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Center for Data Science
Department colloquium

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

In this talk, the speaker will introduce 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.

Ensemble-based kernel learning
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Information Flyer Photo: Department of Mathematics, UiB

Simulator imperfection, often known as model error, is ubiquitous in geophysical 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 talk, we introduce 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 our 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 conventional variational ones. After establishing the ensemble-based learning framework, we proceed to integrate ensemble-based learning into an ensemble-based data assimilation framework to handle simulator imperfection.

For demonstration, we apply the ensemble-based learning framework and the integrated, ensemble-based data assimilation framework to two synthetic problems and a real field case study. 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.

Speaker: Xiaodong Luo, Senior Researcher from NORCE