A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data
This work addresses the problem of predicting complex physical dynamics from limited data, which is significant for scientists and engineers working with real-world, often incomplete, observational data.
This paper proposes a deep learning framework to predict the evolution of spatiotemporal physical processes governed by unknown partial differential equations (PDEs), using only sparsely distributed data. The method is demonstrated on 2D wave and Burgers-Fisher equations in various geometries and a 10D heat equation.
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.