# Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems

arXiv: https://arxiv.org/abs/2409.00160 · HTML: https://mlsanity.com/paper/2409.00160/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks](https://mlsanity.com/paper/2203.08852/) (2022)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Probabilistic Deep Learning for Real-Time Large Deformation Simulations](https://mlsanity.com/paper/2111.01867/) (2021)

## Abstract (arXiv)

Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of computational time and acceptable accuracy, the recent CNN or GNN-based simulation models still struggle to effectively represent complex mechanic simulation caused by the long-range spatial dependency of distance mesh nodes and independently learning local and global representation. In this paper, we propose a novel two-level mesh graph network. The key of the network is to interweave the developed Graph Block and Attention Block to better learn mechanic interactions even for long-rang spatial dependency. Evaluation on three synthetic and one real datasets demonstrates the superiority of our work. For example, on the Beam dataset, our work leads to 54.3% lower prediction errors and 9.87% fewer learnable network parameters.