Autoencoder-based non-intrusive model order reduction for anisotropic and multi-physics problems

Computational Mechanics

Abstract

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.

Authors 5

1. Jannick Kehls corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, 52074, Aachen, Germany

2. Ellen Kuhl

   Stanford University

   Affiliation as printed

   Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA

3. Tim Brepols Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, 52074, Aachen, Germany

4. Kevin Linka Aachen Computational Mechanics in Medicine Institute of Applied Medical Engineering

   RWTH Aachen University

   Affiliation as printed

   Computational Mechanics in Medicine, Institute of Applied Medical Engineering, RWTH Aachen University, 52074, Aachen, Germany

5. Hagen Holthusen

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   Institute of Applied Mechanics, University of Erlangen-Nuremberg, 91058, Erlangen, Germany