Efficient Bayesian inference for large chaotic dynamical systems
<jats:p>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 tempor...
| Main Authors: | , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Copernicus GmbH
2022
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| Online Access: | https://hdl.handle.net/1721.1/145429 |
| _version_ | 1811070595365863424 |
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| author | Springer, Sebastian Haario, Heikki Susiluoto, Jouni Bibov, Aleksandr Davis, Andrew Marzouk, Youssef |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Springer, Sebastian Haario, Heikki Susiluoto, Jouni Bibov, Aleksandr Davis, Andrew Marzouk, Youssef |
| author_sort | Springer, Sebastian |
| collection | MIT |
| description | <jats:p>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.
</jats:p> |
| first_indexed | 2024-09-23T08:38:32Z |
| format | Article |
| id | mit-1721.1/145429 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:38:32Z |
| publishDate | 2022 |
| publisher | Copernicus GmbH |
| record_format | dspace |
| spelling | mit-1721.1/1454292022-09-30T10:12:41Z Efficient Bayesian inference for large chaotic dynamical systems Springer, Sebastian Haario, Heikki Susiluoto, Jouni Bibov, Aleksandr Davis, Andrew Marzouk, Youssef Massachusetts Institute of Technology. Department of Aeronautics and Astronautics <jats:p>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. </jats:p> 2022-09-15T15:43:48Z 2022-09-15T15:43:48Z 2021 2022-09-15T15:39:35Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145429 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). en 10.5194/GMD-14-4319-2021 Geoscientific Model Development Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Copernicus GmbH Copernicus Publications |
| spellingShingle | Springer, Sebastian Haario, Heikki Susiluoto, Jouni Bibov, Aleksandr Davis, Andrew Marzouk, Youssef Efficient Bayesian inference for large chaotic dynamical systems |
| title | Efficient Bayesian inference for large chaotic dynamical systems |
| title_full | Efficient Bayesian inference for large chaotic dynamical systems |
| title_fullStr | Efficient Bayesian inference for large chaotic dynamical systems |
| title_full_unstemmed | Efficient Bayesian inference for large chaotic dynamical systems |
| title_short | Efficient Bayesian inference for large chaotic dynamical systems |
| title_sort | efficient bayesian inference for large chaotic dynamical systems |
| url | https://hdl.handle.net/1721.1/145429 |
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