Autoencoder-based non-intrusive model order reduction in continuum mechanics
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918134290579456 |
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| author | Kehls, Jannick Kuhl, Ellen Brepols, Tim Linka, Kevin Holthusen, Hagen |
| author_facet | Kehls, Jannick Kuhl, Ellen Brepols, Tim Linka, Kevin Holthusen, Hagen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Autoencoder-based non-intrusive model order reduction in continuum mechanics Kehls, Jannick Kuhl, Ellen Brepols, Tim Linka, Kevin Holthusen, Hagen Computational Engineering, Finance, and Science Artificial Intelligence Machine Learning 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. |
| title | Autoencoder-based non-intrusive model order reduction in continuum mechanics |
| topic | Computational Engineering, Finance, and Science Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2509.02237 |