Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue arises in scenarios where the likelihood of error inferred from learned representations follows a bimodal distribution, resulting from the coexistence of confident and ambiguous predictions. Standard regression approaches often struggle to adequately express this predictive uncertainty, as they implicitly assume unimodal Gaussian noise, leading to mean-collapse behavior in such settings. Although Mixture Density Networks (MDNs) can represent different distributions, they suffer from severe optimization instability. We propose a family of distribution-aware loss functions integrating normalized RMSE with Wasserstein and Cramér distances. When applied to standard deep regression models, our approach recovers bimodal distributions without the volatility of mixture models. Validated across four experimental stages, our results show that the proposed Wasserstein loss establishes a new Pareto efficiency frontier: matching the stability of standard regression losses like MSE in unimodal tasks while reducing Jensen-Shannon Divergence by 45% on complex bimodal datasets. Our framework strictly dominates MDNs in both fidelity and robustness, offering a reliable tool for aleatoric uncertainty estimation in trustworthy AI systems.

This work demonstrates the possibilities for improving wildfire and air quality management in the western United States by leveraging the unprecedented hourly data from NASA's TEMPO satellite mission and advances in self-supervised deep learning. Here we demonstrate the efficacy of deep learning for mapping the near real-time hourly spread of wildfire fronts and smoke plumes using an innovative self-supervised deep learning-system: successfully distinguishing smoke plumes from clouds using GOES-18 and TEMPO data, strong agreement across the smoke and fire masks generated from different sensing modalities as well as significant improvement over operational products for the same cases.

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

In particular, Theorem 5 applies when null A δ = { δ }, i.e., when θ null A is just a standard, non-robust, solution. This is different from [56], whose main result is only applicable to solutions satisfying the infinitely many constraints f (θ, δ) 0, δ A δ i, i = 1,...,N, where A δ i is tuned to the Wasserstein bound. As previously noted, R plays the role of a tunable parameter, and the result in Theorem 5 holds for any choice of the value ofR . As a consequence, the user can play with R to optimize the bound on Risk ( θ null A) given in Theorem 5. As R increases, s A, null A (and, thereby, ε (s A, null A)) tends to increase while µ/R diminishes. While the best compromise is difficult to foresee, one can experimentally try various choices R 1 < R 2 < < R i < R h and select the one giving the best result. The corresponding confidence level can be bounded as follows: P Nnull D: Risk (θ null A) > ε (s A, null A,i) + µ R i for at least one i { 1,...h } null h null i =1P Nnull D: Risk (θ null A) > ε (s A, null A,i) + µ R i null h null i =1β = hβ, 29 from which P Nnull D: Risk ( θ null A) ε ( s A, null A,i) + µ R i for all i = 1,...h null 1 hβ.

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.

The increasing complexity of autonomous systems has amplified the need for accurate and reliable labeling of runway and taxiway markings to ensure operational safety. Precise detection and labeling of these markings are critical for tasks such as navigation, landing assistance, and ground control automation. Existing labeling algorithms, like the Automated Line Identification and Notation Algorithm (ALINA), have demonstrated success in identifying taxiway markings but encounter significant challenges when applied to runway markings. This limitation arises due to notable differences in line characteristics, environmental context, and interference from elements such as shadows, tire marks, and varying surface conditions. To address these challenges, we modified ALINA by adjusting color thresholds and refining region of interest (ROI) selection to better suit runway-specific contexts. While these modifications yielded limited improvements, the algorithm still struggled with consistent runway identification, often mislabeling elements such as the horizon or non-relevant background features. This highlighted the need for a more robust solution capable of adapting to diverse visual interferences. In this paper, we propose integrating a classification step using a Convolutional Neural Network (CNN) named AssistNet. By incorporating this classification step, the detection pipeline becomes more resilient to environmental variations and misclassifications. This work not only identifies the challenges but also outlines solutions, paving the way for improved automated labeling techniques essential for autonomous aviation systems.

Ensuring safe separation between aircraft is a critical challenge in air traffic management, particularly in urban air mobility (UAM) environments where high traffic density and low altitudes require precise control. In these environments, conflicts often arise at the intersections of flight corridors, posing significant risks. We propose a tactical separation approach leveraging shared scheduling protocols, originally designed for Ethernet networks and operating systems, to coordinate access to these intersections. Using a decentralized Markov decision process framework, the proposed approach enables aircraft to autonomously adjust their speed and timing as they navigate these critical areas, maintaining safe separation without a central controller. We evaluate the effectiveness of this approach in simulated UAM scenarios, demonstrating its ability to reduce separation violations to zero while acknowledging trade-offs in flight times as traffic density increases. Additionally, we explore the impact of non-compliant aircraft, showing that while shared scheduling protocols can no longer guarantee safe separation, they still provide significant improvements over systems without scheduling protocols.

An interactive map has revealed a disturbing pattern in drone sightings across the US. An unexplained drone invasion has targeted America's military bases worldwide since October, beginning with a swarm over Langley Air Force Base in Virginia. The pattern became evident when similar activity was reported over New Jersey's Picatinny Arsenal on November 18. Less than one week later, US bases in England and Germany began grappling with incursions by'small unmanned aerial systems.' Back in America sightings were gaining traction. 'Multiple' instances of drones appeared over New Jersey's Navy weapons station, and Ohio's Wright-Patterson Air Force Base closed its airspace due to similar activity on December 13.

New reporting about over a dozen unidentified drones that were allowed to fly over Langley Air Force Base has prompted fresh calls for change to a threat that experts say will only become more prevalent. For more than two weeks in December 2023, the mystery drones traipsed into restricted airspace over the installation, home to key national security facilities and the F-22 Raptor stealth fighters. Experts say the incident is likely one of many that U.S. authorities are underprepared to tackle in an evolving threat environment. Lack of a standard protocol for such incursions left Langley officials unsure of what to do – other than allow the 20-foot-long drones to hover near their classified facilities. The Pentagon has said little about the incidents other than to confirm they occurred after a Wall Street Journal report this month.

The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .