Real-time data assimilation for model-error inference

Nonlinear thermoacoustic oscillations can be estimated with reduced-order models, which provide qualitatively accurate estimates at low computational cost. Data assimilation algorithms are employed to improve the accuracy of numerical models. However, quantitative accurate predictions might not be attainable with low-order models as their governing equations do not capture all the physical mechanisms, i.e., low-order models may be statistically biased. We propose a bias-aware sequential ensemble data-assimilation method, which accounts for the model error in the Kalman update; with an echo-state network, which adaptively estimates the model error. In this framework, we perform real-time inference of the physical state, model parameters and model error from reference data. The method is tested on a nonlinear time-delayed low-order model by assimilating data from a higher-order model of the system. Current efforts focus on the application of this framework for on-the-fly state, parameter and model error estimation with experimental data.