CodePDE: LLM-Driven PDE Solver Generation

This document introduces CodePDE, a new framework for using large language models (LLMs) to generate code that solves partial differential equations (PDEs). The authors frame PDE solving as a code generation problem and demonstrate that, with techniques like debugging and refinement, LLMs can create solvers that are competitive with, and sometimes surpass, human-written solvers on various PDE families like Burgers, Advection, and Darcy flow. They highlight the ability of LLMs to reason, debug, and improve code through feedback, suggesting a promising future for LLMs in scientific computing, despite challenges with certain PDE types like Reaction-Diffusion.