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

2025/08/29 by Jannick Kehls, Kehls, Jannick, Ellen Kuhl +7
Engineering · Materials Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Bladed Disk Vibration Dynamics #Computational Engineering #FOS: Computer and information sciences #Finance #Machine Learning (cs.LG) #Machine Learning in Materials Science #Model Reduction and Neural Networks #and Science (cs.CE)

paper · pdf · doi:10.48550/arxiv.2509.02237

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

AutoEncoder Architectures This repository accompanies the preprint“Autoencoder-based non-intrusive model order reduction in continuum mechanics”. It provides the AutoEncoder architectures, regression models, and reference simulation data used in the numerical experiments of the paper. The content is organized by case study, and each folder contains both reference FEM data(PureFEM) and the corresponding AutoEncoder-based surrogate models (AE_and_FFN). Folder Structure 01_Unit_Cell/ 01_PureFEM/ – Reference FEM simulations of the heterogeneous composite unit cell. 02_AE_and_FFN/ – Implementation and training of the AutoEncoder (unsupervised) combined with a Feed-Forward Network for latent space regression. 02_Plate_with_Elliptic_Hole/ 01_PureFEM/ – FEM simulations of a plate with a parametrized elliptic hole (geometry variation with parameters xi, eta). 02_AE_and_FFN/ – Complete AutoEncoder and regression setup. AEscripts/ – AutoEncoder architecture, training steps, and loss functions. FFNtoLSscripts/ – Feed-forward regression models mapping input parameters to the latent space. 01_results/ – Example runs including training histories (lossAE_history.txt, lossFFNtoLS_history.txt) and comparisons of reference and predicted meshes (mesh_reference.vtu, mesh_prediction.vtu). 03_Thermo_imperfection/ 01_PureFEM/ – Thermo-mechanical FEM simulations with geometric imperfections. 02_AE_and_FFN/ – Extended AutoEncoder setup for multi-field problems (temperature + displacement). Includes separate training histories for thermal and mechanical quantities (lossFFNtoLS_Temp_history.txt, lossFFNtoLS_disp_history.txt). 04_Thermo/ 01_PureFEM/ – Thermo-mechanical FEM simulations of a plate for varying parameters (xi, eta). Contains .vtu output files documenting transient solution states. Contents PureFEM folders – Reference finite element solutions (ground truth data). AE_and_FFN folders – AutoEncoder and regression architectures, including training scripts and configuration files. 01_results folders – Training and evaluation results: Loss histories for AutoEncoder and regression networks. Prediction vs. reference mesh files (.vtu, .inp). Timing information (training_evaluation_times.txt). Purpose This dataset provides the complete implementation and results required to reproduce the numerical experiments presented in the paper. It covers: Unit cell with heterogeneous microstructure – Displacement and force prediction. Plate with elliptic hole – Parametric geometry variation and anisotropic elasticity. Thermo-mechanical problem with imperfections – Multi-field AutoEncoder with coupled displacement and temperature. Thermo-mechanical plate – Transient analysis and surrogate reconstruction. The provided files are intended to help users quickly identify the relevant scripts and data for each study and to facilitate reproduction, extension, or adaptation of the presented AutoEncoder-based non-intrusive model order reduction framework.

Citations

• Multi-field decomposed hyper-reduced order modeling of damage-plasticity simulations
• A multi-field decomposed model order reduction approach for thermo-mechanically coupled gradient-extended damage simulations
• Component based model order reduction with mortar tied contact for nonlinear quasi-static mechanical problems
• A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
• Non-intrusive reduced-order modeling using convolutional autoencoders
• Non intrusive reduced order modeling of parametrized PDEs by kernel POD\n and neural networks
• A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
• Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• From Principal Subspaces to Principal Components with Linear Autoencoders
• Testing the Manifold Hypothesis
• Auto-association by multilayer perceptrons and singular value decomposition
• The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

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