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name: operator-learning description: "Use DeepXDE operator-learning data classes and networks: DeepONet, POD-DeepONet, MIONet, PI-DeepONet, function spaces, and ZCS." disable-model-invocation: true metadata: disco-role: operating license: LGPL 2.1

DeepXDE Operator Learning

Use this sub-skill when the task is to build or debug DeepXDE operator-learning workflows: supervised DeepONet data, physics-informed DeepONet data, POD-DeepONet, MIONet, function-space sampling, aligned/cartesian-product shapes, multi-output DeepONets, or Zero Coordinate Shift (ZCS).

Start here

1. Classify the data layout before choosing the network:
   • aligned shared evaluation grid: dde.data.TripleCartesianProd with dde.nn.DeepONetCartesianProd;
   • unaligned sample triples: dde.data.Triple with dde.nn.DeepONet;
   • two-input-function operators: dde.data.QuadrupleCartesianProd with dde.nn.MIONetCartesianProd when using the PyTorch-verified API;
   • physics-informed operators: dde.data.PDEOperator or dde.data.PDEOperatorCartesianProd layered on dde.data.PDE/TimePDE.
2. Read operator workflows for recipe order, shape checks, PI-DeepONet flow, POD/MIONet notes, and ZCS usage.
3. Read API reference for constructor signatures, shape tables, function-space families, multi-output strategy rules, and ZCS support boundaries.
4. Read troubleshooting when labels, branch/trunk widths, PDE auxiliary variables, function-space sensors, or ZCS derivatives fail.
5. For a minimal supervised aligned DeepONet sanity check, run scripts/smoke_deeponet_aligned.py. It defaults to DDE_BACKEND=pytorch, uses synthetic data, performs one Adam iteration, and does not require a GPU.

Routing boundaries

• Generic Model.compile, Model.train, prediction batching, metrics, checkpoints, and callbacks belong in training workflows.
• Backend installation, DDE_BACKEND, dtype/autodiff defaults, GPU, and Horovod setup belong in backend and configuration.
• Ordinary PINN residual and boundary-condition recipes that do not use an operator data class belong in PINN problem setup.

Verification scope

This construction verified a PyTorch CPU environment and a standard aligned DeepONet smoke path. TensorFlow, JAX, Paddle, GPU/Horovod, and full PI-DeepONet/ZCS training are optional or alternative paths and are not claimed as runtime-verified here unless a future verification report adds them.