# Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics

arXiv: https://arxiv.org/abs/2102.12923 · HTML: https://mlsanity.com/paper/2102.12923/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)

## Built on by (most cited first, 14 of 14)

- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [M2N: Mesh Movement Networks for PDE Solvers](https://mlsanity.com/paper/2204.11188/) (2022)
- [Predicting Mechanically Driven Full-Field Quantities of Interest with Deep Learning-Based Metamodels](https://mlsanity.com/paper/2108.03995/) (2021)
- [Learning robust marking policies for adaptive mesh refinement](https://mlsanity.com/paper/2207.06339/) (2022)
- [E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation](https://mlsanity.com/paper/2207.11233/) (2022)
- [Towards Universal Mesh Movement Networks](https://mlsanity.com/paper/2407.00382/) (2024)
- [AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction](https://mlsanity.com/paper/2505.23663/) (2025)
- [3DMeshNet: A Three-Dimensional Differential Neural Network for Structured Mesh Generation](https://mlsanity.com/paper/2407.01560/) (2024)
- [MeshDQN: A Deep Reinforcement Learning Framework for Improving Meshes in Computational Fluid Dynamics](https://mlsanity.com/paper/2212.01428/) (2022)
- [Conformal Predictions Enhanced Expert-guided Meshing with Graph Neural Networks](https://mlsanity.com/paper/2308.07358/) (2023)
- [Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrations](https://mlsanity.com/paper/2406.14161/) (2024)
- [Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks](https://mlsanity.com/paper/2310.06717/) (2023)
- [Machine Learning Optimized Approach for Parameter Selection in MESHFREE Simulations](https://mlsanity.com/paper/2403.13672/) (2024)

## Abstract (arXiv)

Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve physical effects in an appropriate manner. Since all CFD algorithms scale at least linearly with the size of the underlying mesh discretization, finding an optimal mesh is key for computational efficiency. One methodology used to find optimal meshes is goal-oriented adaptive mesh refinement. However, this is typically computationally demanding and only available in a limited number of tools. Within this contribution, we adopt a machine learning approach to identify optimal mesh densities. We generate optimized meshes using classical methodologies and propose to train a convolutional network predicting optimal mesh densities given arbitrary geometries. The proposed concept is validated along 2d wind tunnel simulations with more than 60,000 simulations. Using a training set of 20,000 simulations we achieve accuracies of more than 98.7%. Corresponding predictions of optimal meshes can be used as input for any mesh generation and CFD tool. Thus without complex computations, any CFD engineer can start his predictions from a high quality mesh.