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Foundations of Computational Mathematics
Erschienen in:

17.10.2023

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

verfasst von: Yuchen He, Hongkai Zhao, Yimin Zhong

Erschienen in: Foundations of Computational Mathematics | Ausgabe 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.
Vorheriger Artikel Implicitisation and Parameterisation in Polynomial Functors
Nächster Artikel Error Analysis for 2D Stochastic Navier–Stokes Equations in Bounded Domains with Dirichlet Data

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Metadaten
Titel
How Much Can One Learn a Partial Differential Equation from Its Solution?
verfasst von
Yuchen He
Hongkai Zhao
Yimin Zhong
Publikationsdatum
17.10.2023
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 5/2024
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-023-09620-z

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