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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Integration, Validation, and Application of a PV Snow Coverage Model in SAM

Due to the increasing deployment of PV systems in snowy climates, there is significant interest in a method capable of estimating PV losses resulting from snow coverage that has been verified for a variety of system designs and locations. Many independent snow coverage models have been developed over the last 15 years; however, there has been very little effort verifying these models beyond the system designs and locations on which they were based. Moreover, major PV modeling software products have not yet incorporated any of these models into their workflows. In response to this deficiency, we have integrated the methodology of the snow model developed in the paper by Marion et al. (2013) into the National Renewable Energy Laboratory's (NREL) System Advisor Model (SAM). In this work, we describe how the snow model is implemented in SAM and we discuss our demonstration of the model's effectiveness at reducing error in annual estimations for three PV arrays. Next, we use this new functionality in conjunction with a long term historical data set to estimate average snow losses across the United States for two typical PV system designs. The open availability of the snow loss estimation capability in SAM to the PV modeling community, coupled with our results of the nationwide study, will better equip the industry to accurately estimate PV energy production in areas affected by snowfall.

14 SOLAR ENERGY↗
DOE OSTI2020

A Drift‐Kinetic Method for Obtaining Gradients in Plasma Properties From Single‐Point Distribution Function Data

Abstract In this paper, we derive a new drift‐kinetic method for estimating gradients in the plasma properties through a velocity space distribution at a single point. The gradients are intrinsically related to agyrotropic features of the distribution function. This method predicts the gradients in the magnetized distribution function and can predict gradients of arbitrary moments of the gyrotropic background distribution function. The method allows for estimates on density and pressure gradients on the scale of a Larmor radius, proving to resolve smaller scales than any method currently available to spacecraft. The model is verified with a set of fully kinetic VPIC particle‐in‐cell simulations.

Wetherton, B. A.↗
DOE OSTI2016

Pre-commercial Demonstration of Direct Non-iterative State Estimator for Operational Use of Synchrophasor Management Systems

The objective of this project was to demonstrate functionality and performance of a Direct Non-iterative State Estimator (DNSE) integrated with NYPA’s Energy Management System (EMS) and with enhanced Real Time Dynamics Monitoring System (RTDMS) synchrophasor platform from Electric Power Group (EPG). DNSE is designed to overcome a major obstacle to operational use of Synchro-Phasor Management Systems (SPMS) by providing to synchrophasor management systems (SPMS) applications a consistent and a complete synchrophasor data foundation in the same way that a traditional EMS State Estimator (SE) provides to EMS applications. Specifically, DNSE is designed to use synchrophasor measurements collected by a central PDC, Supervisory Control and Data Acquisition (SCADA) measurements, and Energy Management System (EMS) network model, to obtain the complete state of the utility’s operating model at rates that are close to the synchrophasor data rates. In this way, the system is comprehensive in that it does not only cover the part of the network that is “visible” via synchrophasors, but also the part that is only “visible” through the SCADA measurements. Visualization needs associated with the use of DNSE results are fulfilled through suitably enhanced Real Time Dynamics Monitoring System (RTDMS), with the enhancements implemented by EPG. This project had the following goals in mind: To advance the deployment of commercial grade DNSE software application that relies on synchrophasor and SCADA data ; Apply DNSE at other utilities, to address a generic and fundamental need for “clean” operational data for synchrophasor applications; Provide means for “live” estimated data access by control system operators; Enhance potential for situational awareness through full system operational model coverage; Sub-second execution rate of the Direct Non-iterative State Estimator, eventually at a near-phasor data rate execution speed, i.e. < 0.1 sec. Anticipated benefits from this projects are: Enhanced reliability and improvements in the economic efficiency of bulk power system planning and operations; Providing “clean” data to other synchrophasor applications; Enhancement of situational awareness by providing the full operational model updated at near synchrophasor rate; A production-grade software tool that incorporate synchrophasor and SCADA data; Provides a basis for development of next generation monitoring and control applications, based on both SCADA and PMU data. Quanta Technology (QT) team worked in collaboration with Electric Power Group (EPG) whose team has enhanced its commercial Real Time Dynamics Monitoring System (RTDMS) to accommodate the requirements posed by DNSE application. EPG also provided its ePDC and Model-less Data Conditioning (PDVC) software for integration with DNSE+. QT developed the system requirements for DNSE; developed system architecture and defined interfaces between internal DNSE components. The core DNSE algorithm with all surrounding interfaces was named DNSE+. Since the DNSE development was done in a simulated system environment, QT used its PMU simulator that was enhanced during this project for development and factory acceptance testing (FAT). SCADA data in this stage was simulated by commercial PSS/e software. The output of DNSE are estimates of System states in C37.118-2 format, sent to RTDMS for further processing and display. As the number of these states is large, it was necessary to expand the C37.111-2 standard to accommodate large data sets. This enhancement was implemented in RTDMS. The demonstration of pre-production DNSE technology was done at NYPA using streaming field data from NYPA PMUs and from its RTUs through their SCADA system. NYPA provided ICCP interface as well as Common Information Model (CIM). The relevance of the DNSE+ application is that it provides state estimation of the power system based on hybrid set of data, consisting of both available PMU data and SCADA measurements. As this is a direct, non-iterative method of calculation of the system states, if does not suffer from convergence issues which is potential problem for conventional state estimators. Also, it can take any available PMU measurements, so it does not need to have a high percentage of PMU coverage needed in the case of Linear State Estimator. As the DNSE calculates synchrophasors of the system states (both phase and absolute value) as sub-second rate, this application can provide a basis for development of next generation of applications based both on SCADA and PMU data.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Dynamic thermal behavior of polycrystalline LaB 6 hollow cathodes

