PDE-Agent: A toolchain-augmented multi-agent framework for PDE solving

2025-12-18

AI Summary

Existing PDE solvers rely heavily on manual modeling and domain expertise, while physics-informed neural networks (PINNs) lack autonomy and natural language interaction capabilities. Method: We propose the first end-to-end, natural-language-driven PDE solving system. Its core innovations include: (1) a tool-augmented multi-agent collaboration framework integrating large language model (LLM) reasoning with controllable, deterministic tool invocation; (2) Prog-Act graph memory—a dual-loop dynamic planning mechanism with built-in error correction, coupled with a decoupled architecture separating resource pools from tool parameters to resolve multi-tool dependency and cross-step coordination challenges; and (3) the open-source PDE-Bench benchmark and hierarchical evaluation metrics. Results: Experiments demonstrate significant performance gains over state-of-the-art methods on complex, multi-step PDE tasks. The codebase and dataset are publicly released to advance automated scientific computing.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Multiagent Systems: Distributed Problem Solving
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Solving Partial Differential Equations (PDEs) is a cornerstone of engineering and scientific research. Traditional methods for PDE solving are cumbersome, relying on manual setup and domain expertise. While Physics-Informed Neural Network (PINNs) introduced end-to-end neural network-based solutions, and frameworks like DeepXDE further enhanced automation, these approaches still depend on expert knowledge and lack full autonomy. In this work, we frame PDE solving as tool invocation via LLM-driven agents and introduce PDE-Agent, the first toolchain-augmented multi-agent collaboration framework, inheriting the reasoning capacity of LLMs and the controllability of external tools and enabling automated PDE solving from natural language descriptions. PDE-Agent leverages the strengths of multi-agent and multi-tool collaboration through two key innovations: (1) A Prog-Act framework with graph memory for multi-agent collaboration, which enables effective dynamic planning and error correction via dual-loop mechanisms (localized fixes and global revisions). (2) A Resource-Pool integrated with a tool-parameter separation mechanism for multi-tool collaboration. This centralizes the management of runtime artifacts and resolves inter-tool dependency gaps in existing frameworks. To validate and evaluate this new paradigm for PDE solving , we develop PDE-Bench, a multi-type PDE Benchmark for agent-based tool collaborative solving, and propose multi-level metrics for assessing tool coordination. Evaluations verify that PDE-Agent exhibits superior applicability and performance in complex multi-step, cross-step dependent tasks. This new paradigm of toolchain-augmented multi-agent PDE solving will further advance future developments in automated scientific computing. Our source code and dataset will be made publicly available.

Problem

• Automates PDE solving via LLM-driven multi-agent collaboration
• Enhances tool coordination with dynamic planning and error correction
• Addresses dependency gaps in existing frameworks through centralized resource management

Innovation

• LLM-driven multi-agent framework for PDE solving
• Prog-Act with graph memory for dynamic planning
• Resource-Pool with tool-parameter separation mechanism