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. 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.

References in corpus (39)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• Time Series Forecasting With Deep Learning: A Survey
• Deep learning for universal linear embeddings of nonlinear dynamics
• NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Skillful Precipitation Nowcasting using Deep Generative Models of Radar
• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
• Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
• Chaos as an Intermittently Forced Linear System
• Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
• Predicting catastrophes in nonlinear dynamical systems by compressive sensing
• Deep Neural Networks for Data-Driven Turbulence Models
• Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
• Data-driven Discovery of Cyber-Physical Systems
• Sequential Neural Models with Stochastic Layers
• Optimization for deep learning: theory and algorithms
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• Nonlinear Systems Identification Using Deep Dynamic Neural Networks
• Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
• Learning Stable Deep Dynamics Models
• Sparse nonlinear models of chaotic electroconvection
• From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction
• Physical invariance in neural networks for subgrid-scale scalar flux modeling
• Sea Level Anomaly Prediction using Recurrent Neural Networks
• Learning Latent Dynamics for Partially-Observed Chaotic Systems
• Deep reconstruction of strange attractors from time series
• ANODEV2: A Coupled Neural ODE Evolution Framework
• Neural Closure Models for Dynamical Systems
• Constrained Neural Ordinary Differential Equations with Stability Guarantees
• Joint learning of variational representations and solvers for inverse problems with partially-observed data
• A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks
• Bilinear residual Neural Network for the identification and forecasting of dynamical systems
• Sea surface temperature prediction and reconstruction using patch-level neural network representations
• LyaNet: A Lyapunov Framework for Training Neural ODEs
• Memory-Efficient Learning of Stable Linear Dynamical Systems for Prediction and Control
• Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting
• Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations
• Learning Runge-Kutta Integration Schemes for ODE Simulation and Identification

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