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

by Aditya Kashi
Publication Type
Conference Paper
Book Title
SC-W '23: Proceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis
Publication Date
Page Numbers
102 to 108
Publisher Location
New York, New York, United States of America
Conference Name
The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC-W)
Conference Location
Denver, Colorado, United States of America
Conference Sponsor
Conference Date

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.