Machine learning for modelling unstructured grid data in computational physics: a review
Sibo Cheng, Marc Bocquet, Weiping Ding, Tobias Sebastian Finn, Rui Fu, Jinlong Fu, Yike Guo, Eleda Johnson, Siyi Li, Che Liu, Eric Newton Moro, Jie Pan, Matthew Piggott, Cesar Quilodran, Prakhar Sharma, Kun Wang, Dunhui Xiao, Xiao Xue, Yong Zeng, Mingrui Zhang, Hao Zhou, Kewei Zhu, Rossella Arcucci
TL;DR
The paper comprehensively surveys machine learning methods for unstructured grid data in computational physics, addressing irregular geometries and high-dimensional dynamics. It categorizes approaches into graph neural networks, transformer-based models with spatial attention, mesh-interpolation preprocessing, PINNs, reinforcement learning for mesh generation, generative AI, neural operators, and reduced-order modelling, highlighting their applicability and limitations. It also compiles open-access datasets and benchmarks, providing qualitative guidance for practitioners while comparing the relative strengths and weaknesses of each method. The discussion underscores challenges in computational cost, generalization across unseen meshes, and the need for standardized benchmarks, and points to future directions in neural operators, diffusion models, and geometry-aware physics-informed learning to advance the field.
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.