * +from firedrake.__future__ import interpolate + +from physics_driven_ml.utils import get_logger + + +def random_field(V, N: int = 1, m: int = 5, σ: float = 0.6, + tqdm: bool = False, seed: int = 2023): + """Generate N 2D random fields with m modes.""" + rng = default_rng(seed) + x, y = SpatialCoordinate(V.ufl_domain()) + fields = [] + for _ in trange(N, disable=not tqdm): + f = [] + for _ in range(2): + r = 0 + for _ in range(m): + a, b = rng.standard_normal(2) + k1, k2 = rng.normal(0, σ, 2) + θ = 2 * pi * (k1 * x + k2 * y) + r += Constant(a) * cos(θ) + Constant(b) * sin(θ) + f.append(sqrt(1 / m) * r) + fields.append(assemble(interpolate(as_vector([f[0], f[1]]), V))) + return fields + + +def solve_stokes_cylinder(fs): + # Function spaces + V = VectorFunctionSpace(mesh, "CG", 2) + W = FunctionSpace(mesh, "CG", 1) + Z = V * W + + edge_index = build_adjacency(mesh, V) + + # Boundary conditions + g = Function(V).interpolate(as_vector([1., 0.])) + bcs = [DirichletBC(Z.sub(0), g, (inlet,)), + DirichletBC(Z.sub(0), Constant((1., 0)), bottom_top), + DirichletBC(Z.sub(0), Constant((0, 0)), (circle,))] + # Set nullspace + nullspace = MixedVectorSpaceBasis(Z, [Z.sub(0), VectorSpaceBasis(constant=True)]) + + # Define trial/test functions + us = [] + v, q = TestFunctions(Z) + for f in tqdm(fs): + # Define solution + up = Function(Z) + # Solve + u, p = TrialFunctions(Z) + a = (inner(grad(u), grad(v)) - inner(p, div(v)) + inner(div(u), q))*dx + L = inner(f, v) * dx + solve(a == L, + up, + bcs=bcs, + nullspace=nullspace) + us.append(up) + # solver_parameters={"ksp_type": "gmres", + # "mat_type": "aij", + # "pc_type": "lu", + # "ksp_atol": 1.0e-9, + # "pc_factor_mat_solver_type": "mumps"}) + return us, edge_index + + +def generate_data(V, dataset_dir: str, ntrain: int = 50, ntest: int = 10, + forward: Union[str, Callable] = "heat", noise: Union[str, Callable] = "normal", + scale_noise: float = 1., seed: int = 1234): + """Generate train/test data for a given PDE-based forward problem and noise distribution. + + Parameters: + - V: Firedrake function space + - dataset_dir: directory to save the generated data + - ntrain: number of training samples + - ntest: number of test samples + - forward: forward model (e.g "heat") + - noise: noise distribution to form the observed data (e.g. "normal") + - scale_noise: noise scaling factor + - seed: random seed + + Custom forward problems: + One can provide a custom forward problem by specifying a callable for the `forward` argument. + This callable should take in a list of randomly generated inputs and the function space `V`, and + it should return a list of Firedrake functions corresponding to the PDE solutions. + + Custom noise perturbations: + Likewise, one can provide a custom noise perturbation by specifying a callable for the `noise` argument. + This callable should take in a list of PDE solutions, and it should return a list of Firedrake functions + corresponding to the observed data, i.e. the perturbed PDE solutions. + """ + + logger.info("\n Generate random fields") + + ks = random_field(V, N=ntrain+ntest, tqdm=True, seed=seed) + + logger.info("\n Generate corresponding PDE solutions") + + if forward == "heat": + us = [] + v = TestFunction(V) + x, y = SpatialCoordinate(V.ufl_domain()) + f = Function(V).interpolate(sin(pi * x) * sin(pi * y)) + bcs = [DirichletBC(V, Constant(0.0), "on_boundary")] + for k in tqdm(ks): + u = Function(V) + F = (inner(exp(k) * grad(u), grad(v)) - inner(f, v)) * dx + # Solve PDE using LU factorisation + solve(F == 0, u, bcs=bcs, solver_parameters={'ksp_type': 'preonly', 'pc_type': 'lu'}) + us.append(u) + elif forward == "stokes": + us, edge_index = solve_stokes_cylinder(ks) + elif callable(forward): + us = forward(ks, V) + else: + raise NotImplementedError("Forward problem not implemented. Use 'heat' or provide a callable for your forward problem.") + + logger.info(f"\n Generated {ntrain} training samples and {ntest} test samples.") + + # Split into train/test + ks_train, ks_test = ks[:ntrain], ks[ntrain:] + us_train, us_test = us[:ntrain], us[ntrain:] + + logger.info(f"\n Saving train/test data to {os.path.abspath(dataset_dir)}.") + + # Save train data + with CheckpointFile(os.path.join(dataset_dir, "train_data.h5"), "w") as afile: + afile.h5pyfile["n"] = ntrain + afile.h5pyfile["edge_index"] = edge_index + afile.save_mesh(mesh) + for i, (k, u) in enumerate(zip(ks_train, us_train)): + afile.save_function(k, idx=i, name="f") + afile.save_function(u, idx=i, name="u") + + # Save test data + with CheckpointFile(os.path.join(dataset_dir, "test_data.h5"), "w") as afile: + afile.h5pyfile["n"] = ntest + afile.h5pyfile["edge_index"] = edge_index + afile.save_mesh(mesh) + for i, (k, u) in enumerate(zip(ks_test, us_test)): + afile.save_function(k, idx=i, name="f") + afile.save_function(u, idx=i, name="u") + + +if __name__ == "__main__": + logger = get_logger("Data generation") + + parser = argparse.ArgumentParser() + parser.add_argument("--ntrain", default=50, type=int, help="Number of training samples") + parser.add_argument("--ntest", default=10, type=int, help="Number of test samples") + parser.add_argument("--forward", default="heat", type=str, help="Forward problem (e.g. 