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.

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.

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 .

Nonlinear aeroelastic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative nature of linearization is often favored. Therefore, there is a requirement for novel nonlinear aeroelastic model reduction approaches that are accurate, simple and, most importantly, efficient to generate. This paper proposes a novel formulation for the identification of a compact multi-input Volterra series, where Orthogonal Matching Pursuit is used to obtain a set of optimally sparse nonlinear multi-input ROM coefficients from unsteady aerodynamic training data. The framework is exemplified using the Benchmark Supercritical Wing, considering; forced response, flutter and limit cycle oscillation. The simple and efficient Optimal Sparsity Multi-Input ROM (OSM-ROM) framework performs with high accuracy compared to the full-order aeroelastic model, requiring only a fraction of the tens-of-thousands of possible multi-input terms to be identified and allowing a 96% reduction in the number of training samples.

We outline the principles of classical assurance for computer-based systems that pose significant risks. We then consider application of these principles to systems that employ Artificial Intelligence (AI) and Machine Learning (ML). A key element in this "dependability" perspective is a requirement to have near-complete understanding of the behavior of critical components, and this is considered infeasible for AI and ML. Hence the dependability perspective aims to minimize trust in AI and ML elements by using "defense in depth" with a hierarchy of less complex systems, some of which may be highly assured conventionally engineered components, to "guard" them. This may be contrasted with the "trustworthy" perspective that seeks to apply assurance to the AI and ML elements themselves. In cyber-physical and many other systems, it is difficult to provide guards that do not depend on AI and ML to perceive their environment (e.g., other vehicles sharing the road with a self-driving car), so both perspectives are needed and there is a continuum or spectrum between them. We focus on architectures toward the dependability end of the continuum and invite others to consider additional points along the spectrum. For guards that require perception using AI and ML, we examine ways to minimize the trust placed in these elements; they include diversity, defense in depth, explanations, and micro-ODDs. We also examine methods to enforce acceptable behavior, given a model of the world. These include classical cyber-physical calculations and envelopes, and normative rules based on overarching principles, constitutions, ethics, or reputation. We apply our perspective to autonomous systems, AI systems for specific functions, generic AI such as Large Language Models, and to Artificial General Intelligence (AGI), and we propose current best practice and an agenda for research.