Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanics

Andrieux, Stéphane

doi:10.5802/crmeca.164

Comptes Rendus. Mécanique

2023

DOI: 10.5802/crmeca.164

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Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanics

Stéphane Andrieux¹

Abstract: Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanicsMesures de dissimilarité par divergences de Bregman pour le calcul et l'apprentissage en thermomécanique

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2024

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A review of graph neural network applications in mechanics-related domains

Zhao,

Li,

Zhou

et al. 2024

Artif Intell Rev

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Mechanics-related tasks often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these challenges by adeptly learning from graph data with irregular underlying structures. Consequently, recent years have witnessed a surge in complex mechanics-related applications inspired by the advancements of GNNs. Despite this process, there is a notable absence of a systematic review addressing the recent advancement of GNNs in solving mechanics-related tasks. To bridge this gap, this review article aims to provide an in-depth overview of the GNN applications in mechanics-related domains while identifying key challenges and outlining potential future research directions. In this review article, we begin by introducing the fundamental algorithms of GNNs that are widely employed in mechanics-related applications. We provide a concise explanation of their underlying principles to establish a solid understanding that will serve as a basis for exploring the applications of GNNs in mechanics-related domains. The scope of this paper is intended to cover the categorisation of literature into solid mechanics, fluid mechanics, and interdisciplinary mechanics-related domains, providing a comprehensive summary of graph representation methodologies, GNN architectures, and further discussions in their respective subdomains. Additionally, open data and source codes relevant to these applications are summarised for the convenience of future researchers. This article promotes an interdisciplinary integration of GNNs and mechanics and provides a guide for researchers interested in applying GNNs to solve complex mechanics-related tasks.

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A review of graph neural network applications in mechanics-related domains

Zhao,

Li,

Zhou

et al. 2024

Artif Intell Rev

View full text Add to dashboard Cite

show abstract

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Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanics

Abstract: Bregman divergences for physically informed discrepancy measures for learning and computation in thermomechanicsMesures de dissimilarité par divergences de Bregman pour le calcul et l'apprentissage en thermomécanique

Cited by 1 publication

References 38 publications

A review of graph neural network applications in mechanics-related domains

A review of graph neural network applications in mechanics-related domains

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