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Mathematics > Numerical Analysis

arXiv:2204.04602 (math)
[Submitted on 10 Apr 2022 (v1), last revised 9 Nov 2022 (this version, v2)]

Title:How much can one learn a partial differential equation from its solution?

Authors:Yuchen He, Hongkai Zhao, Yimin Zhong
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Abstract:In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples 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.
Comments: 44 pages
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
MSC classes: 35K15, 47A10, 47F10, 62J05, 65J10, 35R30
Cite as: arXiv:2204.04602 [math.NA]
  (or arXiv:2204.04602v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2204.04602

Submission history

From: Yimin Zhong [view email]
[v1] Sun, 10 Apr 2022 04:58:32 UTC (19,972 KB)
[v2] Wed, 9 Nov 2022 06:03:41 UTC (19,953 KB)
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