Domain-aware Gaussian process state-space models

Gaussian process state-space models are a widely used modeling paradigm for learning and estimation in dynamical systems. Reduced-rank Gaussian process state-space models combine spectral characterization of dynamical systems with Hilbert space methods to enable learning, which scale linearly with the length of the time series. However, the current state of the art algorithms struggle to deal efficiently with the dimensionality of the state-space itself. In this work, we propose a novel algorithm, referred to as Domain-Aware reduced-rank Gaussian Process State-Space Model (DA-GPSSM), which exploits the relationship between state dimensions to model only necessary dynamics resulting in reduced computational cost, by potentially orders of magnitude in comparison to the state-of-the-art. The proposed approach grants modeling flexibility while maintaining comparable performance and thus increasing the applicability of these models. We present implications of the proposed approach and discuss applications where DA-GPSSM can be beneficial. Finally, we conduct simulations to demonstrate the performance and reduced computational cost of our proposed method, compared to the state-of-the-art learning method, and propose future research directions. • We introduce Domain-Aware Gaussian Process State-Space Model (DA-GPSSM), based on Reduced-Rank Gaussian Process State-Space Model (RR-GPSSMs), to explicitly model the relationship between different state-dimension. • Our proposed framework significantly reduces the computational load to upto several orders of magnitude from O ( M 3 D ) for a D dimensional state-space model to O ( M 3 K ) , where K ≤ D depending on the application domain. • We show through simulations the comparable performance of DA-GPSSM w.r.t. the state of the methods, and the significant improvement in computational complexity for multiple applications.