From PDE Numerical Solvers to Neural Emulators and Back: PhD Thesis
chaumian · x · 2026-08-26
This PhD thesis explores the relationship between PDE numerical solvers and neural emulators, arguing they are fundamentally similar. Neural architectures mirror classical discretizations, and their errors are amenable to the same spectral analysis.
Key Contributions:
- APEBench: A comprehensive benchmarking suite for autoregressive PDE neural emulators using fast differentiable pseudo-spectral solvers in JAX.
- Progressively Refined Differentiable Physics: Investigating the effect of unconverged solvers on surrogate training.
- Neural Emulator Superiority: Analyzing the influence of numerical errors and architectural inductive biases.
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