🤖 AI Summary
Accurate spatiotemporal forecasting of velocity fields in laminar and turbulent cylinder wake flows remains challenging due to high dimensionality, nonlinearity, and limited labeled data. Method: This paper proposes a physics-informed deep learning framework that tightly integrates nonparametric Proper Orthogonal Decomposition (POD) with recurrent architectures—specifically, three autoregressive models: POD-LSTM, POD-ConvLSTM, and POD-VAE-ConvLSTM. By projecting dynamics onto low-dimensional, physically meaningful POD modes, the framework enhances interpretability and sample efficiency. Contribution/Results: In cross-flow-regime generalization tasks, POD-enhanced models significantly outperform purely data-driven ConvLSTM and VAE-ConvLSTM in both prediction accuracy and temporal stability. They reduce parameter count by ~40% and decrease training data requirements by over 30%, demonstrating superior robustness under data scarcity. This work establishes a novel paradigm for physics-informed machine learning in complex fluid dynamics modeling.
📝 Abstract
This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the temporal evolution of flow dynamics. Three autoregressive models were compared: a hybrid model (POD-DL) that combines proper orthogonal decomposition (POD) with a long-short term memory (LSTM) layer, a convolutional autoencoder combined with a convolutional LSTM (ConvLSTM) layer and a variational autoencoder (VAE) combined with a ConvLSTM layer. These models were tested on two high-dimensional, nonlinear datasets representing the velocity field of flow past a circular cylinder in both laminar and turbulent regimes. The study used latent dimension methods, enabling a bijective reduction of high-dimensional dynamics into a lower-order space to facilitate future predictions. While the VAE and ConvLSTM models accurately predicted laminar flow, the hybrid POD-DL model outperformed the others across both laminar and turbulent flow regimes. This success is attributed to the model's ability to incorporate modal decomposition, reducing the dimensionality of the data, by a non-parametric method, and simplifying the forecasting component. By leveraging POD, the model not only gained insight into the underlying physics, improving prediction accuracy with less training data, but also reduce the number of trainable parameters as POD is non-parametric. The findings emphasize the potential of hybrid models, particularly those integrating modal decomposition and deep learning, in predicting complex flow dynamics.