arXiv subjects

Michael C. Stanley

Publications and source records attributed to Michael C. Stanley.

3 recordsLinked to original sources

arXiv2026

Latent Generative Modeling of Random Fields from Limited Training Data

The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative models offer a powerful tool for sampling high- or infinite-dimensional uncertainties like random fields, but their reliance on large, dense training datasets limits their applicability in contexts where sufficient data is difficult or expensive to obtain. In this work, we propose a latent-space approach to generative modeling of random fields that incorporates domain knowledge to supplement limited training data. A constraint-aware variational autoencoder (VAE) with a function decoder is first used to learn compact latent representations of continuous functions that adhere to known physical or statistical constraints, even when training data is sparse or indirect. Generative modeling is then performed in the learned latent space, decoupling constraint enforcement from the sampling process. This decoupling enables expressive multi-step generative methods to be deployed in data-limited settings where existing constrained multi-step approaches are not directly applicable. The richer latent distributions captured by the generative model also overcome limitations of standard VAEs, which rely on simple parametric priors and struggle to represent complex, multimodal, or heavy-tailed distributions over functions. Efficacy is demonstrated on two challenging applications: wind velocity field reconstruction from sparse sensors and material property inference from indirect measurements. Results show the effectiveness of incorporating domain knowledge constraints for data-limited problems and the improved sample quality and robustness of the latent generative modeling approach versus directly sampling a constrained VAE.

cs.LG↗

arXiv2025

Bond strength uncertainty quantification via confidence intervals for nondestructive evaluation of bonded composites

As bonded composite materials are used more frequently for aerospace applications, it is necessary to certify that parts achieve desired levels of certain physical characteristics (e.g., strength) for safety and performance. Nondestructive evaluation (NDE) of adhesively bonded structures enables verification of bond physical characteristics, but uncertainty quantification (UQ) of NDE estimates is crucial for understanding risks, especially for NDE estimates like bond strength. To address the critical need for NDE UQ for adhesive bond strength estimates, we propose an optimization--based approach to computing finite--sample confidence intervals showing the range of bond strengths that could feasibly be produced by the observed data. A statistical inverse model approach is used to compute a confidence interval of specimen interfacial stiffness from swept--frequency ultrasonic phase observations and a method for propagating the interval to bond strength via a known interfacial stiffness regression is proposed. This approach requires innovating the optimization--based confidence interval to handle both a nonlinear forward model and unknown variance and developing a calibration approach to ensure that the final bond strength interval achieves at least the desired coverage level. Using model assumptions in line with current literature, we demonstrate our approach on simulated measurement data using a variety of low to high noise settings under two prototypical parameter settings. Relative to a baseline approach, we show that our method achieves better coverage and smaller intervals in high--noise settings and when a nuisance parameter is near the constraint boundary.

stat.ME↗

arXiv2025

Generative Modeling of Microweather Wind Velocities for Urban Air Mobility

Motivated by the pursuit of safe, reliable, and weather-tolerant urban air mobility (UAM) solutions, this work proposes a generative modeling approach for characterizing microweather wind velocities. Microweather, or the weather conditions in highly localized areas, is particularly complex in urban environments owing to the chaotic and turbulent nature of wind flows. Furthermore, traditional means of assessing local wind fields are not generally viable solutions for UAM applications: 1) field measurements that would rely on permanent wind profiling systems in operational air space are not practical, 2) physics-based models that simulate fluid dynamics at a sufficiently high resolution are not computationally tractable, and 3) data-driven modeling approaches that are largely deterministic ignore the inherent variability in turbulent flows that dictates UAM reliability. Thus, advancements in predictive capabilities are needed to help mitigate the unique operational safety risks that microweather winds pose for smaller, lighter weight UAM aircraft. This work aims to model microweather wind velocities in a manner that is computationally-efficient, captures random variability, and would only require a temporary, rather than permanent, field measurement campaign. Inspired by recent breakthroughs in conditional generative AI such as text-to-image generation, the proposed approach learns a probabilistic macro-to-microweather mapping between regional weather forecasts and measured local wind velocities using generative modeling (denoising diffusion probabilistic models, flow matching, and Gaussian mixture models). A simple proof of concept was implemented using a dataset comprised of local (micro) measurements from a Sonic Detection and Ranging (SoDAR) wind profiler along with (macro) forecast data from a nearby weather station over the same time period.

cs.CE↗