Ensemble-based kernel learning for a class of data assimilation problems with imperfect forward simulators

Abstract

Simulator imperfection, often known as model error, is ubiquitous in practical data assimilation problems. Despite the enormous efforts dedicated to addressing this problem, properly handling simulator imperfection in data assimilation remains to be a challenging task. In this work, we propose an approach to dealing with simulator imperfection from a point of view of functional approximation that can be implemented through a certain machine learning method, such as kernel-based learning adopted in the current work. To this end, we start from considering a class of supervised learning problems, and then identify similarities between supervised learning and variational data assimilation. These similarities found the basis for us to develop an ensemble-based learning framework to tackle supervised learning problems, while achieving various advantages of ensemble-based methods over the variational ones. After establishing the ensemble-based learning framework, we proceed to investigate the integration of ensemble-based learning into an ensemble-based data assimilation framework to handle simulator imperfection. In the course of our investigations, we also develop a strategy to tackle the issue of multi-modality in supervised-learning problems, and transfer this strategy to data assimilation problems to help improve assimilation performance. For demonstration, we apply the ensemble-based learning framework and the integrated, ensemble-based data assimilation framework to a supervised learning problem and a data assimilation problem with an imperfect forward simulator, respectively. The experiment results indicate that both frameworks achieve good performance in relevant case studies, and that functional approximation through machine learning may serve as a viable way to account for simulator imperfection in data assimilation problems.

Accounting for model errors of rock physics models in 4D seismic history matching problems: A perspective of machine learning

“…As such, model errors are ubiquitous in geophysical data assimilation problems, whereas at the time being, how to properly handle model errors appears to remain as an open topic in data assimilation community. The practical challenges in dealing with model errors stem from factors like the complexities in quantitatively analyzing and characterizing the sources of model errors, the dependence of model errors on (uncertain) model variables, and consequently the tangled effects of both model errors and model variables on assimilation algorithms (Luo, 2019). Therefore, to account for model errors in data assimilation problems, it is necessary to adopt certain strategies that take into account these noticed challenges.…”

“…There are also investigations dedicated to studying the effects of model errors on history matching, but without assuming the independence between model errors and model variables, see, for example, (Stephen, 2007;Köpke et al, 2018;Luo, 2019). In practice, though, taking into account the dependence of model errors on model variables may nullify the conventional Gaussianity assumption adopted for the purpose of characterizing model errors.…”

Data assimilation with multiple types of observation boreholes via the ensemble Kalman filter embedded within stochastic moment equations

“…In this broad framework, it is noted that the accuracy of parameter estimation for a given environmental system is jointly determined by the ability of the mathematical model to describe the system of interest (Sakov and Bocquet, 2018;Alfonzo and Oliver, 2020;Luo, 2019;Evensen, 2019), the ability of the assimilation algorithm used (Emerick and Reynolds, 2013;Bocquet and Sakov, 2014), as well as by the quantity and quality of available observations (Zha et al, 2019;Xia et al, 2018, and references therein).…”

Data assimilation with multiple types of observation boreholes via ensemble Kalman filter embedded within stochastic moment equations

“…In this broad framework, it is noted that the accuracy of parameter estimation for a given environmental system is jointly determined by the ability of the mathematical model to describe the system of interest (Sakov et al, 2018;Alfonzo and Oliver, 2019;Luo, 2019;Evensen, 2019), the ability of the used assimilation algorithm (Emerick and Reynolds, 2013;Bocquet and Sakov, 2014) as well as by the quantity and quality of available observations (Zha et al, 2019;Xia et al, 2018 and references therein).…”