Andreas E. Robertson

Andreas E. Robertson, Samuel B. Inman, Ashley T. Lenau et al.

Aleatoric uncertainties - irremovable variability in microstructure morphology, constituent behavior, and processing conditions - pose a major challenge to developing uncertainty-robust digital twins. We introduce the Variational Deep Material Network (VDMN), a physics-informed surrogate model that 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.

Adam P. Generale, Andreas E. Robertson, Surya R. Kalidindi

Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of probability distributions representing possible outcomes of a specific process, existing frameworks cannot satisfactorily account for the impact of conditioning variables on these dynamics. Amongst several limitations, existing methods require training data with paired conditions and are developed for discrete conditioning variables. We propose Conditional Variable Flow Matching (CVFM), a framework for learning flows transforming conditional distributions with amortization across continuous conditioning variables - permitting predictions across the conditional density manifold. This is accomplished through several novel advances. In particular, simultaneous sample conditioned flows over the main and conditioning variables, alongside a conditional Wasserstein distance combined with a loss reweighting kernel facilitating conditional optimal transport. Collectively, these advances allow for learning system dynamics provided measurement data whose states and conditioning variables are not in correspondence. We demonstrate CVFM on a suite of increasingly challenging problems, including discrete and continuous conditional mapping benchmarks, image-to-image domain transfer, and modeling the temporal evolution of materials internal structure during manufacturing processes. We observe that CVFM results in improved performance and convergence characteristics over alternative conditional variants.

Michael Buzzy, Andreas Robertson, Peng Chen et al.

Recent advances in Foundation Models for Materials Science are poised to revolutionize the discovery, manufacture, and design of novel materials with tailored properties and responses. Although great strides have been made, successes have been restricted to materials classes where multi-million sample data repositories can be readily curated (e.g., atomistic structures). Unfortunately, for many structural and functional materials (e.g., mesoscale structured metal alloys), such datasets are too costly or prohibitive to construct; instead, datasets are limited to very few examples. To address this challenge, we introduce a novel machine learning approach for learning from hyper-sparse, complex spatial data in scientific domains. Our core contribution is a physics-driven data augmentation scheme that leverages an ensemble of local generative models, trained on as few as five experimental observations, and coordinates them through a novel diversity curation strategy to generate a large-scale, physically diverse dataset. We utilize this framework to construct PolyMicros, the first Foundation Model for polycrystalline materials (a structural material class important across a broad range of industrial and scientific applications). We demonstrate the utility of PolyMicros by zero-shot solving several long standing challenges related to accelerating 3D experimental microscopy. Finally, we make both our models and datasets openly available to the community.