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DOE OSTI2022

Using Ensemble Data Assimilation to Estimate Transient Hydrologic Exchange Flow Under Highly Dynamic Flow Conditions

Abstract Quantifying dynamic hydrologic exchange flows (HEFs) within river corridors that experience high‐frequency flow variations caused by dam regulations is important for understanding the biogeochemical processes at the river water and groundwater interfaces. Heat has been widely used as a tracer to infer steady‐state flow velocities through analytical solutions of heat transport defined by the diurnal temperature signals. Under sub‐daily dynamic flow conditions, however, such analytical solutions are not applicable due to the violation of their fundamental assumptions. In this study, we developed a data assimilation‐based approach to estimate the sub‐daily flux under highly dynamic flow conditions using multi‐depth temperature observations at a 5‐min resolution. If the hydraulic gradient is measured, Darcy's law was used to calculate the flux with permeability estimated from temperature responses below the riverbed. Otherwise, flux was estimated directly by assimilating multi‐depth temperature data at 1‐ or 2‐hr time intervals assuming one‐dimensional flow and heat transport governing equation. By comparing estimated fluxes with model‐generated synthetic truth, we demonstrated that both schemes have robust performance in estimating fluxes under highly dynamic flow conditions. This data assimilation‐based flux estimation method was able to capture the vertical sub‐daily fluxes using multi‐depth high‐resolution temperature data alone, even in the presence of multi‐dimensional flow. This approach has been successfully applied to real field temperature data collected at the Hanford site, which experiences highly dynamic HEFs. Our study shows the promise of adopting distributed 1‐D temperature monitoring to capture spatial and temporal exchange dynamics in river corridors at a watershed scale or beyond.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Coupled Deep Learning Model for Estimating Surface NO 2 Levels from Remote Sensing Data: 15-Year Study Over the Contiguous United States

This study proposes a novel two-step deep learning (DL) model for estimating surface NO 2 concentrations using satellite data over the contiguous United States (CONUS) from 2005 to 2019. The first phase of the model uses partial convolutional neural network (PCNN), an advanced DL model that accurately imputes gaps between surface NO 2 stations and creates 5,478 daily-mean NO 2 grids (PCNN-NO 2 ) of the 2005-2019 period over the study area. We then feed the PCNN-NO 2 , along with other predictor variables, into a deep neural network (DNN) to estimate surface NO 2 levels, achieving exceptional performance with a correlation coefficient of 0.975 to 0.978, a mean absolute bias of 0.99 ppb to 1.38 ppb, and a root mean square error of 1.47 ppb to 1.97 ppb. Spatial cross-validation results also indicate strong spatial performance of PCNN-DNN surface NO 2 estimates. In addition to its accurate estimates, the PCNN-DNN model consistently generates estimated NO 2 grids without any missing values, improving the quality of various applications such as emission reduction strategies and public health studies. Between 2005 and 2019, the 5,478 daily estimated NO 2 grids over the CONUS reveal significant reductions in NO 2 levels in fourteen major urban environments: Washington D.C. (-43%), New York (-45%), Los Angeles (-38%), Chicago (-25%), Boston (-43%), Houston (-34%), Dallas (-40%), Philadelphia (-41%), Phoenix (-38%), Detroit (-20%), Denver (-23%), Atlanta (-0.7%), Cincinnati (-38%), and Pittsburgh (-56%). Furthermore, the study shows that the denser urban regions that in-situ stations are installed in, the higher the difference between in-situ observations and regional-mean NO 2 levels.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Deep Learning Reconstruction of Daily Soil CO 2 Efflux Reveals Biogeochemical Insights and Reduces Annual Estimate Uncertainty Despite Limited Daily Predictability

