弱者比你想象的更强大

arXiv - STAT - Machine Learning Pub Date : 2024-09-10 DOI:arxiv-2409.06751

Daniel A. Messenger, April Tran, Vanja Dukic, David M. Bortz

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引用次数: 0

摘要

在现代计算数学和应用数学中，弱形式是一种无处不在、研究透彻、应用广泛的数学工具。在这项研究中，我们对弱形式能发挥关键作用的几个领域的历史和最新发展进行了调查。我们特别强调了方程学习、参数估计和粗粒化的弱形式版本的最新进展，这些进展提供了令人惊讶的噪声鲁棒性、准确性和计算效率。我们注意到，本手稿是 2024 年 10 月 SIAMNews 同名文章的配套文章。在此，我们提供了更详细的数学发展解释以及更完整的参考文献列表。最后，我们要说明的是，重现本手稿中结果的软件也可在我们小组的 GitHub 网站https://github.com/MathBioCU。

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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The Weak Form Is Stronger Than You Think

The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .

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arXiv - STAT - Machine Learning

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