Generative Modeling of Random Fields from Limited Data via Constrained Latent Flow Matching

Deep generative models are promising tools for science and engineering, but their reliance on abundant, high-quality data limits applicability. We present a novel framework for generative modeling of random fields (probability distributions over continuous functions) that incorporates domain knowledge to supplement limited, sparse, and indirect data. The foundation of the approach is latent flow matching, where generative modeling occurs on compressed function representations in the latent space of a pre-trained variational autoencoder (VAE). Innovations include the adoption of a function decoder within the VAE and integration of physical/statistical constraints into the VAE training process. In this way, a latent function representation is learned that yields continuous random field samples satisfying domain-specific constraints when decoded, even in data-limited regimes. Efficacy is demonstrated on two challenging applications: wind velocity field reconstruction from sparse sensors and material property inference from a limited number of indirect measurements. Results show that the proposed framework achieves significant improvements in reconstruction accuracy compared to unconstrained methods and enables effective inference with relatively small training datasets that is intractable without constraints.

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.