Leveraging time and parameters for nonlinear model reduction methods
This addresses a computational bottleneck in nonlinear model reduction for wave-like or transport-dominated problems, offering a more efficient training process.
The paper tackles the challenge of model order reduction for problems with slowly decaying Kolmogorov n-widths by proposing a method to replace nonlinear encoders with linear ones, reducing the number of hyperparameters by about half without losing accuracy.
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear projections are used, which are often realized numerically using autoencoders. These autoencoders generally consist of a nonlinear encoder and a nonlinear decoder and involve costly training of the hyperparameters to obtain a good approximation quality of the reduced system. To facilitate the training process, we show that extending the to-be-reduced system and its corresponding training data makes it possible to replace the nonlinear encoder with a linear encoder without sacrificing accuracy, thus roughly halving the number of hyperparameters to be trained.