$\text{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Abstract

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 an accurate 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, mentioned as $\text{FastSVD-ML-ROM}$, utilizes $\text{(i)}$ a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, $\text{(ii)}$ convolutional autoencoders for nonlinear dimensionality reduction, $\text{(iii)}$ feed-forward neural networks to map the input parameters to the latent spaces, and $\text{(iv)}$ long short-term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the $\text{FastSVD-ML-ROM}$ framework is demonstrated for a 2D linear convection-diffusion equation, the problem of fluid around a cylinder, and the 3D blood flow inside an arterial segment. The accuracy of the reconstructed results demonstrates the robustness and assesses the efficiency of the proposed approach.

35 pages, 22 figures

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