PINA: Instructions file for Codex

PINA — Physics-Informed Neural Architectures

A PyTorch library for solving differential equations with neural networks (PINNs).

Quick Reference

Workflow: Problem → Model → Solver → Trainer

problem = MyProblem()
problem.discretise_domain(n=256, mode="grid")
model = FeedForward(input_dimensions=2, output_dimensions=1)
solver = PINN(problem=problem, model=model)
trainer = Trainer(solver=solver, max_epochs=1000)
trainer.train()

Problem types

SpatialProblem, TimeDependentProblem, ParametricProblem, InverseProblem. Define output_variables, spatial_domain/temporal_domain, and conditions (dict of Condition).

Condition types

• Condition(domain=..., equation=...) — physics residual on sampled domain
• Condition(input=..., equation=...) — physics residual at fixed points
• Condition(input=..., target=...) — supervised data
• Condition(input=..., n_windows=..., unroll_length=...) — time series

Domains

CartesianDomain, EllipsoidDomain, SimplexDomain. Set ops: Union, Intersection, Difference, Exclusion. Discretise with problem.discretise_domain(n, mode) where mode is "grid", "random", "lh", "chebyshev".

Solvers

PINN, CausalPINN, SelfAdaptivePINN, CompetitivePINN, GradientPINN, RBAPINN, SupervisedSolver, AutoregressiveSolver. Ensembles via *EnsembleSolver variants.

Models

FeedForward, ResidualFeedForward, PirateNet, DeepONet, MIONet, FNO, KolmogorovArnoldNetwork, GraphNeuralOperator, SINDy, and more.

Equation zoo

PoissonEquation, HelmholtzEquation, BurgersEquation, AdvectionEquation, AllenCahnEquation, AcousticWaveEquation, DiffusionReactionEquation. Boundary: FixedValue, FixedGradient, FixedFlux, FixedLaplacian.

Key utilities

• LabelTensor — torch.Tensor with named columns; index via .extract(["x", "y"])
• Differential operators: grad, div, laplacian, advection — not cached, compute once
• Trainer wraps lightning.pytorch.Trainer; handles DataModule, batching, device placement