PINNsAgent: Automated PDE Surrogation with Large Language Models

Qingpo Wuwu, Chonghan Gao, Tianyu Chen, Yihang Huang, Yuekai Zhang, Jianing Wang, Jianxin Li, Haoyi Zhou, Shanghang Zhang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:68143-68165, 2025.

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) 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wuwu25a, title = {{PINN}s{A}gent: Automated {PDE} Surrogation with Large Language Models}, author = {Wuwu, Qingpo and Gao, Chonghan and Chen, Tianyu and Huang, Yihang and Zhang, Yuekai and Wang, Jianing and Li, Jianxin and Zhou, Haoyi and Zhang, Shanghang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {68143--68165}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wuwu25a/wuwu25a.pdf}, url = {https://proceedings.mlr.press/v267/wuwu25a.html}, 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) 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.} }
Endnote
%0 Conference Paper %T PINNsAgent: Automated PDE Surrogation with Large Language Models %A Qingpo Wuwu %A Chonghan Gao %A Tianyu Chen %A Yihang Huang %A Yuekai Zhang %A Jianing Wang %A Jianxin Li %A Haoyi Zhou %A Shanghang Zhang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wuwu25a %I PMLR %P 68143--68165 %U https://proceedings.mlr.press/v267/wuwu25a.html %V 267 %X 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.
APA
Wuwu, Q., Gao, C., Chen, T., Huang, Y., Zhang, Y., Wang, J., Li, J., Zhou, H. & Zhang, S.. (2025). PINNsAgent: Automated PDE Surrogation with Large Language Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:68143-68165 Available from https://proceedings.mlr.press/v267/wuwu25a.html.

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