Explainable data-driven modeling via mixture of experts: towards
  effective blending of grey and black-box models
Jessica Leoni Valentina Breschi Simone Formentin Mara Tanelli
Traditional models grounded in first principles often struggle with accuracy
as the system's complexity increases. Conversely, machine learning approaches,
while powerful, face challenges in interpretability and in handling physical
constraints. Efforts to combine these models often often stumble upon
difficulties in finding a balance between accuracy and complexity. To address
these issues, we propose a comprehensive framework based on a "mixture of
experts" rationale. This approach enables the data-based fusion of diverse
local models, leveraging the full potential of first-principle-based priors.
Our solution allows independent training of experts, drawing on techniques from
both machine learning and system identification, and it supports both
collaborative and competitive learning paradigms. To enhance interpretability,
we penalize abrupt variations in the expert's combination. Experimental results
validate the effectiveness of our approach in producing an interpretable
combination of models closely resembling the target phenomena.