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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Gaussian Process Regression under Computational and Epistemic Misspecification

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Furthermore, our theory also accounts for epistemic misspecification in the choice of kernel parameters.

Gaussian process regression↗

DOE OSTI2023

Two-pion femtoscopic correlations in Be+Be collisions at $\sqrt{s_{\text {NN}}} = 16.84$ GeV measured by the NA61/SHINE at CERN

This paper reports measurements of two-pion femtoscopic correlations in Be+Be collisions at a beam momentum of 150$A\,\hbox {GeV}\!/\!c$ (energy available in the center-of-mass system for nucleon pair $\sqrt{s_{\text {NN}}} = 16.84$ GeV) by the NA61/SHINE experiment at the CERN SPS accelerator. The obtained momentum space correlation functions can be well described by a Lévy distributed source model. The transverse mass dependence of the Lévy source parameters is presented, and their possible theoretical interpretations are discussed. The results show that the Lévy exponent $\alpha $ is approximately constant as a function of $m_{\text {T}}$ , and far from both the Gaussian case of $\alpha = 2$ or the conjectured value at the critical endpoint, $\alpha = 0.5$. The radius scale parameter R shows a slight decrease in $m_{\text {T}}$ , which can be explained as a signature of transverse flow. Finally, an approximately constant trend of the intercept parameter $\lambda $ as a function of $m_{\text {T}}$ was observed, similar to previous NA44 S + Pb results (obtained with a Gaussian approximation, but unlike RHIC results).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Spatially Accelerated Winding Numbers for Curved Geometry

The generalized winding number (GWN) is a scalar field that supports robust containment queries on curved geometry, including non-watertight, overlapping, and nested boundary representations. While queries can be easily parallelized over samples, direct evaluation on parametric curves and surfaces remains costly for large and complex models. Fast, state-of-the-art GWN approaches leverage a spatial index to approximate the GWN, typically coupled with a Taylor expansion which approximates the GWN contribution for far clusters of geometric primitives. However, such methods operate only on discrete inputs such as triangle meshes and point clouds, and would introduce containment errors near boundaries if applied to curved input. We extend support for fast GWN evaluation over arbitrary collections of NURBS curves in 2D and trimmed NURBS patches in 3D via a Bounding Volume Hierarchy that stores efficiently precomputed moment data in the hierarchy nodes. When querying the hierarchy, approximations for far clusters are used alongside direct evaluation for nearby NURBS primitives, achieving sub-linear complexity while preserving the geometric features in the vicinity of the query point. Central to our performance improvements is an adaptive subdivision strategy for NURBS primitives during a preprocessing phase, creating better spatial partitions while retaining the same accuracy for containment decisions as a direct evaluation. We demonstrate the performance and accuracy of our approach across a large collection of 2D and 3D datasets.

Computer science↗

DOE OSTI2020

Heat of Mixing During Fast Charge/Discharge of a Li-Ion Cell: A Study on NMC523 Cathode

Predicting temperature rise accurately during fast charge/discharge of a Li-ion cell is essential to avoid thermal runaway and extend battery life. While modeling the temperature rise, it is necessary to model the heat generation correctly. Heat of mixing, one of the four main sources of heat generation in a Li-ion battery, has often been considered insignificant and therefore excluded from modeling. When included, it is modeled using the expression from a Taylor expansion approximation. In this work, we have shown the conditions when including the heat of mixing becomes important and quantified the error associated with using the Taylor expansion, especially under high charge/discharge conditions. Consequently, we carry out the calculation of the rate of enthalpy change and the heat generation rate from the most fundamental equation for the rate of the total enthalpy change without simplifying assumptions or approximations. The heat generation rate calculated doing so naturally includes irreversible, reversible and mixing heat. We then exclusively separate out the heat of mixing by subtracting the rate of enthalpy change by reaction from the rate of the total enthalpy change. Results show that the contribution of heat of mixing in the total heat generated increases with the charge/discharge rate and is as large as 23% for a 6 C discharge. This result suggests that while modeling heat generation for fast charge/discharge, it is necessary to include the heat of mixing and avoid calculating it using the Taylor expansion approximation.

25 ENERGY STORAGE↗

DOE OSTI2021

Fast All-sky Radiation Model for Solar applications (FARMS) [SWR-16-18]

The Fast All-sky Radiation Model for Solar applications (FARMS) is used to compute cloudy irradiance. Radiative transfer (RT) models simulating broadband solar radiation have been widely used by atmospheric scientists to model solar resources for various energy applications such as operational forecasting. Due to the complexity of solving the RT equation, the computation under cloudy conditions can be extremely time consuming though many approximations (e.g. two-stream approach and delta-M truncation scheme) have been utilized. Thus, a more efficient RT model is crucial for model developers as a new option for approximating solar radiation at the land surface with minimal loss of accuracy. We have developed a fast all-sky radiation model for solar applications (FARMS) using the simplified clear-sky RT model, REST2, and simulated cloud transmittances and reflectances from the Rapid Radiation Transfer Model (RRTM) with a sixteen-stream Discrete Ordinates Radiative Transfer (DISORT). Simulated lookup tables (LUTs) of cloud transmittances and reflectances were created by varying cloud optical thicknesses, cloud particle sizes, and solar zenith angles. Equations with optimized parameters were fitted to the cloud transmittances and reflectances to develop the model. Using this model the all-sky solar irradiance at the land surface can be computed rapidly by combining REST2 with the cloud transmittances and reflectances. This new RT model is more than 1000 times faster than those currently utilized in solar resource assessment and forecasting since it does not explicitly solve the RT equation for each individual cloud condition. Our results indicate the accuracy of the fast radiative transfer model is comparable to or better than two-stream approximation in term of computing cloud transmittance and solar radiation.

