A Priori Estimation of the Non-Linear Compression Potential and Quantification of Autoencoder Non-Linearity in Turbulent Flows

Abstract

Data-driven reduced-order modelling (ROM) of turbulent flows is based on an efficient and physical low-dimensional representation of the flow process. Such a dimension reduction can be achieved using proper orthogonal decomposition (POD) or non-linear autoencoders. Capturing the inherent non-linearities in turbulent flows offers the potential for improved compression rates. This work proposes the local tangent residual (LTR) as an a priori estimate of the potential benefit of non-linear dimension reduction for a given dataset. The LTR is based on the local geometry of the data points, requiring neither prior model training nor the definition of a threshold parameter. For all datasets investigated in this work, namely, two vortex street cases and the turbulent wake flow of a wind turbine, the dominant trends in autoencoder compression performance are reproduced by the proposed LTR. The results are further contextualised through the decoder linearisation error (DLE). The DLE quantifies the non-linearity of the trained decoder by comparing it to a linearised surrogate model, which enables physical interpretability of the non-linearities. Together, a large non-linear compression potential in the turbulent flow, as quantified by the LTR, is corroborated by a large DLE, i.e., a pronounced non-linearity captured in the trained autoencoder. The LTR thus enables practitioners in turbulent flow modelling to determine a priori whether non-linear compression is worthwhile, avoiding the substantial computational cost of autoencoder architecture search and hyperparameter tuning in cases where POD already suffices.