Discovering Interpretable Bodily Fashions utilizing Symbolic Regression and Discrete ExteriorCalculus
Authors: Simone Manti, Alessandro Lucantonio
Summary: Computational modeling is a key useful resource to assemble perception into bodily techniques in fashionable scientific analysis and engineering. Whereas entry to great amount of knowledge has fueled using Machine Studying (ML) to recuperate bodily fashions from experiments and enhance the accuracy of bodily simulations, purely data-driven fashions have restricted generalization and interpretability. To beat these limitations, we suggest a framework that mixes Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of bodily fashions ranging from experimental information. Since these fashions include mathematical expressions, they’re interpretable and amenable to evaluation, and using a pure, general-purpose discrete mathematical language for physics favors generalization with restricted enter information. Importantly, DEC offers constructing blocks for the discrete analogue of area theories, that are past the state-of-the-art purposes of SR to bodily issues. Additional, we present that DEC permits to implement a strongly-typed SR process that ensures the mathematical consistency of the recovered fashions and reduces the search house of symbolic expressions. Lastly, we show the effectiveness of our methodology by re-discovering three fashions of Continuum Physics from artificial experimental information: Poisson equation, the Euler’s Elastica and the equations of Linear Elasticity. Because of their general-purpose nature, the strategies developed on this paper could also be utilized to various contexts of bodily modeling
