PINNsAgent: Automated PDE Surrogation with Large Language Models

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) to bridge the gap between domain-specific knowledge and deep learning. PINNsAgent integrates Physics-Guided Knowledge Replay (PGKR) for efficient knowledge transfer from solved PDEs to similar problems, and Memory Tree Reasoning for exploring the search space of optimal PINNs architectures. We evaluate PINNsAgent on 14 benchmark PDEs, demonstrating its effectiveness in automating the surrogation process and significantly improving the accuracy of PINNs-based solutions.

Solving complex physical equations is crucial in science and engineering, but modern neural methods like Physics-Informed Neural Networks (PINNs) require extensive parameter tuning to work effectively. This tuning process typically demands both physics knowledge and deep learning expertise—a rare combination that creates barriers for many researchers.Our research introduces PINNsAgent, an AI assistant that automates the parameter tuning process for solving these equations. By leveraging large language models, our system intelligently searches for optimal configurations based on the specific properties of each equation. PINNsAgent remembers which parameters worked well for similar equations in the past and systematically explores new options to find the best solution.When tested on 14 different mathematical problems, our automated approach found better configurations than conventional tuning methods, making these powerful equation-solving techniques more accessible to scientists without deep learning expertise. This research saves valuable research time by eliminating tedious manual parameter tuning, allowing scientists to focus on their core scientific questions rather than the technical details of neural networks.