[Paper Review] A Low-Dimensional Learning Model via Convolutional Neural Networks for Unsteady Wake-Body Interaction

T. P. Miyanawala, Rajeev K. Jaiman|arXiv (Cornell University)|Jul 20, 2018

Model Reduction and Neural Networks3 citations

TL;DR

This paper proposes a POD-CNN model that combines proper orthogonal decomposition (POD) with convolutional neural networks (CNNs) to learn low-dimensional dynamics of unsteady wake-body interactions. By training a CNN on POD coefficients from high-fidelity Navier-Stokes simulations, the model accurately predicts long-time flow fields, including in highly nonlinear near-wake regions, with high accuracy compared to full-order simulations.

ABSTRACT

This paper is concerned with the development of a physical model by learning low-dimensional approximation for laminar wake-body interaction systems. Of particular interest is to predict the long time series of unsteady flow dynamics using the learned low-dimensional model. We consider convolutional neural networks (CNN) for the learning dynamics of wake-body interaction, which assemble layers of linear convolutions with nonlinear activations to automatically extract the low-dimensional features. Using high-fidelity time series data from the stabilized finite element Navier-Stokes solver, we first project the dataset to a low-dimensional subspace using proper orthogonal decomposition (POD). The time-dependent coefficients of the POD subspace are mapped to the flow field via a CNN with nonlinear rectification, and the CNN is iteratively trained using the stochastic gradient descent method to predict the POD time coefficient when a new flow field is fed to it. The time-averaged flow field, the POD basis vectors and the trained CNN are used to predict the long time series of the flow fields and results are compared with the full-order (high-dimensional) simulation results. POD-CNN based predictions maintain a remarkable accuracy in the entire fluid domain including the highly nonlinear near wake region for the long time series. The proposed POD-CNN model based on data-driven approximation has a profound impact on the predictive analysis of unsteady wake flow and fluid-structure interaction.

Motivation & Objective

• To develop a data-driven low-dimensional model for predicting long-time series of unsteady wake-body interaction flows.
• To leverage convolutional neural networks (CNNs) for automatic feature extraction from high-fidelity flow data.
• To improve predictive accuracy in nonlinear regions such as the near wake, where traditional reduced-order models may fail.
• To enable efficient long-term simulation of fluid-structure interaction systems using a learned surrogate model.
• To validate the model’s accuracy against high-fidelity full-order simulations across the entire fluid domain.

Proposed method

• High-fidelity time series data from a stabilized finite element Navier-Stokes solver are used as the training dataset.
• Proper orthogonal decomposition (POD) is applied to project the flow fields onto a low-dimensional subspace, extracting temporal coefficients.
• A convolutional neural network (CNN) is trained to map input flow fields to their corresponding POD time coefficients using nonlinear rectification.
• Stochastic gradient descent is used to iteratively train the CNN for accurate coefficient prediction.
• The trained CNN, combined with the time-averaged flow field and POD basis vectors, reconstructs full flow fields over long time series.
• Model predictions are validated against full-order simulation results in both linear and nonlinear regions of the flow field.

Experimental results

Research questions

• RQ1 Can a CNN-based model accurately predict long-time series of unsteady wake-body interaction flows using low-dimensional representations?
• RQ2 How well does the POD-CNN model capture nonlinear dynamics in the near-wake region compared to full-order simulations?
• RQ3 To what extent can the learned model generalize across different flow configurations without retraining?
• RQ4 Does the integration of POD with CNNs improve predictive accuracy and computational efficiency in fluid-structure interaction problems?
• RQ5 What is the role of nonlinear activation in the CNN for capturing complex flow features in reduced-order modeling?

Key findings

• The POD-CNN model maintains high accuracy across the entire fluid domain, including the highly nonlinear near-wake region, over long time series.
• The model achieves accurate predictions of flow fields using only the time-averaged flow, POD basis vectors, and the trained CNN.
• The CNN effectively learns the nonlinear mapping between flow fields and their POD coefficients, enabling precise reconstruction of unsteady dynamics.
• The model demonstrates robustness in capturing complex, transient flow features that are challenging for linear reduced-order models.
• The predicted time series closely match the full-order simulation results, confirming the model's predictive capability.
• The integration of CNNs with POD enables efficient, accurate, and stable long-term simulation of unsteady wake flows.