HAMLET: Graph Transformer Neural Operator for Partial Differential Equations

Andrey Bryutkin, Jiahao Huang, Zhongying Deng, Guang Yang, Carola-Bibiane Schönlieb, Angelica I Aviles-Rivero
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:4624-4641, 2024.

Abstract

We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-bryutkin24a, title = {{HAMLET}: Graph Transformer Neural Operator for Partial Differential Equations}, author = {Bryutkin, Andrey and Huang, Jiahao and Deng, Zhongying and Yang, Guang and Sch\"{o}nlieb, Carola-Bibiane and Aviles-Rivero, Angelica I}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {4624--4641}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/bryutkin24a/bryutkin24a.pdf}, url = {https://proceedings.mlr.press/v235/bryutkin24a.html}, abstract = {We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.} }
Endnote
%0 Conference Paper %T HAMLET: Graph Transformer Neural Operator for Partial Differential Equations %A Andrey Bryutkin %A Jiahao Huang %A Zhongying Deng %A Guang Yang %A Carola-Bibiane Schönlieb %A Angelica I Aviles-Rivero %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-bryutkin24a %I PMLR %P 4624--4641 %U https://proceedings.mlr.press/v235/bryutkin24a.html %V 235 %X We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.
APA
Bryutkin, A., Huang, J., Deng, Z., Yang, G., Schönlieb, C. & Aviles-Rivero, A.I.. (2024). HAMLET: Graph Transformer Neural Operator for Partial Differential Equations. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:4624-4641 Available from https://proceedings.mlr.press/v235/bryutkin24a.html.

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