Many physics-based problems are governed by parameterized phenomenological laws that are consistent with the principles of thermodynamics. While the underlying thermodynamic laws are well established, the associated model parameters are typically identified from experimental data or are otherwise subject to uncertainty. A stochastic description of these parameters leads to a stochastic reformulation of the governing partial differential equations, resulting in high-dimensional problems—either in the stochastic space, the physical discretization space, or both. To construct surrogate models for such problems, neural network–based approaches are often employed to map input features to quantities of interest. However, in high-dimensional settings, this typically requires large network architectures, which are computationally expensive to train and difficult to analyze. In this talk, we consider two complementary strategies to address these challenges: (i) the automatic identification of sparsity in neural network architectures through probabilistic training formulations, and (ii) the decomposition of the input feature space into local subdomains that are more tractable for training and analysis. Both sparsity-driven learning and domain decomposition enable flexible, locally refined architectures and allow for heterogeneous training strategies across subdomains. We demonstrate the effectiveness of these approaches through several examples from nonlinear solid mechanics involving both homogeneous and heterogeneous material parameters. REFERENCES [1] BP van de Weg, L Greve, B Rosic, Lomng short term relevance learning, International Journal for Uncertainty Quantification, Vol. 14, Issues 1, pp. 61-87, 2024 [2] T. Goode and B. Rosic, Doma