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

arXiv: https://arxiv.org/abs/2502.09346 · HTML: https://mlsanity.com/paper/2502.09346/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 113 of its 337 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 30 of 113)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Twins: Revisiting the Design of Spatial Attention in Vision Transformers](https://mlsanity.com/paper/2104.13840/) (2021)

## Built on by (most cited first, 12 of 12)

- [Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage](https://mlsanity.com/paper/2507.19861/) (2025)
- [Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamics](https://mlsanity.com/paper/2508.18565/) (2025)
- [Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model](https://mlsanity.com/paper/2509.01293/) (2025)
- [Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows](https://mlsanity.com/paper/2602.15592/) (2026)
- [Anchored-Branched Steady-state WInd Flow Transformer (AB-SWIFT): a metamodel for 3D atmospheric flow in urban environments](https://mlsanity.com/paper/2603.25635/) (2026)
- [Rooftop Wind Field Reconstruction Using Sparse Sensors: From Deterministic to Generative Learning Methods](https://mlsanity.com/paper/2603.13077/) (2026)
- [Physics Consistency and Latent Dynamics in Spatiotemporal Physics Field Generation](https://mlsanity.com/paper/2505.11578/) (2025)
- [Learning Mappings in Mesh-based Simulations](https://mlsanity.com/paper/2506.12652/) (2025)
- [Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators](https://mlsanity.com/paper/2509.22411/) (2025)
- [Spatiotemporal System Forecasting with Irregular Time Steps via Masked Autoencoder](https://mlsanity.com/paper/2603.25597/) (2026)
- [An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interaction](https://mlsanity.com/paper/2605.00937/) (2026)
- [Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses](https://mlsanity.com/paper/2607.19387/) (2026)

## Abstract (arXiv)

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.