Filtering dynamical systems using observations of statistics Article Swipe
Eviatar Bach
,
Tim Colonius
,
Isabel Scherl
,
Andrew M. Stuart
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1063/5.0171827
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1063/5.0171827
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density ρ(v,t) given noisy observations of the true density ρ†; this contrasts with the standard filtering problem based on observations of the state v. The task is naturally formulated as an infinite-dimensional filtering problem in the space of densities ρ. However, for the purposes of tractability, we seek algorithms in state space; specifically, we introduce a mean-field state-space model, and using interacting particle system approximations to this model, we propose an ensemble method. We refer to the resulting methodology as the ensemble Fokker–Planck filter (EnFPF). Under certain restrictive assumptions, we show that the EnFPF approximates the Kalman–Bucy filter for the Fokker–Planck equation, which is the exact solution to the infinite-dimensional filtering problem. Furthermore, our numerical experiments show that the methodology is useful beyond this restrictive setting. Specifically, the experiments show that the EnFPF is able to correct ensemble statistics, to accelerate convergence to the invariant density for autonomous systems, and to accelerate convergence to time-dependent invariant densities for non-autonomous systems. We discuss possible applications of the EnFPF to climate ensembles and to turbulence modeling.
Related Topics
Concepts
Dynamical systems theory
Kalman filter
Invariant (physics)
Applied mathematics
Filter (signal processing)
Particle filter
Statistical physics
State space
Probability density function
Mathematics
Convergence (economics)
Dynamical system (definition)
Computer science
Algorithm
Statistics
Physics
Economic growth
Quantum mechanics
Economics
Computer vision
Mathematical physics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1063/5.0171827
- https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0171827/19750108/033119_1_5.0171827.pdf
- OA Status
- bronze
- Cited By
- 7
- References
- 42
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4392578939
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4392578939Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1063/5.0171827Digital Object Identifier
- Title
-
Filtering dynamical systems using observations of statisticsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-03-01Full publication date if available
- Authors
-
Eviatar Bach, Tim Colonius, Isabel Scherl, Andrew M. StuartList of authors in order
- Landing page
-
https://doi.org/10.1063/5.0171827Publisher landing page
- PDF URL
-
https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0171827/19750108/033119_1_5.0171827.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
bronzeOpen access status per OpenAlex
- OA URL
-
https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0171827/19750108/033119_1_5.0171827.pdfDirect OA link when available
- Concepts
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Dynamical systems theory, Kalman filter, Invariant (physics), Applied mathematics, Filter (signal processing), Particle filter, Statistical physics, State space, Probability density function, Mathematics, Convergence (economics), Dynamical system (definition), Computer science, Algorithm, Statistics, Physics, Economic growth, Quantum mechanics, Economics, Computer vision, Mathematical physicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
7Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 5, 2024: 1, 2023: 1Per-year citation counts (last 5 years)
- References (count)
-
42Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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