Machine Learning Surrogate Modeling for Homogenization of Hyperelastic Materials with Boolean Microstructures
arXiv:2606.00938v1 Announce Type: cross Abstract: Data-driven surrogate models are an alternative to numerical homogenization of heterogeneous materials. In this contribution, a supervised learning approach is presented for predicting effective Lam\'e parameters of hyperelastic composites from low-dimensional microstructural descriptors. The data set is based on previously published numerical homogenization results for ensembles of two-phase stochastic microstructures generated by planar Boolean models, covering variations of inclusion shape, phase contrast, and area fraction; see Br\"andel, Brands, Maike, Rheinbach, Schr\"oder, Schwarz and Stoyan (2022). A neural network is trained on combinations of scalar and curve-valued statistical descriptors, including the area fraction, a derived scalar shape descriptor $\tau$, the two-point correlation function $S_2(r)$, and the lineal-path function $\ell(z)$. Additional data representing limiting cases of the parameter space are incorporated