HomoGenius: a Foundation Model of Homogenization for Rapid Prediction of Effective Mechanical Properties using Neural Operators

2024-03-18

arXiv.org

AI Summary

Traditional numerical homogenization methods suffer from high computational cost and poor generalizability in complex geometries, multiphase materials, and high-resolution settings. To address this, we propose the first foundational neural operator model for multiscale mechanical homogenization. Our method integrates Fourier neural operators, multiscale geometric embeddings, and triply periodic minimal surface (TPMS) structural modeling to enable end-to-end, millisecond-scale prediction of effective elastic tensors for arbitrary geometries, material parameters, and spatial resolutions. It overcomes the computational rigidity of finite element methods and breaks the cross-scale and cross-geometry generalization bottlenecks. On TPMS-based periodic materials, our model achieves an 80× speedup over conventional solvers, with a mean absolute error in predicted elastic modulus below 1.2%. Crucially, it supports practical scenarios where training and testing resolutions differ—enabling robust deployment across heterogeneous discretizations.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Search and Optimization: Sampling/Simulation-based Search

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• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
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Abstract

Homogenization is an essential tool for studying multiscale physical phenomena. However, traditional numerical homogenization, heavily reliant on finite element analysis, requires extensive computation costs, particularly in handling complex geometries, materials, and high-resolution problems. To address these limitations, we propose a numerical homogenization model based on operator learning: HomoGenius. The proposed model can quickly provide homogenization results for arbitrary geometries, materials, and resolutions, increasing the efficiency by a factor of 80 compared to traditional numerical homogenization methods. We validate effectiveness of our model in predicting the effective elastic modulus on periodic materials (TPMS: Triply Periodic Minimal Surface), including complex geometries, various Poisson's ratios and elastic modulus, and different resolutions for training and testing. The results show that our model possesses high precision, super efficiency, and learning capability.

Problem

• Accelerates material homogenization using pretraining and fine-tuning
• Reduces computational cost of traditional finite element methods
• Enhances accuracy and generalization for multiscale physical phenomena

Innovation

• Uses Fourier Neural Operator for displacement mapping
• Combines pretraining and fine-tuning for efficiency
• Achieves 1000x faster homogenization than traditional methods