A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics

[2406.06837] A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics Skip to main content Search Submit Donate Log in Mathematics > Dynamical Systems arXiv:2406.06837 (math) [Submitted on 10 Jun 2024 ( v1 ), last revised 12 Jun 2024 (this version, v2)] Title: A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics Authors: Johannes Krotz , Juan M. Restrepo , Jorge Ramirez View PDF Abstract: A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems -waves-, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data. Subjects: Dynamical Systems (math.DS) ; Machine Learning (cs.LG); Statistics Theory (math.ST) Cite as: arXiv:2406.06837 [math.DS] (or arXiv:2406.06837v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2406.06837 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Johannes Krotz [ view email ] [v1] Mon, 10 Jun 2024 22:56:56 UTC (4,121 KB) [v2] Wed, 12 Jun 2024 03:01:45 UTC (4,121 KB) Full-text links: Access Paper: View PDF view license Current browse context: math.DS < prev | next > new | recent | 2024-06 Change to browse by: cs cs.LG math math.ST stat stat.TH References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics#677328
• Quantitative Diffusive Limits for Singular Nonlocal Transport#999519
• Dynamic models with $p$ parameters are identified by $2p+1$ random features#927385
• Parameter Estimation for Weakly Interacting Hypoelliptic Diffusions#974215
• On the use of a diffusion equation for room-acoustic prediction#308310