Convolutional causal learning for aerodynamic flows

TL;DR

The paper addresses the challenge of identifying causal links between vortical structures and aerodynamic lift in unsteady flows from snapshot data. It introduces information-theoretic convolutional learning that decomposes the flow field as $\bm q(\bm x,t) = \bm q_I(\bm x,t) + \bm q_R(\bm x,t)$ with the future target $\lambda = C_L(t+\Delta t)$, enforcing $H(\lambda|\bm q_I) = 0$ and $I(\bm q_R;\bm q_I) = 0$ to extract causally informative modes; the mode extractor $\mathcal{F}$ uses a convolutional autoencoder and a CNN, trained with $L = ||\bm q - \bm q_I||_2 + \beta ||I(\bm q_R;\bm q_I)||_2$ under $H(C_L|\bm q_I) = 0$. The method is demonstrated on three cases—extreme vortex gust-airfoil interaction at $Re = 100$, experimental transverse gust encounter at $Re = 20{,}000$, and a turbulent wake at $Re = 20{,}000$—showing time-varying informative modes that predict lift and revealing finite-time causality, while yielding interpretable low-dimensional latent representations. These results establish a data-driven framework for causal modeling and control of unsteady aerodynamics with spatially coherent modal structures, potentially extending to broader unsteady flow problems.

Abstract

This study considers capturing aerodynamic causality from snapshot data with a time-varying mode decomposition technique referred to as information-theoretic machine learning. The current approach extracts time-dependent informative vortical structures, contributing to the future evolution of the aerodynamic coefficients. The present decomposition is employed with a convolutional neural network, enabling the identification of the spatial continuous mode. In addition, a low-order representation, characterizing the informative vortical structures and their corresponding aerodynamic coefficients, can also be identified by considering autoencoder-based data compression. The present technique is applied to a range of aerodynamic examples, including extreme vortex-gust airfoil interactions, experimentally measured transverse jet-wing interaction, and a turbulent separated wake. For the cases of gust-wing interaction, the time-varying gust effect on the lift response is extracted in an interpretable manner. With the example of a turbulent wake, the relationship between large-scale vortical motion and lift force is identified without any spatial length-scale information. The proposed approach could serve as a foundation for data-driven causal modeling and control for a range of unsteady flows.

Figures (6)

• Figure 1: An example of the given state $\bm q$ and the informative component $\bm q _I$ decomposed by a data-driven technique.
• Figure 2: Informative mode extractor $\mathcal{F}$ based on ($a$) convolutional autoencoder and ($b$) convolutional neural network.
• Figure 3: Informative mode decomposition of extreme vortex-airfoil interaction. $(a)$ Vorticity field (Input) and extracted modes (IMD). $(b)$ The time trace of lift coefficient, where convective time is set to be zero when the gust center reaches the leading edge (gray line: undisturbed case). $(c)$ The zoomed-in view of extracted mode at $t = -0.299$ with $\Delta t=0.255$. Latent-variable evolution with ($d$) $\Delta t = 0.0085$ and $(e)$$\Delta t = 0.255$.
• Figure 4: Informative mode decomposition for experimental transverse gust encounter at $Re = 20, 000$. ($a$) Vorticity snapshots, reconstructed flow field via convolutional autoencoder, and extracted fields. ($b$) Time series of lift coefficient. Latent space identified by the models ($c$) without and ($d$) with additional geometric constraints.
• Figure 5: Informative modal structure of spanwise-averaged separated flow over wing section at $Re = 20, 000$ and dependence of decomposed mode on time window.