Nonlinear model reduction based on stochastic obsevability

Abstract

The practical applicability of analytical model reduction methods is limited. In this paper, we show an optimality of Proper Orthogonal Decomposition (POD) based nonlinear model reduction. POD is a simulation-based model reduction method that has been widely applied to nonlinear large-scale systems, but there is no theoretical background in general. An observability-based analytical nonlinear model reduction is not well proposed. In this paper, after deriving a stochastic observability using a duality between optimal control and optimal estimation, we show that the observability-based and simulation-based methodologies with weights are equivalent when the input is only stochastic signal. We also show an example of nonlinear model reduction method using the deep autoencoder.