Unifying Machine Learning and Physics Models Through a Mesoscopic Field Approach
We present a path-integral methods field solution that merges machine learning with microscopic physics models for mesoscopic phenomena. This interpretable multiscale algorithm treats physical and machine learning field solutions as equivalent, enabling seamless integration of microscopic physics intomachine learning algorithms for mesoscopic pattern learning and generation. Our approach incorporates microscopic physics mechanisms as hidden fields and represents their interactions with mesoscopic fields through auxiliary fields. Rather than imposing statistical assumptions on hidden nodes and learning weight statistics from data, our method derives a hidden fields formalism based on physics interaction mechanisms and determines connecting weights through action functional minimization and neural operators machine learning.Combining the strengths of both physicsmodeling and machine learning techniques,our method achieves strong performance in learning and generating mesoscopic patterns from limited data. It can capture physics interactions occurring at different scales,allowing forextrapolation when dealing with patterns with different interacting parameters and pattern evolution dynamics. We demonstrate our solution through a concrete case of two interacting species with microscopic chain structures, widely used for polymer material and biomolecular simulation. Our mesoscopicfield approach unifying machine learning and physics modelscan be readily usedin various areas of material science, biology, and social dynamics.
