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

• URL: http://arxiv.org/abs/2202.12358v1
• Date: Thu, 24 Feb 2022 20:46:52 GMT
• Title: Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations
• Authors: Benjamin Wu, Oliver Hennigh, Jan Kautz, Sanjay Choudhry, Wonmin Byeon
• Abstract summary: We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
• Score: 62.81701992551728
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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