Autoencoder-based non-intrusive model order reduction in continuum mechanics
This work addresses the need for efficient and extensible surrogate models in continuum mechanics, with potential applications in uncertainty quantification, optimization, and digital twins, though it is incremental as it builds on existing Autoencoder and regression methods.
The authors tackled the problem of building efficient surrogate models for continuum mechanics by proposing a non-intrusive, Autoencoder-based framework that integrates unsupervised compression, supervised regression, and end-to-end reconstruction, achieving accurate reconstructions of high-fidelity solutions across nonlinear benchmark problems.
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.