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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

Skills

Skills under .opencode/skills/<name>/SKILL.md give step-by-step guidance. Load the relevant skill when the user's request matches:

Skill When to load
pina-workflow User wants to solve a PDE/ODE or model a physical system — orchestrates the full session
create-problem Defining a problem, setting up variables and outputs
define-domains Creating and discretising domains
define-equations Writing PDEs/ODEs or using the equation zoo
condition-setup Binding equations to domains, data-driven conditions
select-model Choosing or configuring a neural architecture
select-solver Selecting the right solver for the problem
select-trainer Configuring training parameters and callbacks
create-skill User wants to create or edit a skill in this repo
skill-sync-checker Auditing skill references against the codebase

Commands

pytest tests/ -x       # run tests
ruff check .           # lint

Rules

  • Never modify source code (pina/, tests/, docs/). Skills are read-only guidance.
  • Stay conversational — walk through the workflow naturally.