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17-10-2023

How Much Can One Learn a Partial Differential Equation from Its Solution?

Authors: Yuchen He, Hongkai Zhao, Yimin Zhong

Published in: Foundations of Computational Mathematics | Issue 5/2024

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Abstract

In this work, we study the problem of learning a partial differential equation (PDE) from its solution data. PDEs of various types are used to illustrate how much the solution data can reveal the PDE operator depending on the underlying operator and initial data. A data-driven and data-adaptive approach based on local regression and global consistency is proposed for stable PDE identification. Numerical experiments are provided to verify our analysis and demonstrate the performance of the proposed algorithms.

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Appendix
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Metadata
Title
How Much Can One Learn a Partial Differential Equation from Its Solution?
Authors
Yuchen He
Hongkai Zhao
Yimin Zhong
Publication date
17-10-2023
Publisher
Springer US
Published in
Foundations of Computational Mathematics / Issue 5/2024
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-023-09620-z

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