A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials

2025-06-20

AI Summary

To address the high computational cost arising from microscale repetitive calculations in simulating multiscale rate-dependent materials (e.g., viscoelastic solids), this work proposes a neural-operator-driven hybrid micromechanical constitutive model. The method innovatively embeds a neural operator into the evolution equations of microscale internal variables, synergistically integrating physical constraints with data-driven learning to explicitly capture microstructural effects. By coupling computational homogenization with physics-informed deep learning, the model preserves mechanistic interpretability while enabling generalization across material types and mesh resolutions. Experiments demonstrate homogenized stress prediction errors below 6% and approximately 100× speedup over conventional multiscale approaches. The core contribution is a physics-guided neural-operator framework for micromechanical modeling—achieving a balanced trade-off among accuracy, computational efficiency, and generalizability.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential. Numerical methods, such as the $ ext{FE}^2$ approach, account for micro-macro interactions to predict the global response in a concurrent manner. However, these methods are computationally intensive due to the repeated evaluations of the microscale. This challenge has led to the integration of deep learning techniques into computational homogenization frameworks to accelerate multiscale simulations. In this work, we employ neural operators to predict the microscale physics, resulting in a hybrid model that combines data-driven and physics-based approaches. This allows for physics-guided learning and provides flexibility for different materials and spatial discretizations. We apply this method to time-dependent solid mechanics problems involving viscoelastic material behavior, where the state is represented by internal variables only at the microscale. The constitutive relations of the microscale are incorporated into the model architecture and the internal variables are computed based on established physical principles. The results for homogenized stresses ($<6%$ error) show that the approach is computationally efficient ($sim 100 imes$ faster).

Problem

• Develop hybrid model for multiscale simulation of rate-dependent materials
• Accelerate microscale physics prediction using neural operators
• Improve computational efficiency in viscoelastic solid mechanics problems

Innovation

• Neural operators predict microscale physics efficiently
• Hybrid model combines data-driven and physics-based methods
• Computationally efficient with less than 6% error