Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A...

Area of Science:

• Computational modeling
• Data assimilation
• Scientific machine learning

Background:

• Real-world systems are often represented by imperfect models, leading to discrepancies between predictions and reality.
• Model errors, especially in nonlinear and multi-scale systems, can cause significant deviations in numerical solutions.
• Leveraging observational data is crucial for understanding and reducing these model errors.

Purpose of the Study:

• To introduce MEDIDA (Model Error Discovery with Interpretability and Data Assimilation), a novel framework for identifying and representing model errors.
• To demonstrate the framework's ability to improve the accuracy of imperfect models by correcting for model errors.
• To provide an interpretable and parsimonious representation of model errors.

Main Methods:

• Estimating model error from discrepancies between observed and model-predicted states.
• Employing data assimilation techniques (e.g., ensemble Kalman filter) for noisy observations to obtain system analysis states.
• Utilizing equation-discovery techniques (e.g., relevance vector machine) for interpretable model error representation.

Main Results:

• MEDIDA successfully discovers various structural and parametric model errors.
• The framework effectively represents missing physics within the model.
• Demonstrated excellent performance on the chaotic Kuramoto-Sivashinsky system with both noise-free and noisy data.

Conclusions:

• MEDIDA offers a robust approach to quantifying and correcting model errors by integrating data assimilation and equation discovery.
• The framework enhances the reliability of computational models, particularly for complex systems.
• MEDIDA facilitates a deeper understanding of the sources of model error by providing interpretable representations.