从一个偏微分方程的解中可以学到多少？

IF 2.5 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2023-10-17 DOI:10.1007/s10208-023-09620-z

Yuchen He, Hongkai Zhao, Yimin Zhong

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引用次数: 0

摘要

在这项工作中，我们研究了从偏微分方程的解数据中学习偏微分方程（PDE）的问题。各种类型的偏微分方程用于说明解决方案数据可以在多大程度上揭示偏微分方程算子，这取决于底层算子和初始数据。提出了一种基于局部回归和全局一致性的数据驱动和数据自适应方法，用于稳定的PDE识别。数值实验验证了我们的分析，并证明了所提出算法的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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

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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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.