arXiv:2512.16214cs.AI2025-12被引 5

用多智能体和工具链自动求解偏微分方程,无需专家干预。

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

  • 通过双循环机制实现智能体动态规划与错误修正。
  • 在复杂多步任务中表现优于现有方法,支持跨步骤依赖求解。
  • 适合自动化科学计算、非专业用户快速建模求解。

求解偏微分方程(PDE)是工程与科研的核心挑战。传统方法依赖人工设置和领域知识,虽有物理信息神经网络(PINNs)和DeepXDE等框架提升自动化程度,仍需专家介入且缺乏完全自主性。本文将PDE求解建模为大模型驱动的工具调用任务,提出首个工具链增强型多智能体协作框架PDE-Agent,融合大模型推理能力与外部工具可控性,实现从自然语言描述到自动求解的全流程。核心创新包括:(1) 基于图记忆的Prog-Act框架,通过局部修复与全局重构双循环机制实现高效动态规划与纠错;(2) 集成资源池与工具参数分离机制,统一管理运行时产物,解决多工具间依赖缺口。为验证该范式,构建了PDE-Bench——首个面向代理协同求解的多类型PDE基准,设计多层级评估指标。实验表明,PDE-Agent在复杂多步、跨步依赖任务中具备更强适用性与性能。该范式将推动自动化科学计算发展。代码与数据集将公开。

原文摘要 · Abstract (English)

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.

偏微分方程多智能体自动化求解工具链

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