Sparse Sensor-based Flow Estimation Using Artificial Neural Networks and Spectral Proper Orthogonal Decomposition

The application of Artificial Neural Networks (ANNs) in developing sensor-based estimators for unsteady turbulent flows has become an active area of research over the last decade. One of the challenges in this area is in the selection of an optimal low-dimensional subspace which enables the ANN to reconstruct relevant spatiotemporal dynamics in the flow and avoid overfitting data to the underlying stochastic fluctuations. The energetically optimal Proper Orthogonal Decomposition (POD) and the spectrally pure Discrete Fourier Transform (DFT) both have shown promising results, however, these algorithms have intrinsic limitations. These limitations affect how well the physics of different flows can be represented in a sparse basis. The present study aims at demonstrating that for certain flows, the versatile time-domain Spectral Proper Orthogonal Decomposition (SPOD, M. Sieber et al., J. Fluid Mech. (2016), vol. 792, pp.798-828) provides an improved basis compared to the traditional methods (POD, DFT) for neural networks to perform a sensor-based flow estimation task. In the study, the SPOD basis is compared to the other candidate bases (POD, DFT), and the differences in performance of the neural networks are linked to the features that are captured or suppressed in the different mode spaces.