Data-driven reconstruction of partially observed dynamical systems

Abstract. The state of the atmosphere, or ocean, cannot be exhaustively observed. Crucial parts might remain out reach proper monitoring. Also, defining exact set equations driving atmosphere and ocean is virtually impossible because their complexity. goal this paper to obtain predictions a partially observed dynamical system without knowing model equations. In data-driven context, article focuses on Lorenz-63 system, where only second third components are access not allowed. To account for those strong constraints, combination machine learning data assimilation techniques proposed. key aspects following: introduction latent variables, linear approximation dynamics database that updated iteratively, maximizing likelihood. We find variables inferred by procedure related successive derivatives system. method also able reconstruct accurately local Overall, proposed methodology simple, easy code gives promising results, even in case small numbers observations.