Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data

Aditya Kashi

doi:10.1145/3624062.3626088

Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data

Aditya Kashi

Analytics and AI Methods at Scale

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

It is widely hoped that artificial intelligence will boost data-driven surrogate models in science and engineering. However, fundamental spatial aspects of AI surrogate models remain under-studied. We investigate the ability of neural-network surrogate models to predict solutions to PDEs under variable boundary values. We do not wish to retrain the model when the boundary values change but to make them inputs to the model and infer the solution of the PDE under those boundary conditions. Such a capability is essential to making AI-based surrogate models practically useful. While simple feedforward networks are used for one-dimensional (1D) Poisson equation, an encoder-decoder architecture with a tensor-product layer is developed for the two-dimensional Poisson equation posed on a rectangular domain. We show that it is indeed possible to infer solutions to PDEs from variable boundary data using neural networks in this relatively simple setting, and point to future directions.

Original language	English
Title of host publication	Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023
Publisher	Association for Computing Machinery
Pages	102-108
Number of pages	7
ISBN (Electronic)	9798400707858
DOIs	https://doi.org/10.1145/3624062.3626088
State	Published - Nov 12 2023
Event	2023 International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023 - Denver, United States Duration: Nov 12 2023 → Nov 17 2023

Publication series

Name	ACM International Conference Proceeding Series

Conference

Conference	2023 International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023
Country/Territory	United States
City	Denver
Period	11/12/23 → 11/17/23

Funding

This research was sponsored by the Oak Ridge Leadership Computing Facility (OLCF), which is a DOE Office of Science User Facility at the Oak Ridge National Laboratory (ORNL) supported by the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. The author would also like to express thanks to Shreya Kashi for useful discussions and advice on neural network architectures, Hao Lu for discussions on aspects of running simulations, as well as Feiyi Wang for feedback on the direction of the research and mentorship. The name ‘Tencoder’ was inspired from a suggestion by ChatGPT. ∗Oak Ridge National Laboratory, [email protected] 1Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/doe-public-access-plan).

Funders	Funder number
Oak Ridge National Laboratory
U.S. Department of Energy	DE-AC05-00OR22725
Office of Science
Oak Ridge National Laboratory

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10.1145/3624062.3626088

Cite this

Kashi, A. (2023). Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data. In Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023 (pp. 102-108). (ACM International Conference Proceeding Series). Association for Computing Machinery. https://doi.org/10.1145/3624062.3626088

Kashi, Aditya. / Tencoder : tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data. Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. Association for Computing Machinery, 2023. pp. 102-108 (ACM International Conference Proceeding Series).

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abstract = "It is widely hoped that artificial intelligence will boost data-driven surrogate models in science and engineering. However, fundamental spatial aspects of AI surrogate models remain under-studied. We investigate the ability of neural-network surrogate models to predict solutions to PDEs under variable boundary values. We do not wish to retrain the model when the boundary values change but to make them inputs to the model and infer the solution of the PDE under those boundary conditions. Such a capability is essential to making AI-based surrogate models practically useful. While simple feedforward networks are used for one-dimensional (1D) Poisson equation, an encoder-decoder architecture with a tensor-product layer is developed for the two-dimensional Poisson equation posed on a rectangular domain. We show that it is indeed possible to infer solutions to PDEs from variable boundary data using neural networks in this relatively simple setting, and point to future directions.",

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Kashi, A 2023, Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data. in Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. ACM International Conference Proceeding Series, Association for Computing Machinery, pp. 102-108, 2023 International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023, Denver, United States, 11/12/23. https://doi.org/10.1145/3624062.3626088

Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data. / Kashi, Aditya.
Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. Association for Computing Machinery, 2023. p. 102-108 (ACM International Conference Proceeding Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Kashi A. Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data. In Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. Association for Computing Machinery. 2023. p. 102-108. (ACM International Conference Proceeding Series). doi: 10.1145/3624062.3626088

Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data

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