Hybrid machine learning models based on physical patterns to accelerate CFD simulations: a short guide on autoregressive models

2025-04-09

AI Summary

To address the challenge of accurately representing multidimensional structures and nonlinear/chaotic fluid dynamics in reduced-order modeling (ROM), this paper proposes a physics-informed hybrid HOSVD-LSTM model. We introduce high-order singular value decomposition (HOSVD) into fluid ROM for the first time—replacing conventional SVD to better preserve the intrinsic tensor structure of multidimensional flow data. A lightweight LSTM architecture is designed to capture temporal evolution in both periodic and chaotic flows, and the model integrates 2D/3D numerical simulations and experimental data for multiscale modeling. Experimental results demonstrate that the proposed method significantly outperforms the SVD-LSTM baseline across multiple error metrics in laminar and turbulent cylinder wake flows. Moreover, it exhibits strong robustness under noise perturbations, achieving substantial accuracy gains with only a marginal increase in computational cost.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Intelligent Robots: State Estimation
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study presents an innovative integration of High-Order Singular Value Decomposition (HOSVD) with Long Short-Term Memory (LSTM) architectures to address the complexities of reduced-order modeling (ROM) in fluid dynamics. HOSVD improves the dimensionality reduction process by preserving multidimensional structures, surpassing the limitations of Singular Value Decomposition (SVD). The methodology is tested across numerical and experimental data sets, including two- and three-dimensional (2D and 3D) cylinder wake flows, spanning both laminar and turbulent regimes. The emphasis is also on exploring how the depth and complexity of LSTM architectures contribute to improving predictive performance. Simpler architectures with a single dense layer effectively capture the periodic dynamics, demonstrating the network's ability to model non-linearities and chaotic dynamics. The addition of extra layers provides higher accuracy at minimal computational cost. These additional layers enable the network to expand its representational capacity, improving the prediction accuracy and reliability. The results demonstrate that HOSVD outperforms SVD in all tested scenarios, as evidenced by using different error metrics. Efficient mode truncation by HOSVD-based models enables the capture of complex temporal patterns, offering reliable predictions even in challenging, noise-influenced data sets. The findings underscore the adaptability and robustness of HOSVD-LSTM architectures, offering a scalable framework for modeling fluid dynamics.

Problem

• Integrating HOSVD with LSTM to enhance reduced-order fluid dynamics modeling
• Testing HOSVD-LSTM on 2D/3D cylinder wakes in laminar and turbulent flows
• Evaluating LSTM depth impact on predictive accuracy in fluid flow simulations

Innovation

• HOSVD enhances dimensionality reduction in fluid dynamics
• LSTM architectures improve predictive performance efficiently
• HOSVD-LSTM models handle noise and complex dynamics