Physically Based Machine Learning for Hierarchical Materials

In multiscale phenomena, complex structure-function relationships emerge across different scales, making predictive modeling challenging. The recent scientific literature is exploring the possibility of leveraging machine learning, with a predominant focus on neural networks, excelling in data fitting, but often lacking insight into essential physical information. We propose the adoption of a symbolic data modeling technique, the ‘‘Evolutionary Polynomial Regression,’’ which integrates regression capabilities with the genetic programming paradigm, enabling the derivation of explicit analytical formulas, finally delivering a deeper comprehension of the analyzed physical phenomenon. To demonstrate the key advantages of our multiscale numerical approach, we consider the spider silk case. Based on a recent multiscale experimental dataset, we deduce the dependence of the macroscopic behavior from lowerscale arameters, also offering insights for improving a recent theoretical model by some of the authors. Our approach may represent a proof of concept for modeling in fields governed by multiscale, hierarchical differential equations.