From Numerical Simulators of PDEs to Neural Emulators and Back
Simulation is central to modern engineering and science, but the cost of numerical solvers for partial differential equations (PDEs) remains a bottleneck whenever fast or many-query evaluations are required. Neural emulators trained on solver-generated data promise significant speedups, yet they are usually framed as opaque alternatives to the very methods that produce their training signal. This thesis argues the two paradigms are more alike than different: neural architectures mirror classical discretizations, their errors are amenable to the same spectral analysis, and insight flows profitably in both directions. We approach the relationship by disentangling the multiple roles a solver...
| Authors | Felix Koehler |
|---|---|
| Primary category | cs.LG |
| Published | 25 August 2026 |
| Last updated at source | 25 August 2026 |
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