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

2026-02-19

AI Summary

This work proposes a multi-agent framework that automatically designs, implements, and validates transparent, structure-aware numerical solvers for partial differential equations (PDEs) directly from natural language descriptions. Addressing the high expert-dependence and tuning costs of traditional PDE solvers, as well as the computational overhead and poor interpretability of existing neural approaches, the framework integrates classical numerical analysis with autonomous reasoning. It employs a coarse-to-fine execution strategy and a residual-driven self-verification mechanism to balance accuracy and interpretability. Evaluated on 24 benchmark and real-world PDE problems, the method achieves solution accuracy comparable to or better than current neural and large language model baselines, marking the first fully automated, PDE-structure-driven adaptation of numerical schemes.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Multiagent Systems: Distributed Problem Solving
• Machine Learning: Hardware-aware ML

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search

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.

Problem

• PDE
• numerical solver
• scientific computing
• automation
• interpretability

Innovation

• multi-agent framework
• PDE-agnostic
• numerical solver automation
• residual-based self-verification
• interpretable scientific computing