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The inflow velocity and its uncertainty in the Sandia Hypersonic Wind Tunnel (HWT) are the main quantities of interest in this work. This memo describes the velocity uncertainty using the standard tunnel condition measurements and processes in use in the HWT as of February 2026.
Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.
This final technical report summarizes the key accomplishments on the unfolding using diffusion model project, a DOE award received by PI Pierre-Hugues Beauchemin at Tufts University. This project main goal was to investigate the potential of diffusion models for unfolding experimental High Energy Physics data from detector effects while controlling systematics uncertainties. The project accomplished its goals by completing the following objectives: 1) Performing an object-by-object, event-by-event unfolding of various kinematic distributions reconstructed from detector data in HEP in a way that keeps correlations between unfolded observables while demonstrating competitive performance compared to standard algorithms used in the field; 2) Address the generalization problem by developing an unfolding algorithm capable to correctly infer the underlying distributions of observables and processes never seen before, while controlling the dominant theoretical uncertainties affecting the process, therefore increasing the effectiveness, the precision, and the applicability of the developed algorithm; 3) Understand the theoretical foundations between the developed algorithm so to extend it to applications beyond experimental HEP, for broader benefits to the society. This report provides an overview of the accomplishments related to each of these key objectives.
Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.
Soft X-ray off-axis elliptical mirrors bring new challenges for X-ray mirror metrology. These highly asymmetrically curved elliptical cylindrical mirrors with a total slope range >10 mrad are extremely challenging to measure. Their total slope range exceeds the measuring range of most angular sensors used for X-ray mirror inspection. To overcome this problem, it is possible to stitch partial slope data by measuring the mirror at different pitch angles (multi-pitch angles). By revisiting the theory of the multi-pitch Nano-accuracy Surface Profiler (NSP), we derive the sampling position error on the mirror surface as a function of the mirror height profile and the measurement error of the pitch rotation center. When measuring “extreme”, highly asymmetrically curved, elliptical mirrors, the calculation of the mirror height profile with iterative reconstruction outperforms the classical “flat assumption” (i.e., assuming that the mirror sag is negligible). As demonstrated by our simulations, a proper tolerance evaluation on the measurement of pitch rotation center is needed to assess the measurement accuracy (systematic error) for these strongly aspherical mirrors using the multi-pitch NSP technique. Taking a real design of an “extreme” elliptical mirror as a case study, we conduct a Monte Carlo simulation to mimic the measurement and characterization process to analyze the impact of several error sources. With the measurement uncertainty of the pitch rotation center, the multi-pitch NSP measurement can estimate the grazing angle θ and the chief ray location x o with their uncertainties, as well as the slope residuals.
Wind turbine-related mortality may pose a population-level threat for migratory tree-roosting bats, such as the hoary bat (Lasiurus cinereus) in North America. These species are dispersed within their range, making it impractical to estimate census populations size using traditional survey methods. Nonetheless, understanding population size and trends is essential for evaluating and mitigating risk from wind turbine mortality. Using various sampling techniques, including systematic acoustic sampling and genetic analyses, we argue that building a weight of evidence regarding bat population status and trends is possible to (1) assess the sustainability of mortality associated with wind turbines; (2) determine the level of mitigation required; and (3) evaluate the effectiveness of mitigation measures to ensure population viability for these species. Long-term, systematic data collection remains the most viable option for reducing uncertainty regarding population trends for migratory tree-roosting bats. We recommend collecting acoustic data using the statistically robust North American Bat Monitoring Program (NABat) protocols and that genetic diversity is monitored at repeated time intervals to show species trends. There are no short-term actions to resolve these population-level questions; however, we discuss opportunities for relatively short-term investments that will lead to long-term success in reducing uncertainty.
Prescribed fire is a vital tool for ecosystem management and wildfire risk reduction but its escalation is constrained by overly conservative burn windows because of uncertainties, for instance, in wind forecasts. This review describes the state of the art in weather product use by fire/smoke models and identifies three priority research gaps that artificial intelligence/machine learning (AI/ML) is well positioned to address: (1) spatial and temporal downscaling to meter-scale, sub-hourly wind fields; (2) bias correction for systematic model errors in complex terrain; and (3) robust uncertainty quantification to inform ensemble-based simulations. Emerging AI/ML techniques offer promising frameworks to address all three challenges. By providing high-resolution, bias-corrected, and probabilistic wind fields, AI/ML-enhanced forecasts will allow for expanded burn windows, improved ignition strategy design and a reduced reliance on expert intuition, especially when a prescribed fire is introduced into new areas.
