Generalization capabilities and robustness of hybrid models grounded in physics compared to purely deep learning models

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.

24 pages, two column, 26 figures and 11 tables

References in corpus (23)

• Adam: A Method for Stochastic Optimization
• Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting
• Variational Inference: A Review for Statisticians
• Machine Learning for Fluid Mechanics
• Neural General Circulation Models for Weather and Climate
• Spectral proper orthogonal decomposition
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• Assessment of supervised machine learning methods for fluid flows
• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Machine-learning-based reduced order modeling for unsteady flows around bluff bodies of various shapes
• A new prediction method of unsteady wake flow by the hybrid deep neural network
• A deep learning enabler for non-intrusive reduced order modeling of fluid flows
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• A Deep Learning based Approach to Reduced Order Modeling for Turbulent Flow Control using LSTM Neural Networks
• Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network
• Data-driven modal decomposition methods as feature detection techniques for flow problems: a critical assessment
• Multiscale Proper Orthogonal Decomposition (mPOD) of TR-PIV data-- a Case Study on Stationary and Transient Cylinder Wake Flows
• Forecasting small scale dynamics of fluid turbulence using deep neural networks
• Time-series machine-learning error models for approximate solutions to parameterized dynamical systems
• Data-driven assessment of arch vortices in simplified urban flows
• Forecasting through deep learning and modal decomposition in two-phase concentric jets