DeepAI AI Chat
Log In Sign Up

Bayesian inference of dynamics from partial and noisy observations using data assimilation and machine learning

by   Marc Bocquet, et al.
Ecole nationale des Ponts et Chausses
University of Reading

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. Implementations and approximations of these methods are also discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.


page 1

page 2

page 3

page 4


Online learning of both state and dynamics using ensemble Kalman filters

The reconstruction of the dynamics of an observed physical system as a s...

Deep learning delay coordinate dynamics for chaotic attractors from partial observable data

A common problem in time series analysis is to predict dynamics with onl...

Koopman-theoretic Approach for Identification of Exogenous Anomalies in Nonstationary Time-series Data

In many scenarios, it is necessary to monitor a complex system via a tim...

Identifying nonlinear dynamical systems from multi-modal time series data

Empirically observed time series in physics, biology, or medicine, are c...

Scalable Bayesian inference for time series via divide-and-conquer

Bayesian computational algorithms tend to scale poorly as data size incr...

On Contrastive Representations of Stochastic Processes

Learning representations of stochastic processes is an emerging problem ...

Low-pass filtering as Bayesian inference

We propose a Bayesian nonparametric method for low-pass filtering that c...