Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
This work addresses forecasting limitations in geophysical systems like ocean-atmosphere dynamics, where partial observations hinder long-term predictions, though it appears incremental as it builds on existing neural ODE frameworks.
The paper tackled the challenge of forecasting partially observed geophysical systems with hidden variables by developing a physics-constrained deep learning method using neural ODEs, achieving improved generalization and boundedness compared to state-of-the-art schemes in case studies.
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.