# PINNsAgent: Automated PDE Surrogation with Large Language Models

arXiv: https://arxiv.org/abs/2501.12053 · HTML: https://mlsanity.com/paper/2501.12053/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2025.

## Built on by (most cited first, 17 of 17)

- [AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2511.07262/) (2025)
- [Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework](https://mlsanity.com/paper/2510.05158/) (2025)
- [PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation](https://mlsanity.com/paper/2605.09636/) (2026)
- [ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2512.03476/) (2025)
- [GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2605.11117/) (2026)
- [Re4: Scientific Computing Agent with Rewriting, Resolution, Review and Revision](https://mlsanity.com/paper/2508.20729/) (2025)
- [Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materials](https://mlsanity.com/paper/2512.01735/) (2025)
- [Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards](https://mlsanity.com/paper/2607.10474/) (2026)
- [EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks](https://mlsanity.com/paper/2607.26490/) (2026)
- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)
- [Physics-Audited Agentic Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2607.07379/) (2026)
- [Agentic Neural Architecture Search](https://mlsanity.com/paper/2607.07984/) (2026)
- [LLM-driven design of physics-constrained constitutive models: two agents are better than one](https://mlsanity.com/paper/2605.23754/) (2026)
- [Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design](https://mlsanity.com/paper/2607.15560/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)
- [PINNForge: Execution-Grounded Evolutionary Design of Physics-Informed Neural Networks](https://mlsanity.com/paper/2609.23023/) (2026)
- [Enhancing Transformer Representations of Symbolic ODE Expressions](https://mlsanity.com/paper/2609.24746/) (2026)

## Abstract (arXiv)

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.