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

TL;DR

This paper introduces a novel physics-informed RNN-DCT network that effectively solves time-dependent PDEs by combining discrete cosine transforms and recurrent neural networks, achieving state-of-the-art results on Navier-Stokes simulations.

Contribution

The paper presents a new physics-informed neural network architecture that integrates DCT and RNNs to better handle complex time-dependent PDEs, improving accuracy and efficiency.

Findings

Achieves state-of-the-art performance on Taylor-Green vortex simulations

Effectively encodes spatio-temporal dynamics using DCT and RNNs

Outperforms existing physics-informed models in accuracy

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.