Soil CO 2 efflux is commonly measured monthly or seasonally, leaving daily dynamics poorly resolved and contributing to global estimation uncertainty. We trained a single Long Short-Term Memory (LSTM) model to predict daily soil CO 2 efflux across 82 globally distributed sites in COSORE, with 0.2%–46.9% daily data coverage from 2003 to 2020. Despite using far fewer sites than are typically used to train a single deep learning model, with observations biased toward temperate mesic sites, the LSTM model performed well at approximately one-third of sites, reconstructed nearly 2 decades of daily efflux, and outperformed commonly used approaches for estimating daily efflux when applied to the same data set. Performance was weakest at pronounced peaks and troughs and at non-temperate sites with <1.5 years of observations and irregular data patterns. Nevertheless, annual efflux from reconstructed daily data had <40% error even at underperforming sites, substantially improving estimates derived from monthly and seasonal sampling (maximum errors of 95% and 136%, respectively). Temperature sensitivity (Q 10 ) estimated from reconstructed daily predictions closely matched estimates from daily observations, whereas Q 10 values derived from monthly or seasonal observations deviated substantially, suggesting that coarse temporal sampling may contribute to uncertainty in reported Q 10 values. Consistent daily reconstructions further enabled trend analyses for well-performing, predominantly temperate sites and showed increasing soil CO 2 efflux at most sites from 2003 to 2020, with more variable summer trends. Despite limitations, these results demonstrate the potential of LSTM models to reconstruct daily soil CO 2 efflux and reduce estimation uncertainties from sparse observations.

Smykalov, Valerie [Pennsylvania State University, ↗
DOE OSTI2025

LandScan mosaic enables high-resolution gridded population estimates with explicit uncertainty

Gridded population datasets represent high-resolution distributions of human occupancy, enabling informed decision-making across a broad range of fields. These data products are valuable for assessing environmental risk, urban development, disaster preparedness and resource allocation—areas where accurate population estimates directly enhance policy effectiveness and optimize resource distribution. Despite the importance of gridded population datasets, traditional population modeling approaches often overlook inherent uncertainties in the estimation process. This limitation can create a false sense of certainty in population estimates, potentially leading to flawed decisions by those who rely on the data. To address this methodological gap, we introduce a probabilistic machine learning modeling framework, LandScan Mosaic, that explicitly incorporates uncertainty into the population modeling process. Our approach systematically quantifies uncertainty in three key modeling parameters of the LandScan HD gridded population dataset: building use types, floor counts, and occupancy rates. By employing Monte Carlo simulations, we propagate these uncertainties through the modeling process, yielding probability distributions of population counts in place of deterministic point estimates. We demonstrate the practical application of this framework in Iloilo City, Philippines, using structured decision-making techniques and our probabilistic estimates to identify and prioritize areas most affected by projected flooding, supporting targeted interventions that address both economic and social risks. In doing so, we propose a population-specific approach for incorporating confidence into structured decision making processes. Through a comparative analysis with conventional deterministic approaches and point estimate approaches, including LandScan HD and WorldPop, we evaluate how the incorporation of machine learning and uncertainty influences decision rankings. This research advances population distribution modeling by offering a robust, quantitative approach that explicitly accounts for uncertainty in the underlying data, along with guidance for how users can apply uncertainty in their decision-making.

Environmental sciences↗
DOE OSTI2022

Extension of the flux fit method for estimating power deposition profiles

The flux fit method is used to self-consistently estimate the power deposition profile and heat transport profiles from temperature measurements originating from perturbative experiments with a modulated source. Furthermore, this letter improves on this method by addressing the limitations and assumptions. The most crucial improvement is the additional freedom in the source deposition profile. Allowing for a variable central deposition location and height and including a skewness parameter produces deposition profiles more consistent with the measurement data, but still wider than equilibrium ray tracing in two different DIII-D discharges. Moreover, we show that the quality of the estimated deposition profile is key to the accuracy of diffusivity and connectivity estimates, but inversely, the estimated transport parameters hardly affect the quality of the power deposition estimate. Using this method, we show that the power deposition profile estimate is broadened with respect to ray-tracing by about 1.7-1.8 times in two DIII-D discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Fast uncertainty estimates in deep learning interatomic potentials

Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and material properties. A common short-coming shared by current approaches, however, is that neural networks only give point estimates of their predictions and do not come with predictive uncertainties associated with these estimates. Existing uncertainty quantification efforts have primarily leveraged the standard deviation of predictions across an ensemble of independently trained neural networks. This incurs a large computational overhead in both training and prediction, resulting in order-of-magnitude more expensive predictions. Here, we propose a method to estimate the predictive uncertainty based on a single neural network without the need for an ensemble. This allows us to obtain uncertainty estimates with virtually no additional computational overhead over standard training and inference. We demonstrate that the quality of the uncertainty estimates matches those obtained from deep ensembles. We further examine the uncertainty estimates of our methods and deep ensembles across the configuration space of our test system and compare the uncertainties to the potential energy surface. Finally, we study the efficacy of the method in an active learning setting and find the results to match an ensemble-based strategy at order-of-magnitude reduced computational cost.

