Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations

[arxiv]  

• Some parts of this paper were presented at NeurIPS’21 Workshop: ML and the Physical Science. [workshop page]   [paper]   [poster]  

• This model is released as part of NVIDIA Modulus.   [blog]   [repo].

Abstract

Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to their architectural nature. In this work, we present a novel physics-informed framework for solving time-dependent partial differential equations. Using only the governing differential equations and problem initial and boundary conditions, we generate a latent representation of the problem’s spatio-temporal dynamics. Our model utilizes discrete cosine transforms to encode spatial frequencies and recurrent neural networks to process the time evolution. This efficiently and flexibly produces a compressed representation which is used for additional conditioning of physics-informed models. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations. Our proposed model achieves state-of-the-art performance on the Taylor-Green vortex relative to other physics-informed baseline models.

@misc{wu2022physics,
      title={Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations}, 
      author={Benjamin Wu and Oliver Hennigh and Jan Kautz and Sanjay Choudhry and Wonmin Byeon},
      year={2022},
      eprint={2202.12358},
      archivePrefix={arXiv},
      primaryClass={physics.comp-ph}
}