AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing

Jianda Du, Youran Sun, Haizhao Yang

Keywords: AI for PDEs, Multi-Agent Systems, Large Language Models, Scientific Computing, Automated PDE Solver Synthesis, Scientific Code Generation, Numerical Methods, Verification-aware Generation

TL;DR: A multi-agent LLM framework that automatically designs, debugs, and verifies interpretable classical PDE solvers from natural language descriptions using coarse-to-fine execution and residual-based self-verification.

Abstract:

PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning.
Recent neural network-based approaches improve flexibility but often demand high computational cost and suffer from limited interpretability.
We introduce \texttt{AutoNumerics}, a multi-agent framework that autonomously designs, implements, debugs, and verifies numerical solvers for general PDEs directly from natural language descriptions.
Unlike black-box neural solvers, our framework generates transparent solvers grounded in classical numerical analysis.
We introduce a coarse-to-fine execution strategy and a residual-based self-verification mechanism.
Experiments on 24 canonical and real-world PDE problems demonstrate that \texttt{AutoNumerics} achieves competitive or superior accuracy compared to existing neural and LLM-based baselines, and correctly selects numerical schemes based on PDE structural properties, suggesting its viability as an accessible paradigm for automated PDE solving.

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Submission Number: 125