Learning Dynamical Systems from Partial Observations

2019/02/26 by Ibrahim Ayed, Emmanuel de Bézenac, Ayed, Ibrahim +7 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Computational Physics and Python Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Reservoir Engineering and Simulation Methods #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1902.11136

openalex publication_date 2019/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled by an unknown time-varying differential equation, and the evolution term is estimated from the data, using a neural network. Any future state can then be computed by placing the associated differential equation in an ODE solver. We first evaluate our approach on shallow water and Euler simulations. We find that our method not only demonstrates high quality long-term forecasts, but also learns to produce hidden states closely resembling the true states of the system, without direct supervision on the latter. Additional experiments conducted on challenging, state of the art ocean simulations further validate our findings, while exhibiting notable improvements over classical baselines.

Citations

• Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting
• Long Short-Term Memory
• PDE-Net: Learning PDEs from Data
• Bilinear residual Neural Network for the identification and forecasting of dynamical systems
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial\n Differential Equations
• PredRNN++: Towards A Resolution of the Deep-in-Time Dilemma in Spatiotemporal Predictive Learning
• Optimal Unsupervised Domain Translation
• Deep Learning for Physical Processes: Incorporating Prior Scientific\n Knowledge

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• Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data

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