Uniform convergence guarantees for the deep Ritz method for nonlinear problems.

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2022-01-01 Epub Date: 2022-07-15 DOI:10.1186/s13662-022-03722-8

Patrick Dondl, Johannes Müller, Marius Zeinhofer

引用次数: 7

Abstract

We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear variational problems such as the p-Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform across bounded families of right-hand sides.

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非线性问题的深里兹方法的一致收敛保证。

我们提供了抽象变分能量的深里兹方法的收敛性保证。我们的结果涵盖了非线性变分问题，如p-拉普拉斯方程或具有本质或自然边界条件的Modica-Mortola能量。在附加的假设下，我们证明了收敛性在右边有界族上是一致的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464

期刊介绍： ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.