Multi-scale Time-stepping of Partial Differential Equations with
Transformers
- URL: http://arxiv.org/abs/2311.02225v1
- Date: Fri, 3 Nov 2023 20:26:43 GMT
- Title: Multi-scale Time-stepping of Partial Differential Equations with
Transformers
- Authors: AmirPouya Hemmasian, Amir Barati Farimani
- Abstract summary: We develop fast surrogates for Partial Differential Equations (PDEs)
Our model achieves similar or better results in predicting the time-evolution of Navier-Stokes equations.
- Score: 8.430481660019451
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Developing fast surrogates for Partial Differential Equations (PDEs) will
accelerate design and optimization in almost all scientific and engineering
applications. Neural networks have been receiving ever-increasing attention and
demonstrated remarkable success in computational modeling of PDEs, however;
their prediction accuracy is not at the level of full deployment. In this work,
we utilize the transformer architecture, the backbone of numerous
state-of-the-art AI models, to learn the dynamics of physical systems as the
mixing of spatial patterns learned by a convolutional autoencoder. Moreover, we
incorporate the idea of multi-scale hierarchical time-stepping to increase the
prediction speed and decrease accumulated error over time. Our model achieves
similar or better results in predicting the time-evolution of Navier-Stokes
equations compared to the powerful Fourier Neural Operator (FNO) and two
transformer-based neural operators OFormer and Galerkin Transformer.
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