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

Area of Science:

• Data Assimilation
• Machine Learning
• Scientific Computing

Background:

• Simulator imperfection, or model error, is a significant challenge in data assimilation.
• Existing methods struggle to effectively address this ubiquitous problem.

Purpose of the Study:

• To propose a novel approach for handling simulator imperfection in data assimilation.
• To leverage functional approximation via machine learning for improved assimilation.

Main Methods:

• Developed an ensemble-based learning framework by identifying similarities between supervised learning and variational data assimilation.
• Integrated this framework into an ensemble-based data assimilation system.
• Addressed multi-modality issues in both learning and assimilation problems.

Main Results:

• Demonstrated the effectiveness of the ensemble-based learning framework on a supervised learning task.
• Showcased improved assimilation performance using the integrated framework on a problem with an imperfect simulator.
• Validated the functional approximation approach for accounting for simulator imperfection.

Conclusions:

• Machine learning, specifically functional approximation, offers a viable solution for simulator imperfection in data assimilation.
• The proposed ensemble-based learning and assimilation frameworks achieve good performance.
• This approach enhances the robustness and accuracy of data assimilation systems.