# A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data

arXiv: https://arxiv.org/abs/2011.14965 · HTML: https://mlsanity.com/paper/2011.14965/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

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

- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Generalized Neural Closure Models with Interpretability](https://mlsanity.com/paper/2301.06198/) (2023)
- [Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics](https://mlsanity.com/paper/2203.08655/) (2022)

## Abstract (arXiv)

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and predicts its evolution using sparsely distributed data sites. Deep learning has shown promising results in modeling physical dynamics in recent years. However, most of the existing deep learning methods for modeling physical dynamics either focus on solving known PDEs or require data in a dense grid when the governing PDEs are unknown. In contrast, our method focuses on learning prediction models for unknown PDE-driven dynamics only from sparsely observed data. The proposed method is spatial dimension-independent and geometrically flexible. We demonstrate our method in the forecasting task for the two-dimensional wave equation and the Burgers-Fisher equation in multiple geometries with different boundary conditions, and the ten-dimensional heat equation.