# Combined State and Parameter Estimation in Level-Set Methods

arXiv: https://arxiv.org/abs/1903.00321 · HTML: https://mlsanity.com/paper/1903.00321/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [Online parameter inference for the simulation of a Bunsen flame using heteroscedastic Bayesian neural network ensembles](https://mlsanity.com/paper/2104.13201/) (2021)
- [Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation](https://mlsanity.com/paper/2602.23188/) (2026)

## Abstract (arXiv)

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 onedimensional 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.