Chemistry↗
DOE OSTI2024

A three-point velocity estimation method for two-dimensional coarse-grained imaging data

Time delay and velocity estimation methods have been widely studied subjects in the context of signal processing, with applications in many different fields of physics. The velocity of waves or coherent fluctuation structures is commonly estimated as the distance between two measurement points divided by the time lag that maximizes the cross correlation function between the measured signals, but this is demonstrated to result in erroneous estimates for two spatial dimensions. We present an improved method to accurately estimate both components of the velocity vector, relying on three non-aligned measurement points. We introduce a stochastic process describing the fluctuations as a superposition of uncorrelated pulses moving in two dimensions. Using this model, we show that the three-point velocity estimation method, using time delays calculated through cross correlations, yields the exact velocity components when all pulses have the same velocity. The two- and three-point methods are tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results reveal the superiority of the three-point technique. Finally, we demonstrate the applicability of the velocity estimation on gas puff imaging data of strongly intermittent plasma fluctuations due to the radial motion of coherent, blob-like structures at the boundary of the Alcator C-Mod tokamak.

Materials Science↗
DOE OSTI2013

Active galactic nucleus black hole mass estimates in the era of time domain astronomy

We investigate the dependence of the normalization of the high-frequency part of the X-ray and optical power spectral densities (PSDs) on black hole mass for a sample of 39 active galactic nuclei (AGNs) with black hole masses estimated from reverberation mapping or dynamical modeling. We obtained new Swift observations of PG 1426+015, which has the largest estimated black hole mass of the AGNs in our sample. We develop a novel statistical method to estimate the PSD from a light curve of photon counts with arbitrary sampling, eliminating the need to bin a light curve to achieve Gaussian statistics, and we use this technique to estimate the X-ray variability parameters for the faint AGNs in our sample. We find that the normalization of the high-frequency X-ray PSD is inversely proportional to black hole mass. We discuss how to use this scaling relationship to obtain black hole mass estimates from the short timescale X-ray variability amplitude with precision ∼0.38 dex. The amplitude of optical variability on timescales of days is also anticorrelated with black hole mass, but with larger scatter. Instead, the optical variability amplitude exhibits the strongest anticorrelation with luminosity. We conclude with a discussion of the implications of our results for estimating black hole mass from the amplitude of AGN variability.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Single-epoch black hole mass estimators for broad-line active galactic nuclei: recalibrating Hβ with a new approach

Based on an updated Hβ reverberation mapping (RM) sample of 44 nearby active galactic nuclei (AGNs), we propose a novel approach for black hole (BH) mass estimation using two filtered luminosities computed from single-epoch (SE) AGN spectra around the Hβ region. We found that the two optimal-filter luminosities extract virial information (size and virial velocity of the broad-line region, BLR) from the spectra, justifying their usage in this empirical BH mass estimator. The major advantages of this new recipe over traditional SE BH mass estimators utilizing continuum luminosity and broad-line width are (1) it has a smaller intrinsic scatter of 0.28 dex calibrated against RM masses, (2) it is extremely simple to use in practice, without any need to decompose the spectrum, and (3) it produces unambiguous and highly repeatable results even with low signal-to-noise spectra. The combination of the two luminosities can also cancel out, to some extent, systematic luminosity errors potentially introduced by uncertainties in distance or flux calibration. In addition, we recalibrated the traditional SE mass estimators using broad Hβ FWHM and monochromatic continuum luminosity at 5100 Å (L {sub 5100}). We found that using the best-fit slopes on FWHM and L {sub 5100} (derived from fitting the BLR radius-luminosity relation and the correlation between rms line dispersion and SE FWHM, respectively) rather than simple assumptions (e.g., 0.5 for L {sub 5100} and 2 for FWHM) leads to more precise SE mass estimates, improving the intrinsic scatter from 0.41 dex to 0.36 dex with respect to the RM masses. We compared different estimators and discussed their applications to the Sloan Digital Sky Survey quasar sample. Due to the limitations of the current RM sample, application of any SE recipe calibrated against RM masses to distant quasars should be treated with caution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

