Solving inverse problems using data-driven models

IF 16.3 1区数学 Q1 MATHEMATICS

Acta Numerica Pub Date : 2019-05-01 DOI:10.1017/S0962492919000059

S. Arridge, P. Maass, O. Öktem, C. Schönlieb

引用次数: 415

Abstract

Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical–analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

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使用数据驱动模型求解逆问题

最近对反问题的研究试图建立一个数学上连贯的基础，将数据驱动的模型，特别是基于深度学习的模型，与物理分析模型中包含的特定领域知识相结合。重点是解决不适定逆问题，这些问题是自然科学、医学和生命科学以及工程和工业应用中许多具有挑战性的应用的核心。本文旨在介绍数据驱动反问题中的一些主要贡献。

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

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.