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

TL;DR

This paper introduces FastSVD-ML-ROM, a machine learning-based reduced-order modeling framework designed for real-time simulation of complex, nonlinear systems, significantly reducing computational costs while maintaining accuracy.

Contribution

The work presents a novel combination of SVD updates, autoencoders, neural networks, and LSTMs to develop efficient ROMs for large-scale nonlinear PDE problems.

Findings

Accurately models 2D convection-diffusion and fluid flow around a cylinder.

Successfully predicts 3D blood flow dynamics.

Demonstrates robustness and efficiency in complex simulations.

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.