State Estimation Using Sparse DEIM and Recurrent Neural Networks

Discrete Empirical Interpolation Method (DEIM) estimates a function from its pointwise incomplete observations. In particular, this method can be used to estimate the state of a dynamical system from observational data gathered by sensors. However, when the number of observations are limited, DEIM returns large estimation errors. Sparse DEIM (S-DEIM) was recently developed to address this problem by introducing a kernel vector which previous DEIM-based methods had ignored. Unfortunately, estimating the optimal kernel vector in S-DEIM is a difficult task. Here, we introduce a data-driven method to estimate this kernel vector from sparse observational time series using recurrent neural networks. Using numerical examples, we demonstrate that this machine learning approach together with S-DEIM leads to nearly optimal state estimations.