Xie, Yu↗

DOE OSTI2025

Pxl

The code consists of several scripts. The image is fetched from a predefined URL, downloaded, and is displayed in the virtual environment at a predefined location. The image is also dynamically scaled to fit in the virtual environment depending on its size. The image is sent to have each pixel's value written to a CSV file. While the CSV is being written, a dictionary is populated with values that map each pixel to a temperature reading. The image's height, width, position and references to its corners are sent to make a button that is the same size as the image and placed right behind the image in the virtual scene. The button defines behavior that should be triggered when the user pushes the image. Unity provides visual cues that alert the user when they are about to touch something in the virtual environment. The code holds references to the cues for the left and right hands. The button queries the cue tracker and receives the position of the active cue in the form of a 3D vector. The 3D vector is compared to the bottom left corner of the image to transform the world space coordinates of the cue to the pixel space of the image. The specific pixel is approximated relative to how far left and up the user touched from the bottom left corner of the image. The approximated pixel value, which is represented as a coordinate in 2D space, is used to retrieve the temperature value associated with the approximated pixel. A window of text is then updated to display the temperature reading.

. Otis, KrystianeS [Idaho National Laboratory (INL↗

DOE OSTI2024

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A unified framework of stabilized finite element method for solving the Boltzmann transport equation

This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Bayesian Monte Carlo Evaluation Framework for Cross Sections Nuclear Data and Integral Benchmark Experiments

The new Bayesian Monte Carlo (MC) evaluation framework described in this abstract has been conceived as an attempt to improve nuclear data evaluations of differential crosssection data by removing the following two approximations conventionally employed for nuclear data evaluations: all probability density functions (PDFs) of all data and model parameters, both prior and posterior, are assumed to be normal (i.e., Gaussian) PDFs, and all uncertainties and covariances are propagated using a linear approximation. With these approximations removed, the Bayesian MC (BMC) framework could be used to account for nonlinear effects and would enable improved evaluations of differential cross sections and IBE data that are presently performed based on the assumptions itemized above. The BMC would also improve upon the uniform sampling of IBE parameters from within ranges defined by their evaluated uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Bayesian Monte Carlo Evaluation Framework for Imperfect Nuclear Data

Bayesian evaluation of resolved resonance region (RRR) nuclear data has historically been carried out using the generalized least squares (GLS) formalism, as implemented in, e.g., SAMMY. We have recently developed a prototype of Bayesian Monte Carlo (BMC) evaluation framework, implemented using a Markov Chain Monte Carlo (MCMC) method with a Metropolis-Hastings (MH) acceptance criterion. This was done in order to remove the approximations underlying the conventional GLS evaluations, namely, the linear approximation, and the approximation that all probability density functions (PDFs) are of the normal kind. Recent works by others have used similar stochastic approaches to quantify cross section uncertainties from ENDF evaluated co-variances, and/or, from integral benchmark data, but those have not been conceived as an evaluation framework like the one presented here.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗

DOE OSTI2025

AmeriFlux US-MEF Manitou Experimental Forest

This is the AmeriFlux version of the carbon flux data for the site US-MEF Manitou Experimental Forest. Site Description - This site was established on an existing 30-m tower structure at the Forest Service's Manitou Experimental Forest, Colorado. Manitou Experimental Forest is located approximately 38 km northwest of Colorado Springs, within the Pike National Forest. The tower was constructed and used between 2008 and 2013 by NCAR for the BEACHON project and has line power and internet connections. The tower is located in approximately 12 km^2 of ponderosa pine forest and savannah with a land use history of thinning and prescribed burning, though these disturbances have not occurred for many years. The tower is situated in a broad, flat valley that drains to the north. Early research at the site was focused mainly on grazing, while more recently it has turned broadly to the ecology and management of ponderosa pine ecosystems. In 2002, the Hayman Fire burned approximately 56,000 ha to the west and northwest of the tower location.