DARK MATTER MASS FRACTION IN LENS GALAXIES: NEW ESTIMATES FROM MICROLENSING

We present a joint estimate of the stellar/dark matter mass fraction in lens galaxies and the average size of the accretion disk of lensed quasars based on microlensing measurements of 27 quasar image pairs seen through 19 lens galaxies. The Bayesian estimate for the fraction of the surface mass density in the form of stars is α = 0.21 ± 0.14 near the Einstein radius of the lenses (∼1-2 effective radii). The estimate for the average accretion disk size is R{sub 1/2}=7.9{sub −2.6}{sup +3.8}√(M/0.3 M{sub ⊙}) light days. The fraction of mass in stars at these radii is significantly larger than previous estimates from microlensing studies assuming quasars were point-like. The corresponding local dark matter fraction of 79% is in good agreement with other estimates based on strong lensing or kinematics. The size of the accretion disk inferred in the present study is slightly larger than previous estimates.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A new black hole mass estimate for obscured active galactic nuclei

We propose a new method for estimating the mass of a supermassive black hole, applicable to obscured active galactic nuclei (AGNs). This method estimates the black hole mass using the width of the narrow core of the neutral FeKα emission line in X-rays and the distance of its emitting region from the black hole based on the isotropic luminosity indicator via the luminosity scaling relation. Assuming the virial relation between the locations and the velocity widths of the neutral FeKα line core and the broad Hβ emission line, the luminosity scaling relation of the neutral FeKα line core emitting region is estimated. We find that the velocity width of the neutral FeKα line core falls between that of the broad Balmer emission lines and the corresponding value at the dust reverberation radius for most of the target AGNs. The black hole mass M{sub BH,FeKα} estimated with this method is then compared with other black hole mass estimates, such as the broad emission-line reverberation mass M{sub BH,rev} for type 1 AGNs, the mass M{sub BH,H{sub 2O}} based on the H{sub 2}O maser, and the single-epoch mass estimate M{sub BH,pol} based on the polarized broad Balmer lines for type 2 AGNs. We find that M{sub BH,FeKα} is consistent with M{sub BH,rev} and M{sub BH,pol}, and find that M{sub BH,FeKα} correlates well with M{sub BH,H{sub 2O}}. These results suggest that M{sub BH,FeKα} is a potential indicator of the black hole mass for obscured AGNs. In contrast, M{sub BH,FeKα} is systematically larger than M{sub BH,H{sub 2O}} by about a factor of 5, and the possible origins are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Linearly supporting feature extraction for automated estimation of stellar atmospheric parameters

We describe a scheme to extract linearly supporting (LSU) features from stellar spectra to automatically estimate the atmospheric parameters T{sub eff}, log g, and [Fe/H]. “Linearly supporting” means that the atmospheric parameters can be accurately estimated from the extracted features through a linear model. The successive steps of the process are as follow: first, decompose the spectrum using a wavelet packet (WP) and represent it by the derived decomposition coefficients; second, detect representative spectral features from the decomposition coefficients using the proposed method Least Absolute Shrinkage and Selection Operator (LARS){sub bs}; third, estimate the atmospheric parameters T{sub eff}, log g, and [Fe/H] from the detected features using a linear regression method. One prominent characteristic of this scheme is its ability to evaluate quantitatively the contribution of each detected feature to the atmospheric parameter estimate and also to trace back the physical significance of that feature. This work also shows that the usefulness of a component depends on both the wavelength and frequency. The proposed scheme has been evaluated on both real spectra from the Sloan Digital Sky Survey (SDSS)/SEGUE and synthetic spectra calculated from Kurucz's NEWODF models. On real spectra, we extracted 23 features to estimate T{sub eff}, 62 features for log g, and 68 features for [Fe/H]. Test consistencies between our estimates and those provided by the Spectroscopic Parameter Pipeline of SDSS show that the mean absolute errors (MAEs) are 0.0062 dex for log T{sub eff} (83 K for T{sub eff}), 0.2345 dex for log g, and 0.1564 dex for [Fe/H]. For the synthetic spectra, the MAE test accuracies are 0.0022 dex for log T{sub eff} (32 K for T{sub eff}), 0.0337 dex for log g, and 0.0268 dex for [Fe/H].

