Analytic field solution for machine learning integrating physics model and data driven approach

We derive analytical formulas for machine learning that merge a physics model with a data driven approach. We use a path integral method to find a field solution that calculates machine learning statistics while considering the physics model’s uncertainty, data limitations, geometry complexity, and mixed probability distributions due to field interactions. The formulas are exact and smoothly combine the physics model with observational data. The numerical realization of analytical expressions produces an interpretable, generative machine learning algorithm. We show the different machine learning options and their performances through examples of machine learning fields over complex geometries with interacting “hidden” nodes under data limitations, model uncertainty, and measurement noise constraints.