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name: pinn-problem-setup description: "Assemble DeepXDE forward and inverse PINN problems with geometry, residuals, conditions, data classes, and sampling." disable-model-invocation: true metadata: disco-role: operating license: LGPL 2.1

PINN problem setup

Use this sub-skill when a task needs the DeepXDE objects that define a physics-informed problem: geometry, time domain, PDE residual callbacks, boundary/initial/point-set constraints, inverse variables, and dde.data.PDE-family data objects. It is the setup layer before model compile/train/predict.

Route first

• Backend selection, installation, dtype, random seed, autodiff mode, GPU, or Horovod questions: use ../backend-and-configuration/SKILL.md.
• Optimizers, callbacks, save/restore, plotting, training schedules, metrics, or prediction lifecycle: use ../training-workflows/SKILL.md.
• DeepONet, PI-DeepONet, MIONet, Cartesian-product operator data, or operator networks: use ../operator-learning/SKILL.md.

Setup checklist

1. Select the geometry and optional time domain. Use dde.geometry.Interval, Rectangle, Disk, Cuboid, Hypercube, Hypersphere, polygonal/point-cloud geometries, CSG (|, -, &), and GeometryXTime as appropriate.
2. Write the residual callback as def pde(x, y): ... (or def pde(x, y, int_mat): ... for IDE/FPDE). Use backend tensor operations inside the residual and DeepXDE gradients (dde.grad.jacobian, dde.grad.hessian).
3. Add soft constraints with dde.icbc.* classes or exact constraints with net.apply_output_transform.
4. Pick dde.data.PDE, TimePDE, IDE, or FPDE, including num_domain, num_boundary, num_initial, train_distribution, anchors, exclusions, and num_test deliberately.
5. For inverse PINNs, create dde.Variable unknowns, use them inside the residual, and pass them to Model.compile(..., external_trainable_variables=...) in the training workflow.

References

• Build complete forward/inverse workflows from references/pinn-workflows.md.
• Check constructor signatures, shape contracts, and backend verification notes in references/api-reference.md.
• Diagnose residual, BC, point-set, sampling, and exact-constraint failures with references/troubleshooting.md.

Smoke script

Run the bundled tiny PyTorch CPU-safe Poisson smoke when you need to check that basic problem assembly, compile, one or two training iterations, prediction, and residual prediction work:

python scripts/smoke_poisson_1d.py --help
python scripts/smoke_poisson_1d.py --iterations 2

The bundled smoke runs only with the PyTorch backend and sets DDE_BACKEND=pytorch for the run. This construction verified PyTorch CPU for the basic PDE path; TensorFlow, JAX, Paddle, GPU, Horovod, and backend-limited IDE/FPDE examples are optional alternatives and must be verified before relying on them.