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

TL;DR

This paper introduces a physics-constrained deep learning approach using neural ODEs to model partially observed, nonlinear geophysical systems, emphasizing boundedness for improved generalization in forecasting complex ocean-atmosphere dynamics.

Contribution

It proposes a novel neural ODE-based architecture that enforces boundedness constraints, enhancing the modeling of partially observed geophysical systems beyond existing methods.

Findings

The method improves long-term forecast stability.

It outperforms state-of-the-art schemes in case studies.

Boundedness constraints enhance generalization.

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. A key objective is to constrain their boundedness, which promotes the generalization of the learned dynamics to arbitrary initial condition. 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.