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autoregressive-neural-pde-solver
Training patterns for autoregressive neural PDE solvers (FNO, DeepONet, CNO). Covers rollout training, noise injection for stability, multi-component loss functions (H1, frequency-sensitive, boundary-aware), per-channel normalization for coupled multi-variable systems, and the PDEBench nRMSE metric. Use when training any neural operator that predicts time-dependent PDE solutions.
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- neural-operator Declared skill tag
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# Autoregressive Neural PDE Solvers — Training Patterns
## When to Use
- Training any neural operator (FNO, DeepONet, CNO, etc.) to predict time-dependent PDE solutions
- The model predicts one (or few) timesteps ahead, then feeds predictions back as input
- Multi-variable PDE systems (compressible NS, MHD, multi-species reaction, etc.)
- Problems where single-step accuracy is insufficient — rollout stability matters
## Core Principle: Train How You Infer
The single biggest mistake in neural PDE solving is training on single-step predictions but inferring with multi-step rollout. The model never learns to handle its own errors.
```python
# WRONG: Teacher forcing (single-step)