Machine learning for modelling unstructured grid data in computational physics: a review

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.

@article{cheng2025_2502.09346,
  title={ Machine learning for modelling unstructured grid data in computational physics: a review },
  author={ Sibo Cheng and Marc Bocquet and Weiping Ding and Tobias Sebastian Finn and Rui Fu and Jinlong Fu and Yike Guo and Eleda Johnson and Siyi Li and Che Liu and Eric Newton Moro and Jie Pan and Matthew Piggott and Cesar Quilodran and Prakhar Sharma and Kun Wang and Dunhui Xiao and Xiao Xue and Yong Zeng and Mingrui Zhang and Hao Zhou and Kewei Zhu and Rossella Arcucci },
  journal={arXiv preprint arXiv:2502.09346},
  year={ 2025 }
}