Current mid-fidelity modeling approaches for floating offshore wind turbines (FOWTs) have been found to underpredict the nonlinear, low-frequency wave excitation and the response of semisubmersible FOWTs. To examine the cause of this underprediction, the OC6 project is using computational fluid dynamics (CFD) tools to investigate the wave loads on the OC5-DeepCwind semisubmersible, with a focus on the nonlinear difference-frequency excitation. This paper focuses on assessing the uncertainty of the CFD predictions from simulations of the semisubmersible in a fixed condition under bichromatic wave loading and on establishing confidence in the results for use in improving mid-fidelity models. The uncertainty for the nonlinear wave excitation is found to be acceptable but larger than that for the wave-frequency excitation, with the spatial discretization error being the dominant contributor. Further, unwanted free waves at the difference frequency have been identified in the CFD solution. A wave-splitting and wave load-correction procedure are presented to remove the contamination from the free waves in the results. A preliminary comparison to second-order potential-flow theory shows that the CFD model predicted significantly higher difference-frequency wave excitations, especially in surge, suggesting that the CFD results can be used to better calibrate the mid-fidelity tools.
Controlled islanding plays an essential role in preventing the blackout of power systems. Although there are several studies on this topic in the past, not enough attention is paid to the uncertainty brought by renewable energy sources (RESs) that may cause unpredictable unbalanced power and the observability of power systems after islanding that is essential for back-up black-start measures. Therefore, a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming (MISOCCP) is proposed to address these issues. First, the uncertainty of RESs is characterized by their possibility distribution models with chance constraints, and the requirements, e. g., system observ-ability, for rapid back-up black-start measures are also considered. Then, a law of large numbers (LLN) based method is employed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex one. Finally, case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed model. The results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.
Abstract Type Ia supernova (SN) measurements of the Hubble constant, H 0 ; cosmic mass density, Ω M ; and dark energy equation-of-state parameter, w , rely on heterogeneous SN surveys across three decades of observation. These distinct surveys may have undiagnosed, relative photometric zero-point errors. We determine the sensitivities of the SH0ES+Pantheon+ cosmological constraints to unknown gray systematics in the photometric zero-point calibration between the 19 surveys that comprise the Pantheon+ SN compendium. Varying the surveys’ gray zero-points simultaneously with cosmological parameters, we determine that the SH0ES+Pantheon+ measurement of H 0 is robust against gray intersurvey photometric miscalibration. Specifically, uncalibrated intersurvey systematics could represent a source of uncertainty no larger than 0.39 km s −1 Mpc −1 for H 0 . This modest increase in H 0 uncertainty could not account for the 7 km s −1 Mpc −1 “Hubble tension” between the SH0ES measurement of H 0 and the Planck ΛCDM-based inference of H 0 . However, the SH0ES+Pantheon+ best-fit values of Ω M and w are not robust against gray zero-point error, slipping by up to 0.16 and −0.63. Because measurements of Ω M and w depend on intrasurvey cross-band calibration, the hypothetical gray miscalibration underestimates the sensitivity of these measurements to zero-point miscalibration. Because the Pantheon+ compendium contains many surveys that share low- z Hubble flow (HF) and Cepheid-paired SNe, intersurvey photometric calibration errors do not significantly impede the joint use of SH0ES and Pantheon+ to measure H 0 to 1% accuracy. However, H 0 constraints that rely on one HF survey but numerous galactic distance calibration surveys are susceptible to intersurvey photometric miscalibration.
Abstract The observation of X-rays during quiescence from transiently accreting neutron stars provides unique clues about the nature of dense matter. This, however, requires extensive modeling of the crusts and matching the results to observations. The pycnonuclear fusion reaction rates implemented in these models are theoretically calculated by extending phenomenological expressions and have large uncertainties spanning many orders of magnitude. We present the first sensitivity studies of these pycnonuclear fusion reactions in realistic network calculations. We also couple the reaction network with the thermal evolution code dStar to further study their impact on the neutron star cooling curves in quiescence. Varying the pycnonuclear fusion reaction rates alters the depth at which nuclear heat is deposited although the total heating remains constant. The enhancement of the pycnonuclear fusion reaction rates leads to an overall shallower deposition of nuclear heat. The impurity factors are also altered depending on the type of ashes deposited on the crust. These total changes correspond to a variation of up to 9 eV in the modeled cooling curves. While this is not sufficient to explain the shallow heat source, it is comparable to the observational uncertainties and can still be important for modeling the neutron star crust.
The precise atomic structure and therefore the wavelength-dependent opacities of lanthanides are highly uncertain. This uncertainty introduces systematic errors in modeling transients like kilonovae and estimating key properties such as mass, characteristic velocity, and heavy metal content. Here, we quantify how atomic data from across the literature as well as choices of thermalization efficiency of r-process radioactive decay heating impact the light curve and spectra of kilonovae. Specifically, we analyze the spectra of a grid of models produced by the radiative transfer code Sedona that span the expected range of kilonova properties to identify regions with the highest systematic uncertainty. Our findings indicate that differences in atomic data have a substantial impact on estimates of lanthanide mass fraction, spanning approximately 1 order of magnitude for lanthanide-rich ejecta, and demonstrate the difficulty in precisely measuring the lanthanide fraction in lanthanide-poor ejecta. Mass estimates vary typically by 25%–40% for differing atomic data. Similarly, the choice of thermalization efficiency can affect mass estimates by 20%–50%. Observational properties such as color and decay rate are highly model dependent. Velocity estimation, when fitting solely based on the light curve, can have a typical error of ∼100%. Atomic data of light r-process elements can strongly affect blue emission. Even for well-observed events like GW170817, the total lanthanide production estimated using different atomic data sets can vary by a factor of ∼6.
