Title: Machine learning for modelling unstructured grid data in computational physics: a review Show Chinese title

Title: 机器学习在计算物理中对非结构化网格数据建模的综述

Abstract: Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field. Show Chinese abstract

Abstract: 非结构化网格数据在计算物理中的复杂几何和动力学建模中是必不可少的。然而，它们固有的不规则性给传统机器学习（ML）技术带来了重大挑战。本文全面回顾了旨在处理高维动力系统中非结构化网格数据的先进机器学习方法。讨论的关键方法包括图神经网络、具有空间注意力机制的变压器模型、集成插值的机器学习方法以及无网格技术，如物理信息神经网络。这些方法已在多个领域证明了其有效性，包括流体动力学和环境模拟。本综述旨在作为计算科学家的指南，帮助他们在各自领域应用机器学习方法处理非结构化网格数据，同时也为希望解决计算物理中挑战的机器学习研究人员提供参考。本文特别关注机器学习方法如何克服传统数值技术的固有局限性，以及计算物理的见解如何指导机器学习的发展。为了支持基准测试，本文还总结了计算物理中非结构化网格数据的开源数据集。最后，讨论了生成模型与非结构化数据、用于网格生成的强化学习以及混合物理-数据驱动范式等新兴方向，以激发该不断发展的领域未来的进步。