Discovering Interpretable Bodily Fashions utilizing Symbolic Regression and Discrete ExteriorCalculus
Authors: Simone Manti, Alessandro Lucantonio
Summary: Computational modeling is a key useful resource to collect perception into bodily methods in trendy scientific analysis and engineering. Whereas entry to great amount of knowledge has fueled using Machine Studying (ML) to get well 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 knowledge. Since these fashions encompass 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 knowledge. Importantly, DEC gives constructing blocks for the discrete analogue of subject theories, that are past the state-of-the-art functions 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 area of symbolic expressions. Lastly, we show the effectiveness of our methodology by re-discovering three fashions of Continuum Physics from artificial experimental knowledge: 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 numerous contexts of bodily modeling
