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

TL;DR

This review explores advanced machine learning methods like graph neural networks and physics-informed neural networks for modeling complex unstructured grid data in computational physics, highlighting challenges, solutions, and future directions.

Contribution

It provides a comprehensive overview of ML techniques tailored for unstructured grid data, including benchmarking datasets and emerging research directions in the field.

Findings

ML methods effectively handle complex geometries in physics simulations.

Graph neural networks and transformers improve modeling of unstructured data.

Open datasets facilitate benchmarking and future research.

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.