# Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrations

arXiv: https://arxiv.org/abs/2406.14161 · HTML: https://mlsanity.com/paper/2406.14161/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 60 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [HG-DAgger: Interactive Imitation Learning with Human Experts](https://mlsanity.com/paper/1810.02890/) (2018)
- [Defining and Characterizing Reward Hacking](https://mlsanity.com/paper/2209.13085/) (2022)
- [Revisiting Fundamentals of Experience Replay](https://mlsanity.com/paper/2007.06700/) (2020)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [ThriftyDAgger: Budget-Aware Novelty and Risk Gating for Interactive Imitation Learning](https://mlsanity.com/paper/2109.08273/) (2021)
- [EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1807.08364/) (2018)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [Deep Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2209.12351/) (2022)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [Grounding Graph Network Simulators using Physical Sensor Observations](https://mlsanity.com/paper/2302.11864/) (2023)
- [Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics](https://mlsanity.com/paper/2102.12923/) (2021)
- [Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes](https://mlsanity.com/paper/2402.10681/) (2024)
- [E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation](https://mlsanity.com/paper/2207.11233/) (2022)
- [Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2211.00801/) (2022)
- [Scaling Face Interaction Graph Networks to Real World Scenes](https://mlsanity.com/paper/2401.11985/) (2024)

## Built on by (most cited first, 1 of 1)

- [Generating Sizing Fields for Mesh Generation via GCN-based Simplification of Adaptive Background Grids](https://mlsanity.com/paper/2510.08645/) (2025)

## Abstract (arXiv)

Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost and accuracy of the FEM scale with the resolution of the underlying computational mesh. To balance computational speed and accuracy meshes with adaptive resolution are used, allocating more resources to critical parts of the geometry. Currently, practitioners often resort to hand-crafted meshes, which require extensive expert knowledge and are thus costly to obtain. Our approach, Adaptive Meshing By Expert Reconstruction (AMBER), views mesh generation as an imitation learning problem. AMBER combines a graph neural network with an online data acquisition scheme to predict the projected sizing field of an expert mesh on a given intermediate mesh, creating a more accurate subsequent mesh. This iterative process ensures efficient and accurate imitation of expert mesh resolutions on arbitrary new geometries during inference. We experimentally validate AMBER on heuristic 2D meshes and 3D meshes provided by a human expert, closely matching the provided demonstrations and outperforming a single-step CNN baseline.