Submitted as: methods for assessment of models 26 Oct 2020

Submitted as: methods for assessment of models | 26 Oct 2020

Review status: a revised version of this preprint is currently under review for the journal GMD.

Efficient Bayesian inference for large chaotic dynamical systems

Sebastian Springer1, Heikki Haario1,2, Jouni Susiluoto1,3, Aleksandr Bibov1,5, Andrew Davis3,4, and Youssef Marzouk3 Sebastian Springer et al.
  • 1Department of Computational and Process Engineering, Lappeenranta University of Technology, Lappeenranta, Finland
  • 2Finnish Meteorological Institute, Helsinki, Finland
  • 3Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA
  • 4Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
  • 5Varjo Technologies Oy, Helsinki, Finland

Abstract. Estimating parameters of chaotic geophysical models is challenging due to these models' inherent unpredictability. With temporally sparse long-range observations, these models cannot be calibrated using standard least squares or filtering methods. 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 attractor's geometry, 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 via local approximation Markov chain Monte Carlo, which in our simulations reduces the time required for accurate inference by orders of magnitude. We investigate the behavior of the resulting algorithm on model problems, and then use a quasi-geostrophic model to demonstrate its large-scale application.

Sebastian Springer et al.

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Status: final response (author comments only)
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Sebastian Springer et al.

Sebastian Springer et al.


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Short summary
The model predictions always contain uncertainty. But in some cases, such as weather forecasting or climate modelling, chaotic unpredictability increases the difficulty to say exactly how much uncertainty there is. We combine two recently proposed mathematical methods to show how the uncertainty can be analyzed in models that are simplifications of true weather models. The results can be extended in the future to show how forecasts from the large-scale models can be improved.