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In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier–Stokes-α model. Rigorous estimates are presented for the convergence of continuous data assimilation methods when the parameters of the turbulence models are not known a priori. Our approach involves creating an approximate solution for the turbulence models by employing an interpolant operator based on the observational data of the systems. The estimation depends on the parameter alpha in the models. Additionally, numerical simulations are presented to validate our theoretical results.
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Data assimilation of synthetic data as a novel strategy for predicting disease progression in alopecia areata
Abstract The goal of patient-specific treatment of diseases requires a connection between clinical observations with models that are able to accurately predict the disease progression. Even when realistic models are available, it is very difficult to parameterize them and often parameter estimates that are made using early time course data prove to be highly inaccurate. Inaccuracies can cause different predictions, especially when the progression depends sensitively on the parameters. In this study, we apply a Bayesian data assimilation method, where the data are incorporated sequentially, to a model of the autoimmune disease alopecia areata that is characterized by distinct spatial patterns of hair loss. Using synthetic data as simulated clinical observations, we show that our method is relatively robust with respect to variations in parameter estimates. Moreover, we compare convergence rates for parameters with different sensitivities, varying observational times and varying levels of noise. We find that this method works better for sparse observations, sensitive parameters and noisy observations. Taken together, we find that our data assimilation, in conjunction with our biologically inspired model, provides directions for individualized diagnosis and treatments.
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- Award ID(s):
- 1720222
- PAR ID:
- 10279968
- Date Published:
- Journal Name:
- Mathematical Medicine and Biology: A Journal of the IMA
- ISSN:
- 1477-8599
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imammb/dqab008
