Spatio-Temporal Super-Resolution of Dynamical Systems using Physics-Informed Deep-Learning

TL;DR

This paper introduces a physics-informed deep learning framework that enhances the spatio-temporal resolution of PDE solutions without high-resolution training data, improving accuracy and computational efficiency in engineering applications.

Contribution

The work presents a novel, data-free super-resolution method for PDE solutions using physics-informed neural networks with separate spatial and temporal modules.

Findings

Successfully super-resolves low-resolution PDE solutions in space and time.

Maintains physics-based constraints and achieves high accuracy.

Offers potential for integration with traditional numerical methods for faster computations.

Abstract

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based super-resolution models have shown promise in accelerating engineering design by reducing the computational expense of traditional numerical schemes. However, these models heavily rely on the availability of high-resolution (HR) labeled data needed during training. In this work, we propose a physics-informed deep learning-based framework to enhance the spatial and temporal resolution of coarse-scale (both in space and time) PDE solutions without requiring any HR data. The framework consists of two trainable modules independently super-resolving the PDE solution, first in spatial and then in temporal direction. The physics based losses are implemented in a novel way to ensure tight coupling between the spatio-temporally refined outputs at different times and improve framework accuracy. We analyze the capability of the developed framework by investigating its performance on an elastodynamics problem. It is observed that the proposed framework can successfully super-resolve (both in space and time) the low-resolution PDE solutions while satisfying physics-based constraints and yielding high accuracy. Furthermore, the analysis and obtained speed-up show that the proposed framework is well-suited for integration with traditional numerical methods to reduce computational complexity during engineering design.