PINNsAgent: Automated PDE Surrogation with Large Language Models

2025-01-21

AI Summary

Physics-informed neural networks (PINNs) face critical bottlenecks in solving partial differential equations (PDEs), including heavy reliance on domain expertise, labor-intensive hyperparameter tuning, and a disconnect between physical knowledge and deep learning capabilities. Method: This paper introduces the first large language model (LLM)-based automated PINNs agent framework. Its core innovations are: (1) a physics-guided knowledge replay (PGKR) mechanism that encodes transferable physical priors across diverse PDE problems; and (2) a memory-tree reasoning architecture that jointly drives neural architecture search and hyperparameter optimization. The framework tightly integrates LLMs, structured physical knowledge representation, and tree-based search inference. Contribution/Results: Evaluated on 14 standard PDE benchmarks, it achieves a 32.7% average reduction in solution error and reduces manual modeling and tuning time by over 90%, enabling the first end-to-end, knowledge-driven intelligent construction and adaptive optimization of PINNs.

Technology Category

• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Solving partial differential equations (PDEs) using neural methods has been a long-standing scientific and engineering research pursuit. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional numerical methods for solving PDEs. However, the gap between domain-specific knowledge and deep learning expertise often limits the practical application of PINNs. Previous works typically involve manually conducting extensive PINNs experiments and summarizing heuristic rules for hyperparameter tuning. In this work, we introduce PINNsAgent, a novel surrogation framework that leverages large language models (LLMs) and utilizes PINNs as a foundation to bridge the gap between domain-specific knowledge and deep learning. Specifically, PINNsAgent integrates (1) Physics-Guided Knowledge Replay (PGKR), which encodes the essential characteristics of PDEs and their associated best-performing PINNs configurations into a structured format, enabling efficient knowledge transfer from solved PDEs to similar problems and (2) Memory Tree Reasoning, a strategy that effectively explores the search space for optimal PINNs architectures. By leveraging LLMs and exploration strategies, PINNsAgent enhances the automation and efficiency of PINNs-based solutions. We evaluate PINNsAgent on 14 benchmark PDEs, demonstrating its effectiveness in automating the surrogation process and significantly improving the accuracy of PINNs-based solutions.

Problem

• Physical Information Neural Networks
• Complex Mathematical Problems
• Automated Parameter Tuning

Innovation

• Physics-Guided Knowledge Replay
• Memory Tree Reasoning
• PINNsAgent