Orateur
Description
Proper orthogonal decomposition (POD) can be viewed as the linear limit of autoencoders. This connection is exploited to construct interpretable nonlinear reduced order models. By introducing learnable polynomial activation functions, the autoencoder can be initialized as an exact POD decomposition, allowing for an optimal linear reconstruction error even before training begins. Initializing autoencoders with POD also accelerates training convergence by an order of magnitude in terms of the number of gradient descent epochs required. The addition of convolutional layers (CNN) reduces reconstruction errors by an order of magnitude, compared to the baseline autoencoder. The learned filters can be interpreted as spatial derivative operators, revealing how additional nonlinear mode couplings are captured. The results are presented for the flow around an oscillating cylinder, in a quasi-periodic regime. It is shown that the best autoencoders completely outperform POD when encoding the first few most energetic modes, while POD remains competitive in the tail of the energy spectrum.