University of Oulu

Springer, S., Haario, H., Susiluoto, J., Bibov, A., Davis, A., and Marzouk, Y.: Efficient Bayesian inference for large chaotic dynamical systems, Geosci. Model Dev., 14, 4319–4333,, 2021

Efficient Bayesian inference for large chaotic dynamical systems

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Author: Springer, Sebastian1,2; Haario, Heikki1,3; Susiluoto, Jouni1,3,4;
Organizations: 1Department of Computational and Process Engineering, Lappeenranta University of Technology, Lappeenranta, Finland
2Research unit of Mathematical Sciences, University of Oulu, Oulu, Finland
3Finnish Meteorological Institute, Helsinki, Finland
4Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA
5Varjo Technologies Oy, Helsinki, Finland
6Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 8.3 MB)
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Language: English
Published: Copernicus Publications, 2021
Publish Date: 2021-09-17


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.

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Series: Geoscientific model development
ISSN: 1991-959X
ISSN-E: 1991-9603
ISSN-L: 1991-959X
Volume: 14
Issue: 7
Pages: 4319 - 4333
DOI: 10.5194/gmd-14-4319-2021
Type of Publication: A1 Journal article – refereed
Field of Science: 1171 Geosciences
Funding: This research has been supported by the Academy of Finland (grant no. 312122).
Copyright information: © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License.