Towards General Neural Surrogate Solvers with Specialized Neural Accelerators

Chenkai Mao, Robert Lupoiu, Tianxiang Dai, Mingkun Chen, Jonathan Fan
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:34693-34711, 2024.

Abstract

Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary conditions. We propose Specialized Neural Accelerator-Powered Domain Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which subdomain problems containing arbitrary boundary conditions and geometric parameters are accurately solved using an ensemble of specialized neural operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems and show how innovations in network architecture and loss function engineering can produce specialized surrogate subdomain solvers with near unity accuracy. We utilize these solvers with standard DDM algorithms to accurately solve freeform electromagnetics and fluids problems featuring a wide range of domain sizes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-mao24b, title = {Towards General Neural Surrogate Solvers with Specialized Neural Accelerators}, author = {Mao, Chenkai and Lupoiu, Robert and Dai, Tianxiang and Chen, Mingkun and Fan, Jonathan}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {34693--34711}, 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/mao24b/mao24b.pdf}, url = {https://proceedings.mlr.press/v235/mao24b.html}, abstract = {Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary conditions. We propose Specialized Neural Accelerator-Powered Domain Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which subdomain problems containing arbitrary boundary conditions and geometric parameters are accurately solved using an ensemble of specialized neural operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems and show how innovations in network architecture and loss function engineering can produce specialized surrogate subdomain solvers with near unity accuracy. We utilize these solvers with standard DDM algorithms to accurately solve freeform electromagnetics and fluids problems featuring a wide range of domain sizes.} }
Endnote
%0 Conference Paper %T Towards General Neural Surrogate Solvers with Specialized Neural Accelerators %A Chenkai Mao %A Robert Lupoiu %A Tianxiang Dai %A Mingkun Chen %A Jonathan Fan %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-mao24b %I PMLR %P 34693--34711 %U https://proceedings.mlr.press/v235/mao24b.html %V 235 %X Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary conditions. We propose Specialized Neural Accelerator-Powered Domain Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which subdomain problems containing arbitrary boundary conditions and geometric parameters are accurately solved using an ensemble of specialized neural operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems and show how innovations in network architecture and loss function engineering can produce specialized surrogate subdomain solvers with near unity accuracy. We utilize these solvers with standard DDM algorithms to accurately solve freeform electromagnetics and fluids problems featuring a wide range of domain sizes.
APA
Mao, C., Lupoiu, R., Dai, T., Chen, M. & Fan, J.. (2024). Towards General Neural Surrogate Solvers with Specialized Neural Accelerators. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:34693-34711 Available from https://proceedings.mlr.press/v235/mao24b.html.

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