AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing
2026-02-19 • Artificial Intelligence
Artificial IntelligenceMachine Learning
AI summaryⓘ
The authors created AutoNumerics, a system that automatically builds and checks math solvers for partial differential equations (PDEs) using natural language instructions. Unlike neural network methods that can be hard to understand, this system makes transparent solvers based on traditional math techniques. It uses a step-by-step approach and self-checks to improve accuracy. Tests on many PDE problems show the system performs as well as or better than existing methods and picks suitable solving strategies based on the equation type.
Partial Differential EquationsNumerical solversNeural networksNatural language processingClassical numerical analysisMulti-agent systemsResidual-based verificationCoarse-to-fine strategy
Authors
Jianda Du, Youran Sun, Haizhao Yang
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.