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.
This study investigates uncertainties in greenhouse gas (GHG) emission factors related to switchgrass-based biofuel production in Michigan. Using three life cycle assessment (LCA) databases— US lifecycle inventory database (USLCI), GREET, and Ecoinvent—each with multiple versions, we recalculated the global warming intensity (GWI) and GHG mitigation potential in a static calculation. Employing Monte Carlo simulations along with local and global sensitivity analyses, we assess uncertainties and pinpoint key parameters influencing GWI.
Abstract. Gap-filling eddy covariance CO2 fluxes is challenging at dryland sites due to small CO2 fluxes. Here, four machine learning (ML) algorithms including artificial neural network (ANN), k-nearest neighbors (KNNs), random forest (RF), and support vector machine (SVM) are employed and evaluated for gap-filling CO2 fluxes over a semiarid sagebrush ecosystem with different lengths of artificial gaps. The ANN and RF algorithms outperform the KNN and SVM in filling gaps ranging from hours to days, with the RF being more time efficient than the ANN. Performances of the ANN and RF are largely degraded for extremely long gaps of 2 months. In addition, our results suggest that there is no need to fill the daytime and nighttime net ecosystem exchange (NEE) gaps separately when using the ANN and RF. With the ANN and RF, the gap-filling-induced uncertainties in the annual NEE at this site are estimated to be within 16 g C m−2, whereas the uncertainties by the KNN and SVM can be as large as 27 g C m−2. To better fill extremely long gaps of a few months, we test a two-layer gap-filling framework based on the RF. With this framework, the model performance is improved significantly, especially for the nighttime data. Therefore, this approach provides an alternative in filling extremely long gaps to characterize annual carbon budgets and interannual variability in dryland ecosystems.
Abstract. This study investigated the computational benefits of using multi-fidelity statistical estimation (MFSE) algorithms to quantify uncertainty in the mass change of Humboldt Glacier, Greenland, between 2007 and 2100 using a single climate change scenario. The goal of this study was to determine whether MFSE can use multiple models of varying cost and accuracy to reduce the computational cost of estimating the mean and variance of the projected mass change of a glacier. The problem size and complexity were chosen to reflect the challenges posed by future continental-scale studies while still facilitating a computationally feasible investigation of MFSE methods. When quantifying uncertainty introduced by a high-dimensional parameterization of the basal friction field, MFSE was able to reduce the mean-squared error in the estimates of the statistics by well over an order of magnitude when compared to a single-fidelity approach that only used the highest-fidelity model. This significant reduction in computational cost was achieved despite the low-fidelity models used being incapable of capturing the local features of the ice-flow fields predicted by the high-fidelity model. The MFSE algorithms were able to effectively leverage the high correlation between each model's predictions of mass change, which all responded similarly to perturbations in the model inputs. Consequently, our results suggest that MFSE could be highly useful for reducing the cost of computing continental-scale probabilistic projections of sea-level rise due to ice-sheet mass change.
Simple climate models (SCMs) are frequently used in research and decision-making communities because of their flexibility, tractability, and low computational cost. SCMs can be idealized, flexibly representing major climate dynamics as impulse response functions, or process-based, using explicit equations to model possibly nonlinear climate and Earth system dynamics. Each of these approaches has strengths and limitations. Here we present and test a hybrid impulse response modeling framework (HIRM) that combines the strengths of process-based SCMs in an idealized impulse response model, with HIRM's input derived from the output of a process-based model. This structure enables the model to capture some of the major nonlinear dynamics that occur in complex climate models as greenhouse gas emissions transform to atmospheric concentration to radiative forcing to climate change. As a test, the HIRM framework was configured to emulate the total temperature of the simple climate model Hector 2.0 under the four Representative Concentration Pathways and the temperature response of an abrupt 4 times CO 2 concentration step. HIRM was able to reproduce near-term and long-term Hector global temperature with a high degree of fidelity. Additionally, we conducted two case studies to demonstrate potential applications for this hybrid model: examining the effect of aerosol forcing uncertainty on global temperature and incorporating more process-based representations of black carbon into a SCM. The open-source HIRM framework has a range of applications including complex climate model emulation, uncertainty analyses of radiative forcing, attribution studies, and climate model development.
This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.