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Architectures and techniques for neural operators on discontinuous PDE solutions (shocks, contact discontinuities, steep gradients). Covers local-global spectral design (ShockFNO), reflection padding for non-periodic BCs, resolution scaling for shock width, and frequency-band error diagnostics. Use for low-viscosity Burgers, compressible Euler, Riemann problems, or any PDE where standard FNO produces Gibbs oscillations.
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Train neural operators (FNO, DeepONet) to learn solution maps for parametric PDE families. Once trained, solve new PDE instances in milliseconds. Use when you need to solve many instances of the same PDE with different parameters/ICs/BCs.
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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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Patterns for loading PDE simulation datasets (PDEBench, PhiFlow, JAX-CFD) from HDF5 files. Handles layout detection (single tensor vs separate variables), spatial/temporal downsampling, multi-variable systems, HuggingFace and DaRUS data sources, and efficient PyTorch DataLoader creation. Use when preparing PDE data for neural operator training.
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