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...
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2021-01-01
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| Online Access: | https://ieeexplore.ieee.org/document/9416427/ |
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doaj-c97e6af36de5413693c3d44341bc8cfa2021-04-30T23:01:02ZengIEEEIEEE Access2169-35362021-01-019642006421010.1109/ACCESS.2021.30758999416427A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed DataPriyabrata Saha0https://orcid.org/0000-0002-6933-0660Saibal Mukhopadhyay1https://orcid.org/0000-0002-8894-3390School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USASchool of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USAIn 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.https://ieeexplore.ieee.org/document/9416427/Collocation methoddeep learningPDEsradial basis functionsscattered data interpolationspatiotemporal dynamics |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Priyabrata Saha Saibal Mukhopadhyay |
| spellingShingle |
Priyabrata Saha Saibal Mukhopadhyay A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data IEEE Access Collocation method deep learning PDEs radial basis functions scattered data interpolation spatiotemporal dynamics |
| author_facet |
Priyabrata Saha Saibal Mukhopadhyay |
| author_sort |
Priyabrata Saha |
| title |
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data |
| title_short |
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data |
| title_full |
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data |
| title_fullStr |
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data |
| title_full_unstemmed |
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data |
| title_sort |
deep learning approach for predicting spatiotemporal dynamics from sparsely observed data |
| publisher |
IEEE |
| series |
IEEE Access |
| issn |
2169-3536 |
| publishDate |
2021-01-01 |
| description |
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. |
| topic |
Collocation method deep learning PDEs radial basis functions scattered data interpolation spatiotemporal dynamics |
| url |
https://ieeexplore.ieee.org/document/9416427/ |
| work_keys_str_mv |
AT priyabratasaha adeeplearningapproachforpredictingspatiotemporaldynamicsfromsparselyobserveddata AT saibalmukhopadhyay adeeplearningapproachforpredictingspatiotemporaldynamicsfromsparselyobserveddata AT priyabratasaha deeplearningapproachforpredictingspatiotemporaldynamicsfromsparselyobserveddata AT saibalmukhopadhyay deeplearningapproachforpredictingspatiotemporaldynamicsfromsparselyobserveddata |
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1721497446488473600 |