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

TL;DR

This paper compares hybrid physics-based models with pure deep learning models for predicting flow dynamics, showing hybrid models with modal decomposition outperform purely data-driven approaches in accuracy and robustness.

Contribution

It introduces a hybrid POD-DL model that effectively combines modal decomposition with deep learning, enhancing prediction accuracy and interpretability in complex fluid flow scenarios.

Findings

Hybrid POD-DL outperforms other models in both laminar and turbulent flows.

Modal decomposition reduces data dimensionality, improving model efficiency.

Hybrid models require less training data and fewer parameters.

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.