Combined state and parameter estimation in level-set methods

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous learning algorithm for state and parameter estimation with leve...

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Bibliographic Details
Published in:Journal of computational physics 2019-12, Vol.399, p.108950, Article 108950
Main Authors: Yu, Hans, Juniper, Matthew P., Magri, Luca
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Computational physics
Data assimilation
Ensemble Kalman filter
Kalman filters
Level-set method
Machine learning
Mathematical models
Nonlinear dynamics
Parameter estimation
Parameter uncertainty
Predictions
Premixed flames
Reduced order models
State estimation
Statistical analysis
Uncertainty quantification
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Summary:Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous learning algorithm for state and parameter estimation with level-set methods. A Bayesian approach based on data assimilation is introduced. Data assimilation is enabled by the ensemble Kalman filter and smoother, which are used in their probabilistic formulations. The level-set data assimilation framework is verified in one-dimensional and two-dimensional test cases, where state estimation, parameter estimation and uncertainty quantification are performed. The statistical performance of the proposed ensemble Kalman filter and smoother is quantified by twin experiments. In the twin experiments, the combined state and parameter estimation fully recovers the reference solution, which validates the proposed algorithm. The level-set data assimilation framework is then applied to the prediction of the nonlinear dynamics of a forced premixed flame, which exhibits the formation of sharp cusps and intricate topological changes, such as pinch-off events. The proposed physics-informed statistical learning algorithm opens up new possibilities for making reduced-order models of interfaces quantitatively predictive, any time that reference data is available.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2019.108950