用于本构建模的神经网络——从通用函数逼近器到高级模型及物理的融合
Neural Networks for Constitutive Modeling -- From Universal Function Approximators to Advanced Models and the Integration of Physics
AI总结：
本综述从方法论角度概述基于神经网络的本构模型，总结比较了通用函数逼近器、高级模型及集成物理知识的神经网络方法，并指出该领域未来需解决的挑战。
摘要：
分析和建模材料的本构行为是材料科学的核心领域，也是开展以材料行为为中心的数值模拟的前提。本构模型自19世纪初开始发展，至今仍在不断演进。除了基于物理动机和现象学的模型外，过去几十年中，基于机器学习的本构模型的发展丰富了本构建模领域，尤其是通过使用神经网络。后者是本综述的重点，旨在从方法论角度概述基于神经网络的本构模型。本综述总结并比较了众多概念上不同的基于神经网络的本构建模方法，包括用作通用函数逼近器的神经网络、高级神经网络模型以及集成了物理知识的神经网络方法。这些方法的出现与计算机科学领域的进步密切相关，这进一步为本综述增添了时间维度的视角。我们以本构关系学习领域近期需要解决的重要挑战来总结本综述论文。
英文摘要：
Analyzing and modeling the constitutive behavior of materials is a core area in materials sciences and a prerequisite for conducting numerical simulations in which the material behavior plays a central role. Constitutive models have been developed since the beginning of the 19th century and are still under constant development. Besides physics-motivated and phenomenological models, during the last decades, the field of constitutive modeling was enriched by the development of machine learning-based constitutive models, especially by using neural networks. The latter is the focus of the present review, which aims to give an overview of neural networks-based constitutive models from a methodical perspective. The review summarizes and compares numerous conceptually different neural networks-based approaches for constitutive modeling including neural networks used as universal function approximators, advanced neural network models and neural network approaches with integrated physical knowledge. The upcoming of these methods is in-turn closely related to advances in the area of computer sciences, what further adds a chronological aspect to this review. We conclude this review paper with important challenges in the field of learning constitutive relations that need to be tackled in the near future.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
