Machine learning for fluid flow reconstruction from limited measurements.

• Machine learning framework for the reconstruction of unsteady fluid flows fields. • Variational approach for a robust reduction of the high dimensional field. • Investigations on three canonical cases. • Combination of linear or nonlinear reduction with regressive or direct reconstruction. This paper investigates the use of data-driven methods for the reconstruction of unsteady fluid flow fields. The proposed framework is based on the combination of machine learning tools: dimensionality reduction to extract dominant spatial directions from data, reconstruction algorithm to recover encoded data by limited measurements and cross-validation for hyperparameter optimization. For the encoding part, linear and nonlinear extraction of patterns are considered: proper orthogonal decomposition (POD), linear autoencoder (LAE) and variational autoencoder (VAE). For the reconstruction part, regressive reconstruction (neural network, linear, support vector, gradient boosting) and library-based reconstruction are compared, each method being cross-validated to ensure good generalization on testing data. The position of sensors is optimized using an enhanced clustering algorithm. The robustness of regressive reconstructions to noise measurements is also addressed, showing the benefits of variational approaches in the reduction phase. The strategy is tested for three increasing complexity flows: 2D vortex shedding (R e = 200), 2D spatial mixing layer and 3D vortex shedding (R e = 20000). The results suggest that proper machine learning approaches to fluid flow data can lead to effective reconstruction models that can be used for the rapid estimation of complex flows. [ABSTRACT FROM AUTHOR]