'heat')") + parser.add_argument("--noise", default="normal", type=str, help="Noise distribution (e.g. 'normal')") + parser.add_argument("--scale_noise", default=5e-3, type=float, help="Noise scaling") + parser.add_argument("--nx", default=50, type=int, help="Number of cells in x-direction") + parser.add_argument("--ny", default=50, type=int, help="Number of cells in y-direction") + parser.add_argument("--Lx", default=1., type=float, help="Length of the domain") + parser.add_argument("--Ly", default=1., type=float, help="Width of the domain") + parser.add_argument("--degree", default=1, type=int, help="Degree of the finite element CG space") + parser.add_argument("--data_dir", default=os.environ["DATA_DIR"], type=str, help="Data directory") + parser.add_argument("--dataset_name", default="heat_conductivity", type=str, help="Dataset name") + + args = parser.parse_args() + + # Set up mesh and finite element space + mesh_path = os.path.join("/home/nacime/tests/physics-driven-ml/data/datasets/meshes", "symmetric_mesh.msh") + inlet = 10 + circle = 13 + bottom_top = (12,) + mesh = Mesh(mesh_path) + V = VectorFunctionSpace(mesh, "CG", 2) + # Set up data directory + dataset_dir = os.path.join(args.data_dir, "datasets", args.dataset_name) + # Make data directory while dealing with parallelism + try: + os.makedirs(dataset_dir) + except FileExistsError: + # Another process created the directory + pass + # Generate data + generate_data(V, dataset_dir=dataset_dir, ntrain=args.ntrain, + ntest=args.ntest, forward=args.forward, + noise=args.noise, scale_noise=args.scale_noise) diff --git a/physics_driven_ml/dataset_processing/pde_dataset.py b/physics_driven_ml/dataset_processing/pde_dataset.py index 3b4d6b9..e9b383d 100644 --- a/physics_driven_ml/dataset_processing/pde_dataset.py +++ b/physics_driven_ml/dataset_processing/pde_dataset.py @@ -7,7 +7,7 @@ from firedrake.ml.pytorch import * from torch.utils.data import Dataset -from physics_driven_ml.dataset_processing import BatchElement, BatchedElement +from physics_driven_ml.dataset_processing import BatchElement, BatchedElement, GraphBatchElement, GraphBatchedElement class PDEDataset(Dataset): @@ -69,3 +69,44 @@ def collate(self, batch_elements: List[BatchElement]) -> BatchedElement: return BatchedElement(u_obs=u_obs, target=target, target_fd=target_fd, u_obs_fd=u_obs_fd, batch_elements=batch_elements) + + +class StokesDataset(PDEDataset): + """Dataset reader for Stokes problems generated using Firedrake.""" + + def __init__(self, dataset: str = "stokes_cylinder", dataset_split: str = "train", data_dir: str = ""): + # Check dataset directory + dataset_dir = os.path.join(data_dir, dataset) + if not os.path.exists(dataset_dir): + raise ValueError(f"Dataset directory {os.path.abspath(dataset_dir)} does not exist") + + # Get mesh and batch elements (Firedrake functions) + name_file = dataset_split + "_data.h5" + mesh, edge_index, batch_elements = self.load_dataset(os.path.join(dataset_dir, name_file)) + self.mesh = mesh + self.edge_index = edge_index + self.batch_elements_fd = batch_elements + + def load_dataset(self, fname: str): + data = [] + # Load data + with CheckpointFile(fname, "r") as afile: + n = int(np.array(afile.h5pyfile["n"])) + # Load adjacency list + edge_index = np.array(afile.h5pyfile["edge_index"]) + # Load mesh + mesh = afile.load_mesh("mesh") + # Load data + for i in range(n): + f = afile.load_function(mesh, "f", idx=i) + u = afile.load_function(mesh, "u", idx=i) + data.append((f, u)) + return mesh, edge_index, data + + def __getitem__(self, idx: int) -> GraphBatchElement: + target_f_fd, target_u_fd = self.batch_elements_fd[idx] + # Convert Firedrake functions to PyTorch tensors + target_f, target_u = [to_torch(e) for e in [target_f_fd, target_u_fd]] + return GraphBatchElement(u=target_u, f=target_f, + u_fd=target_u_fd, f_fd=target_f_fd) + diff --git a/physics_driven_ml/utils/graph/mesh_to_graph.py b/physics_driven_ml/utils/graph/mesh_to_graph.py index b903ec0..90ae201 100644 --- a/physics_driven_ml/utils/graph/mesh_to_graph.py +++ b/physics_driven_ml/utils/graph/mesh_to_graph.py @@ -1,4 +1,4 @@ -from adjacency_dofs import build_dof_adjacency +from physics_driven_ml.utils.graph.adjacency_dofs import build_dof_adjacency def build_adjacency(mesh, V):