The most robust representations of flow trajectories are Lagrangian coherent structures

Abstract

What is the most robust way to communicate flow trajectories? To answer this question, we employ two neural networks to respectively deconstruct (the encoder) and reconstruct (the decoder) trajectories, where information is passed between the two networks through a low-dimensional latent space in a set-up known as an autoencoder. To ensure that their communications are robust, we add noise to the coded information passed through this latent space. In the low-noise limit the latent space structures are non-spatial in nature, resembling modes of a principle component analysis (PCA). However, as the signal-to-noise ratio is decreased, we uncover Lagrangian coherent structures (LCS) as the most compact representations which still allow the decoder to accurately reconstruct trajectories. This relationship offers increased interpretability to both PCA and LCS analysis, and helps to bridge the gap between two methods of flow analysis.

Passive bionic motion of a flexible film in the wake of a circular cylinder: chaos and periodicity, flow–structure interactions and energy evolution

“…We select an integration time length |T | of three times the dominant period of the flow field to reveal enough details of the LCS (Shadden et al 2005;Green et al 2007;He et al 2016). The algorithm employed to determine the FTLEs using discrete data, as described above, has been demonstrated to possess high robustness (Green et al 2007); besides, LCS are the most robust structures in flow fields (MacMillan & Richter 2021). Therefore, the LCS identified based on FTLEs portray the intrinsic characteristics of the flow-field evolution.…”

“…The algorithm employed to determine the FTLEs using discrete data, as described above, has been demonstrated to possess high robustness (Green et al. 2007); besides, LCS are the most robust structures in flow fields (MacMillan & Richter 2021). Therefore, the LCS identified based on FTLEs portray the intrinsic characteristics of the flow–field evolution.…”