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

arXiv: https://arxiv.org/abs/2212.04457 · HTML: https://mlsanity.com/paper/2212.04457/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 13 of 13)

- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks](https://mlsanity.com/paper/2008.13547/) (2020)
- [Physics-informed neural networks for modeling rate- and temperature-dependent plasticity](https://mlsanity.com/paper/2201.08363/) (2022)
- [Physics-informed Deep Super-resolution for Spatiotemporal Data](https://mlsanity.com/paper/2208.01462/) (2022)
- [PhySRNet: Physics informed super-resolution network for application in computational solid mechanics](https://mlsanity.com/paper/2206.15457/) (2022)
- [Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity](https://mlsanity.com/paper/2112.08676/) (2021)
- [Predicting Peak Stresses In Microstructured Materials Using Convolutional Encoder-Decoder Learning](https://mlsanity.com/paper/2201.00722/) (2022)

## Built on by (most cited first, 3 of 3)

- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I](https://mlsanity.com/paper/2307.04121/) (2023)

## Abstract (arXiv)

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.