neural-pde-solvers

This paper introduces ADSL-PDE, a domain-specific language that provides a structured search space for auto-designing neural PDE solvers, improving search efficiency and optimization stability by abstracting away low-level implementation details. The evolutionary agent built on this representation achieves over 52% performance improvement within the first ten iterations across PDE benchmarks.

This paper introduces breakeven complexity, a metric to determine when neural PDE solvers become cost-effective compared to traditional numerical solvers. The framework uses scaling laws to allocate training budgets and evaluates multiple neural solvers on diverse PDE benchmarks.