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

• URL: http://arxiv.org/abs/2207.11842v1
• Date: Sun, 24 Jul 2022 23:11:07 GMT
• Title: $\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications
• Authors: G. I. Drakoulas, T. V. Gortsas, G. C. Bourantas, V. N. Burganos, D. Polyzos
• Abstract summary: High-fidelity numerical simulations constitute the backbone of engineering design. Reduced order models (ROMs) are employed to approximate the high-fidelity solutions. The present work proposes a new machine learning (ML) platform for the development of ROMs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\textit{FastSVD-ML-ROM}$, utilizes $\textit{(i)}$ a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, $\textit{(ii)}$ convolutional autoencoders for nonlinear dimensionality reduction, $\textit{(iii)}$ feed-forward neural networks to map the input parameters to the latent spaces, and $\textit{(iv)}$ long short-term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the $\textit{FastSVD-ML-ROM}$ 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.

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