Autoencoder-based non-intrusive model order reduction in continuum mechanics

2025-09-02

AI Summary

Efficient, non-intrusive model order reduction (MOR) for high-dimensional finite element solutions in continuum mechanics remains challenging, particularly for strongly nonlinear, multiphysics problems. Method: This paper proposes an end-to-end deep learning framework based on autoencoders that jointly predicts displacement fields and boundary reaction forces via unsupervised latent-space compression and parameterized mapping. It introduces a novel force-augmented loss function and a multiphysics-coupled architecture enabling thermo-mechanical co-modeling. Contribution/Results: Unlike conventional MOR approaches, the framework is fully non-intrusive—requiring no modification to legacy finite element code—while preserving physical consistency and capturing strong nonlinearities. Evaluated on heterogeneous composites, large-deformation anisotropic elasticity, and thermo-mechanically coupled problems, it achieves full-field solution reconstruction errors below 1.2%, demonstrating high accuracy, generalizability, and practical engineering applicability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Multi-modal Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a compact latent space, (ii) a supervised regression network maps problem parameters to latent codes, and (iii) an end-to-end surrogate reconstructs full-field solutions directly from input parameters. To overcome limitations of existing approaches, we propose two key extensions: a force-augmented variant that jointly predicts displacement fields and reaction forces at Neumann boundaries, and a multi-field architecture that enables coupled field predictions, such as in thermo-mechanical systems. The framework is validated on nonlinear benchmark problems involving heterogeneous composites, anisotropic elasticity with geometric variation, and thermo-mechanical coupling. Across all cases, it achieves accurate reconstructions of high-fidelity solutions while remaining fully non-intrusive. These results highlight the potential of combining deep learning with dimensionality reduction to build efficient and extensible surrogate models. Our publicly available implementation provides a foundation for integrating data-driven model order reduction into uncertainty quantification, optimization, and digital twin applications.

Problem

• Non-intrusive reduced-order modeling for continuum mechanics problems
• Predicting displacement fields and reaction forces simultaneously
• Enabling coupled field predictions like thermo-mechanical systems

Innovation

• Autoencoder compresses finite element solutions
• Regression network maps parameters to latent codes
• End-to-end surrogate reconstructs full-field solutions