arXiv:2410.10523stat.MLcs.LG2024-10被引 8

用机器学习方法解决反问题与数据同化难题

Machine Learning for Inverse Problems and Data Assimilation

  • 从反问题视角系统介绍机器学习核心思想
  • 提供数学严谨的机器学习理论基础
  • 适合跨领域研究者快速入门机器学习

本书旨在展示机器学习思想在反问题与数据同化领域的应用潜力。其视角面向来自反问题和/或数据同化领域的研究人员,希望他们能通过数学化的表述理解机器学习在自身领域中的应用。作为副产品,书中还对机器学习及计算数学相关领域的若干基础性主题进行了简洁而严谨的数学处理。

原文摘要 · Abstract (English)

The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product, we include a succinct mathematical treatment of various fundamental underpinning topics in machine learning, and adjacent areas of (computational) mathematics.

反问题数据同化机器学习数学建模

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