A1 Journal article (refereed), original research

Efficient Bayesian inference for large chaotic dynamical systems


Open Access publication

Publication Details
Authors: Springer Sebastian, Haario Heikki, Susiluoto Jouni, Bibov Aleksandr, Davis Andrew, Marzouk Youssef
Publisher: European Geosciences Union (EGU) / Copernicus Publications
Publication year: 2021
Language: English
Related journal or series: Geoscientific Model Development
Volume number: 14
Issue number: 7
Start page: 4319
End page: 4333
Number of pages: 15
ISSN: 1991-959X
eISSN: 1991-9603
JUFO level of this publication: 2
Open Access: Open Access publication

Abstract

Estimating parameters of chaotic geophysical models is challenging due
to their inherent unpredictability. These models cannot be calibrated
with standard least squares or filtering methods if observations are
temporally sparse. Obvious remedies, such as averaging over temporal and
spatial data to characterize the mean behavior, do not capture the
subtleties of the underlying dynamics. We perform Bayesian inference of
parameters in high-dimensional and computationally demanding chaotic
dynamical systems by combining two approaches:
(i) measuring model–data mismatch by comparing chaotic attractors and
(ii) mitigating the computational cost of inference by using surrogate
models. Specifically, we construct a likelihood function suited to
chaotic models by evaluating a distribution over distances between
points in the phase space; this distribution defines a summary statistic
that depends on the geometry of the attractor, rather than on
pointwise matching of trajectories.
This statistic is computationally expensive to simulate, compounding the
usual challenges of Bayesian computation with physical models. Thus, we
develop
an inexpensive surrogate for the log likelihood with the local
approximation Markov chain Monte Carlo method, which in our simulations
reduces the time required for accurate inference by orders of magnitude.
We investigate the behavior of the resulting algorithm with two
smaller-scale problems and then use a quasi-geostrophic model to
demonstrate its large-scale application.


Last updated on 2021-03-08 at 10:54