Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning

Abstract

The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially observed couplings, or forcings in coupled systems. This is the case in ocean–atmosphere dynamics, for which unknown interior dynamics can affect surface observations. The identification of computationally-relevant representations of such partially-observed and highly nonlinear systems is thus challenging and often limited to short-term forecast applications. Here, we investigate the physics-constrained learning of implicit dynamical embeddings, leveraging neural ordinary differential equation (NODE) representations. In particular, we restrict the NODE representation to linear–quadratic dynamics and enforce a global boundedness constraint, which promotes the generalization of the learned dynamics to arbitrary initial conditions. The proposed architecture is implemented within a deep learning framework, and its relevance is demonstrated with respect to state-of-the-art schemes for different case studies representative of geophysical dynamics.