CodePDE: An Inference Framework for LLM-driven PDE Solver Generation

Understand

Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge.

• Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while neural-network-based solvers require large training datasets and often lack interpretability.
• In this work, we frame PDE solving as a code generation task and introduce CodePDE, the first inference framework for generating PDE solvers using large language models (LLMs).
• With CodePDE, we present a thorough evaluation on critical capacities of LLM for PDE solving: reasoning, debugging, self-refinement, and test-time scaling.