arXiv subjects

Andreas E. Robertson

Publications and source records attributed to Andreas E. Robertson.

6 recordsLinked to original sources

arXiv2026

Materials Behavior as Mechanism Ensembles: A Probabilistic Framework for Emergent Behaviors

Materials behavior is often treated as a deterministic mapping from structure to properties, yet many important phenomena emerge from the conditional activation of multiple mechanisms across scales. This is especially evident in fatigue of metals, where crack growth is typically modeled as monotonic and irreversible process, despite evidence that local microstructure, loading history, and competing unit processes can shift the balance among propagation, arrest, and self-healing. Here we present a probabilistic framework that describes materials behavior as an ensemble of constituent mechanisms whose activation, interaction, and evolution determine emergent outcomes. The framework connects mechanism activation, state evolution, and macroscopic observables in a probabilistic way. In the case of fatigue crack propagation, it reframes damage tolerance as an inference problem over mechanism competition and provides a basis for integrating multiscale simulation, multimodal characterization, and machine learning. The same logic extends to other physical and chemical systems suggesting a portable framework for any system in which emergent behavior reflects mechanism competition under changing conditions. The broader ambition of this perspective review is a shift from correlating structure and performance after the fact to identifying, in advance, the conditions that make desired emergent behavior probable.

cond-mat.mtrl-sci↗

arXiv2026

Modeling Stochastic Conditional Dynamics from Sparse Observations via Kernel-Stabilized Flow Matching

Learning to transform conditional probability densities over time is a fundamental challenge spanning probabilistic modeling and the natural sciences. This task is paramount when forecasting the evolution of stochastic nonlinear dynamical systems in biological and physical domains. While flow-based models can predict the temporal evolution of probability distributions, existing approaches often assume discrete conditioning with samples that are paired across time, limiting their scientific applicability where frequently only sparse data with unpaired continuous conditioning is available. We propose Conditional Variable Flow Matching (CVFM), a framework for learning flows transforming conditional distributions with amortization across the continuous space of conditional densities. CVFM addresses the high-variance instability of prior methods by jointly sampling flows over state and conditioning variables, utilizing a conditioning mismatch kernel alongside a conditional Wasserstein distance to reweight the conditional optimal transport objective. Collectively, these advances allow for learning dynamics from sparse unpaired measurements of state-condition across time. We evaluate CVFM on conditional mapping benchmarks and a case study modeling the temporal evolution of materials internal structure during manufacturing processes, observing improved performance and convergence characteristics over existing conditional variants. Code is available at https://github.com/agenerale/conditional-variable-flow-matching.

cs.LG↗

arXiv2025

Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins

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.

cs.LG↗

arXiv2025

Equilibrium Conserving Neural Operators for Super-Resolution Learning

Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-resolution training data. In this paper, we break this limitation; we introduce a framework for super-resolution learning in solid mechanics problems. Our approach allows one to train a high-resolution neural network using only low-resolution data. Our Equilibrium Conserving Operator (ECO) architecture embeds known physics directly into the network to make up for missing high-resolution information during training. We evaluate this ECO-based super-resolution framework that strongly enforces conservation-laws in the predicted solutions on two working examples: embedded pores in a homogenized matrix and randomly textured polycrystalline materials. ECO eliminates the reliance on high-fidelity data and reduces the upfront cost of data collection by two orders of magnitude, offering a robust pathway for resource-efficient surrogate modeling in materials modeling. ECO is readily generalizable to other physics-based problems.

cs.LG↗

arXiv2021

Digital representation and quantification of discrete dislocation networks

Dislocation networks and their evolution are known to control the mechanical properties of metal samples. However, the lack of computationally efficient and statistically rigorous descriptors for such defect systems has hindered the development and adoption of rational protocols for the optimal design of these material systems. This study presents a framework for the rigorous statistical quantification and low dimensional representation of dislocation networks using the formalism of 2-point spatial correlations (also called 2-point statistics) along with Principle Component Analysis (PCA). The usefulness of this basic framework for comparing and observing dislocation networks is exemplified and discussed with suitable examples.

cond-mat.dis-nn↗

arXiv2015

Mesoscale solubilization and critical phenomena in binary and quasi binary solutions of hydrotropes

Hydrotropes are substances consisting of amphiphilic molecules that are too small to self assemble in equilibrium structures in aqueous solutions, but can form dynamic molecular clusters H bonded with water molecules. Some hydrotropes, such as low molecular weight alcohols and amines, can solubilize hydrophobic compounds in aqueous solutions at a mesoscopic scale, around 100 nm, with formation of long lived mesoscale droplets. In this work, we report on the studies of near critical and phase behavior of binary, 2,6-lutidine - H2O, and quasibinary, 2,6-lutidine - H2O - D2O, and tert-butanol - 2-butanol - H2O solutions in the presence of a solubilized hydrophobic impurity, cyclohexane. In additional to visual observation of fluid phase equilibria, two experimental techniques were used - light scattering and small - angle neutron scattering. It was found that the increase of the tert-butanol to 2-butanol ratio affects the liquid - liquid equilibria in the quasi-binary system at ambient pressure in the same way as the increase of pressure modifies the phase behavior of binary 2-butanol - H2O solutions. The correlation length of critical fluctuations near the liquid-liquid separation and the size of mesoscale droplets of solubilized cyclohexane were obtained by dynamic light scattering and by small - angle neutron scattering. It is shown that the effect of the presence of small amounts of cyclohexane on the near - critical phase behavior is twofold - the transition temperature changes towards increasing the two-phase domain, and long-lived mesoscopic inhomogeneities emerge in the macroscopically homogeneous domain. These homogeneities remain unchanged upon approach to the critical point of macroscopic phase separation and do not alter the universal nature of criticality. However, a larger amount of cyclohexane generates additional liquid-liquid phase separation at lower temperatures.

cond-mat.soft↗