Data-driven Modeling of Parameterized Nonlinear Fluid Dynamical Systems with a Dynamics-embedded Conditional Generative Adversarial Network

TL;DR

This paper introduces a dynamics-embedded conditional GAN model that predicts parameterized nonlinear fluid flow fields by capturing temporal dynamics and parameter dependence, validated through numerical studies on flow over a cylinder and cavity problems.

Contribution

The paper develops a novel dynamics-generator conditional GAN (Dyn-cGAN) that integrates a dynamics block for improved prediction of parameterized nonlinear fluid systems, advancing surrogate modeling techniques.

Findings

Dyn-cGAN accurately predicts flow fields across different Reynolds numbers.

Optimal number of training time steps improves prediction accuracy.

Reynolds number significantly influences model prediction performance.

Abstract

This work presents a data-driven solution to accurately predict parameterized nonlinear fluid dynamical systems using a dynamics-generator conditional GAN (Dyn-cGAN) as a surrogate model. The Dyn-cGAN includes a dynamics block within a modified conditional GAN, enabling the simultaneous identification of temporal dynamics and their dependence on system parameters. The learned Dyn-cGAN model takes into account the system parameters to predict the flow fields of the system accurately. We evaluate the effectiveness and limitations of the developed Dyn-cGAN through numerical studies of various parameterized nonlinear fluid dynamical systems, including flow over a cylinder and a 2-D cavity problem, with different Reynolds numbers. Furthermore, we examine how Reynolds number affects the accuracy of the predictions for both case studies. Additionally, we investigate the impact of the number of time steps involved in the process of dynamics block training on the accuracy of predictions, and we find that an optimal value exists based on errors and mutual information relative to the ground truth.