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

• URL: http://arxiv.org/abs/2202.05750v1
• Date: Fri, 11 Feb 2022 16:40:46 GMT
• Title: Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
• Authors: Said Ouala, Steven L. Brunton, Ananda Pascual, Bertrand Chapron, Fabrice Collard, Lucile Gaultier, Ronan Fablet
• Abstract summary: 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.
• Score: 30.238425143378414
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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