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Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems

Jiasheng Shi, Fu Lin, Weixiong Rao

TL;DR

A novel two-level mesh graph network is proposed to interweave the developed Graph Block and Attention Block to better learn mechanic interactions even for long-rang spatial dependency.

Abstract

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.

Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems

TL;DR

A novel two-level mesh graph network is proposed to interweave the developed Graph Block and Attention Block to better learn mechanic interactions even for long-rang spatial dependency.

Abstract

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.
Paper Structure (29 sections, 11 equations, 6 figures, 2 tables)

This paper contains 29 sections, 11 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. CNN-based Models
  4. GNN-based Models
  5. Neural Operator-based Models
  6. Problem Definition
  7. Methodology
  8. Framework
  9. Encoder
  10. Processor
  11. Decoder
  12. Graph Block
  13. Attention Block
  14. Node Embedding Aggregation
  15. Laplacian Position Encoding
  16. ...and 14 more sections

Figures (6)

  • Figure 1: Bending Test of Steering Wheels applied with external force $F$ and fixed on the bottom plane $B$. (a) FEM-divided mesh structure; (b) Stress field simulation result.
  • Figure 2: Overall Framework
  • Figure 3: Attention Block (Ag: Aggregate, Di: Disseminate).
  • Figure 4: The Transformer Layer and Multi-head Attention
  • Figure 5: Prediction and Gradient Visualization
  • ...and 1 more figures

Theorems & Definitions (1)

  • Definition 1: Complex Mechanic System Simulation