Frank, John [US Forest Service, Rocky Mountain Res↗

DOE OSTI2026

AmeriFlux FLUXNET-1F US-MEF Manitou Experimental Forest

This is the AmeriFlux Management Project (AMP) created FLUXNET-1F version of the carbon flux data for the site US-MEF Manitou Experimental Forest. This is the FLUXNET version of the carbon flux data for the site US-MEF Manitou Experimental Forest produced by applying the standard ONEFlux (1F) software. Site Description - This site was established on an existing 30-m tower structure at the Forest Service's Manitou Experimental Forest, Colorado. Manitou Experimental Forest is located approximately 38 km northwest of Colorado Springs, within the Pike National Forest. The tower was constructed and used between 2008 and 2013 by NCAR for the BEACHON project and has line power and internet connections. The tower is located in approximately 12 km^2 of ponderosa pine forest and savannah with a land use history of thinning and prescribed burning, though these disturbances have not occurred for many years. The tower is situated in a broad, flat valley that drains to the north. Early research at the site was focused mainly on grazing, while more recently it has turned broadly to the ecology and management of ponderosa pine ecosystems. In 2002, the Hayman Fire burned approximately 56,000 ha to the west and northwest of the tower location.

Frank, John [US Forest Service, Rocky Mountain Res↗

DOE OSTI2020

Investigation of Thermolytic Hydrogen Generation Rate in Tank 44 Dissolved Saltcake Samples

Saltcake core samples collected from Tank 44 in 2006 were dissolved to provide material for HGR measurements applicable to F-Area dissolved saltcake material. Additionally, characterization was performed on the Tank 44 saltcake material. The following are key results from the Tank 44 saltcake characterization. The Tank 44 Upper Saltcake Composite, corresponding to the 171 to 285 inch tank level, contained by mass approximately 69% sodium nitrate, 11% sodium carbonate, 8% sodium nitrite, smaller amounts of other salts and components, and 9% unquantified (which includes water, water of hydration, oxygen/hydrogen content of oxides and hydroxides, and uncertainty). The Tank 44 Lower Saltcake Composite, corresponding to the 76 to 114 inch tank level, contained by mass approximately 49% sodium carbonate, 18% sodium nitrate, smaller amounts of other salts, at least 8% sludge, and 9% unquantified (see above). The dissolved saltcake contained free hydroxide less than quantifiable (<0.01 M) due to the limited quantity of material that could be removed from the Shielded Cells based on the sample radioactivity. Measurement by pH paper provided an approximate pH of 12. The following are key results from the Tank 44 HGR testing. During boiling at 106.7 °C, HGR for Tank 44 dissolved saltcake without added glycolate was 7.2×10 -8 ft 3 h -1 ga l-1 . During boiling at 106.9 °C, HGR for Tank 44 dissolved saltcake with 1000 mg/L of added glycolate was 8.2×10 -8 ft 3 h -1 gal -1 . ∙ For the test without added glycolate, the first several HGR measurements at 70, 85, and 100 °C gave indication of the release of dissolved hydrogen and should not be used to represent the sustained thermolytic HGR for those temperatures. The measurements at boiling are the best representation of thermolysis in this testing. Carbon dioxide was observed at concentrations up to 6 vol% in the flow-system offgas for the test at boiling. ∙ Methane generation was observed at 100 °C and boiling. Methane concentration in the total gas generated during testing remained well below the lower flammability limit for methane in air. The addition of 1000 mg/L of glycolate did not have a significant impact on the hydrogen generation rates measured during this testing. The low hydroxide concentration in the Tank 44 dissolved saltcake likely influenced the relatively low thermolytic HGR and high carbon dioxide release observations in this testing. Based on the observation that methane was generated or released upon heating SRS radioactive Tank 44 waste samples to 100 °C and above, we recommend gaining a greater understanding of the cause and mechanism of its generation. First, the applicable literature should be reviewed to reveal the thermolytic methane generation mechanisms of possible methane generating species in the SRS CSTF. If warranted, a plan should be developed for simulant tests with methylated siloxanes and other applicable compounds in order to gain a better mechanistic understanding of methane generation in the SRS CSTF.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Performance Assessment for the Environmental Restoration Disposal Facility (FY 2019 Annual Status Report)

DOE O 435.1 and DOE M 435.1-1 require that a determination of continued adequacy of the performance assessment (PA), composite analysis, and disposal authorization statement (DAS) be annually, and it must consider the results of data collection and analysis from research, field studies, and monitoring as well as update any Radioactive Waste Management Basis documents. Beginning in 1996, the Environmental Restoration Disposal Facility (ERDF) has accepted low-level radioactive, hazardous, and mixed wastes that were generated during cleanup activities at the Hanford Site. ERDF is composed of a series of cells (currently 10) or disposal areas and can accommodate future design expansions as needed. During this reporting period (fiscal year 2019, October 1, 2018, to September 30, 2019). approximately 139,721 U.S. tons of waste was disposed at ERDF. From inception through September 30, 2019, ERDF has received approximately 18.5 million U.S. tons of waste, which equates to consumption of approximately 88% of the disposal volume. As a condition of the DAS, disposal operations within ERDF must be in accordance with the waste acceptance criteria (WAC) that provide specific radionuclide disposal limits, waste from restrictions, and descriptions of acceptable waste packages in compliance with DOE M 435-1.1 requirements. The ERDF WAC stipulates that waste destined for disposal at ERDF be controlled based on source, physical form, and containment concentration and activity levels

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