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Quantum Krylov subspace algorithms for ground- and excited-state energy estimation

Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground- and excited-state energies of a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form $\langle \phi_i|e^{-\widehat{H}τ}|\phi_j\rangle$, the associated quantum circuits require an ancilla qubit with controlled multiqubit gates that can be quite costly for near-term quantum hardware. In this paper, we show that a wide class of Hamiltonians relevant to condensed-matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We propose a multifidelity estimation protocol that can be used to compute such quantities, showing that our approach, when combined with efficient single-fidelity estimation protocols, provides a substantial reduction in circuit depth. In addition, here we develop a unified theory of quantum Krylov subspace algorithms and present three quantum-classical algorithms for the ground- and excited-state energy estimation problems, where each algorithm provides various advantages and disadvantages in terms of total number of calls to the quantum computer, gate depth, classical complexity, and stability of the generalized eigenvalue problem within the Krylov subspace.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

mBEEF-vdW: Robust fitting of error estimation density functionals

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Multiparameter Estimation in Networked Quantum Sensors

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A direct approach to estimate the anisotropy of protein structures from small-angle X-ray scattering

In the field of small-angle X-ray scattering (SAXS), the task of estimating the size of particles in solution is usually synonymous with the Guinier plot. The approximation behind this plot, developed by Guinier in 1939, provides a simple yet accurate characterization of the scattering behavior of particles at low scattering angle or momentum transfer q , together with a computationally efficient way of inferring their radii of gyration R G . Moreover, this approximation is valid beyond spherical scatterers, making its use ubiquitous in the SAXS world. However, when it is important to estimate further particle characteristics, such as the anisotropy of the scatterer's shape, no similar or extended approximations are available. Existing tools to characterize the shape of scatterers rely either on prior knowledge of the scatterers' geometry or on iterative procedures to infer the particle shape ab initio . In this work, a low-angle approximation of the scattering intensity I ( q ) for ellipsoids of revolution is developed and it is shown how the size and anisotropy information can be extracted from the parameters of that approximation. The goal of the approximation is not to estimate a particle's full structure in detail, and thus this approach will be less accurate than well known iterative and ab initio reconstruction tools available in the literature. However, it can be considered as an extension of the Guinier approximation and used to generate initial estimates for the aforementioned iterative techniques, which usually rely on R G and D max for initialization. This formulation also demonstrates that nonlinearity in the Guinier plot can arise from anisotropy in the scattering particles. Beyond ideal ellipsoids of revolution, it is shown that this approximation can be used to estimate the size and shape of molecules in solution, in both computational and experimental scenarios. The limits of the approach are discussed and the impact of a particle's anisotropy in the Guinier estimate of R G is assessed.

catalysis (homogeneous), catalysis (heterogeneous)↗
DOE OSTI2025

Output Current Estimation and Control in Primary Side LCC Secondary Side Series Compensated Wireless Power Transfer System without Secondary Side Sensors

The estimation (and control) of the output variables is often challenging for wireless power transfer (WPT) systems. This paper presents a secondary side sensor-less closed loop estimation technique to estimate the output current in a primary side LCC and secondary side series compensated WPT system. Using information of primary side variables, the proposed estimation can estimate the output current over a wide range of load current variations. Results are presented to verify the efficacy of the proposed estimation.

Mukherjee, Subho [ORNL] (ORCID:0009000672297925)↗
DOE OSTI2024

Artificial Neural Network-based State Estimation for Low Observable, Unbalanced Microgrids for Microgrid Building Blocks

The microgrid building blocks (MBB) were proposed as microgrid components with combined sub-components with power conversion, communication, and microgrid control capability, or a subset of such sub-components. This work addresses the microgrid controller, present in an MBB, which requires accurate state estimation to perform its tasks, including for monitoring, power flow (dispatch), fault detection, etc. In this paper, an artificial neural network (ANN)-based framework for state estimation is proposed for an MBB, especially for unbalanced and low observable microgrids. To overcome the challenge of low observability in unbalanced systems, a concept of extended adjacent matrix is introduced to reduce the required number of measurements for state estimation. Addressing the challenges, a feed forward neural network (FNN) is utilized to enhance estimation accuracy and reliability with the reduced number of measurements. The proposed state estimation is validated through extensive simulations on a microgrid, which was achieved from the modified IEEE 34-bus distribution test feeder with multiple distributed energy resources (DERs) and demonstrated superior performance in estimation accuracy and low observability.

Choi, Jongchan↗