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

• URL: http://arxiv.org/abs/2509.02237v1
• Date: Tue, 02 Sep 2025 12:05:00 GMT
• Title: Autoencoder-based non-intrusive model order reduction in continuum mechanics
• Authors: Jannick Kehls, Ellen Kuhl, Tim Brepols, Kevin Linka, Hagen Holthusen,
• Abstract summary: We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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