Plastic deformation and creep of structural metals and alloys is stochastic. This variability arises from uncontrollable variations in microstructure morphology and underlying constituent response. Such irremovable aleatoric uncertainty poses a major challenge to developing uncertainty-robust digital twins. We introduce high-throughput experimental methodologies, based on automated image tracking using Digital Image Correlation, to track stochastic response of structural metals while maintaining conformity to ASTM standards for testing. In the first half of the presentation, we will explore the use of this high-throughput methodology to calibrate uncertainty-aware constitutive models for logarithmic creep in stainless steels. We compare the constitutive response of additively manufactured and wrought austenitic stainless steels, and attribute differences to microstructural distinctions. In the second half, we use experimental data to calibrate a new machine learned stochastic constitutive model for elastoplastic response. The Variational Deep Material Network (VDMN), a physics-informed surrogate model enables efficient and probabilistic forward and inverse predictions of material behavior. The VDMN captures microstructure-induced variability by embedding variational distributions within its hierarchical, mechanistic architecture. Using an analytic propagation scheme based on Taylor-series expansion and automatic differentiation, the VDMN efficiently propagates uncertainty through the network during training and prediction. We demonstrate its capabilities in two digital twin-driven applications: (1) as an uncertainty-aware materials digital twin, it predicts and experimentally validates the nonlinear mechanical variability in additively manufactured polymer composites; and (2) as an inverse calibration engine, it disentangles and quantitatively identifies overlapping sources of uncertainty in constituent properties. Together, these results establish the VDMN as a foundation for uncertainty-robust materials digital twins. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.