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

TL;DR

The paper tackles data-driven surrogate modeling for parameterized nonlinear fluid dynamics by introducing a dynamics-embedded conditional GAN (Dyn-cGAN) that jointly learns temporal evolution and parameter dependence. The Dyn-cGAN’s dynamics block recursively predicts flow-field sequences conditioned on system parameters, yielding accurate spatial and temporal predictions for flow over a cylinder and a 2-D cavity across Reynolds numbers. A key finding is the existence of an optimal training horizon (~25 time steps) that maximizes mutual information with the ground truth while minimizing prediction error, with accuracy decreasing as flow complexity grows at higher Reynolds numbers. The work demonstrates a practical, parameter-aware surrogate capable of accelerating CFD-like predictions, while highlighting limitations in long-term robustness and suggesting adaptive horizons and validation on turbulent/three-dimensional data as future directions.

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.

Figures (12)

• Figure 1: two-dimensional cavity problem: flow has a rich fluid flow physics including multiple rotating recirculating regions specially on the corners of the cavity which is dependent on the Reynolds number.
• Figure 2: Dyn-Gen Model architecture: using few but important information of system, this model generates multi-step predicted flow fields with embedded dynamic block
• Figure 3: Discriminator Model: using fake/predicted flow fields with their corresponding physical parameters ($Re_D$), the discriminator distinguish the real data with the presented architecture
• Figure 4: Steady-state stream-wise velocity prediction for three time steps and corresponding $L2$ Error in spatial domain and time domain prediction for three randomly selected points in the flow
• Figure 5: Steady-state transverse velocity prediction for three time steps and corresponding $L2$ Error in spatial domain and time domain prediction for three randomly selected points in the flow