Efficient Bayesian inference for large chaotic dynamical systems
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gmd-14-4319-2021.pdf
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Published version
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8.32 MB
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Author(s)
Springer, Sebastian
Haario, Heikki
Susiluoto, Jouni
Bibov, Aleksandr
Davis, Andrew
Marzouk, Youssef
Date Issued
2021
Journal
Geoscientific Model Development
Publisher
Copernicus GmbH
Citation
Springer, Sebastian, Haario, Heikki, Susiluoto, Jouni, Bibov, Aleksandr, Davis, Andrew et al. 2021. "Efficient Bayesian inference for large chaotic dynamical systems." Geoscientific Model Development, 14 (7).
Version
Final published version
Abstract
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.
(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.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.5194/GMD-14-4319-2021
