FastSVD-ML-ROM: A reduced-order modeling framework based on machine learning for real-time applications

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing insight into the performance of complex systems. However, large-scale, dynamic, non-linear models require significant computational resources and are prohibitive for real-time digital twin applications. To this end, reduced order models (ROMs) are employed, to approximate the high-fidelity solutions while accurately capturing the dominant aspects of the physical behavior. The present work proposes a new machine learning (ML) platform for the development of ROMs to handle large-scale numerical problems dealing with transient nonlinear partial differential equations. Our framework, named as FastSVD-ML-ROM, utilizes (i) a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, (ii) convolutional autoencoders for nonlinear dimensionality reduction, (iii) feed-forward neural networks to map the input parameters to the latent spaces, and (iv) long-short term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the FastSVD-ML-ROM framework is demonstrated for a 2D linear convection-diffusion benchmark, the problem of fluid flow around a cylinder, the 2D lid-driven cavity problem at high Reynolds numbers, and the 3D blood flow inside an arterial segment. The accuracy of the reconstructed results indicates the robustness of the proposed approach.& COPY; 2023 Elsevier B.V. All rights reserved.