A Deep Learning Approach for Predicting Spatiotemporal Dynamics from Sparsely Observed Data

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 site...

Full description

Saved in:
Bibliographic Details
Published in:IEEE access 2021-01, Vol.9, p.1-1
Main Authors: Saha, Priyabrata, Mukhopadhyay, Saibal
Format: Article
Language:English
Subjects:
Boundary conditions
Collocation method
Data models
Deep learning
Differential operators
Dynamics
Interpolation
Mathematical model
Modelling
Partial differential equations
PDEs
Prediction models
Predictive models
radial basis functions
scattered data interpolation
spatiotemporal dynamics
Spatiotemporal phenomena
Thermodynamics
Wave equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2021.3075899