Lanthanum hexaboride (LaB6) hollow cathodes have demonstrated a capability for long life operation, which is critical to many space exploration missions. Thermal characterization of LaB6 hollow cathodes has revealed lower than expected electron emitter temperatures when the cathode reaches a steady state. This phenomenon is observed at discharge currents ranging from 5 to 35 A and xenon mass flow rates of 5–25 SCCM in cathodes with three different orifice diameters. Thus, the currently accepted value of the work function for polycrystalline LaB 6 , 2.67 eV, does not describe well the emission characteristics of LaB6 hollow cathodes operating with internal gas discharges at a steady state. We use empirically measured temperatures combined with a model of the hollow cathode emitter and xenon discharge to estimate the value of the work function, yielding a value ranging from 2.1 to 2.44 eV. This lower work function value implies that LaB6 hollow cathodes are expected to have even longer lifetimes than previously anticipated, further establishing them as a more suited alternative to other conventional cathode technologies for the task of long duration travel. Direct measurements of the work function as a function of depth on a hollow cathode emitter using x-ray photoelectron spectroscopy and ion beam milling indicate that the work function decreases with depth. We postulate several mechanisms that could explain the observed work function enhancement. Altogether, our results have important implications to the design, study approach, and operation of LaB 6 cathodes and potentially other cathodes with hollow configuration. Finally, our work opens the question of why the work function is reduced upon interaction with Xe plasma.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Green Routing Fuel Saving Opportunity Assessment: A Case Study on California Large-Scale Real-World Travel Data

New technologies, such as connected and automated vehicles, have attracted more and more researchers for improving the energy efficiency and environmental impact of current transportation systems. The green routing strategy instructs a vehicle to select the most fuel-efficient route before the vehicle departs. It benefits the current transportation system with fuel saving opportunity through identifying the greenest route. This paper introduces an evaluation framework for estimating benefits of green routing based on large-scale, real-world travel data. The framework has the capability to quantify fuel savings by estimating the fuel consumption of actual routes and comparing to routes procured by navigation systems. A route-based fuel consumption estimation model, considering road traffic conditions, functional class, and road grade is proposed and used in the framework. An experiment using a large-scale data set from the California Household Travel Survey global positioning system trajectory data base indicates that 31% of actual routes have fuel savings potential with a cumulative estimated fuel savings of 12%.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2017

Green Routing Fuel Saving Opportunity Assessment: A Case Study on California Large-Scale Real-World Travel Data: Preprint

New technologies, such as connected and automated vehicles, have attracted more and more researchers for improving the energy efficiency and environmental impact of current transportation systems. The green routing strategy instructs a vehicle to select the most fuel-efficient route before the vehicle departs. It benefits the current transportation system with fuel saving opportunity through identifying the greenest route. This paper introduces an evaluation framework for estimating benefits of green routing based on large-scale, real-world travel data. The framework has the capability to quantify fuel savings by estimating the fuel consumption of actual routes and comparing to routes procured by navigation systems. A route-based fuel consumption estimation model, considering road traffic conditions, functional class, and road grade is proposed and used in the framework. An experiment using a large-scale data set from the California Household Travel Survey global positioning system trajectory data base indicates that 31% of actual routes have fuel savings potential with a cumulative estimated fuel savings of 12%.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2016

Planck 2015 results: XVII. Constraints on primordial non-Gaussianity

We report that the Planck full mission cosmic microwave background (CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity (NG). Using three classes of optimal bispectrum estimators – separable template-fitting (KSW), binned, and modal – we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone ƒ local NL = 2.5 ± 5.7, ƒ equil NL = -16 ± 70, , and ƒ ortho NL = -34 ± 32 (68% CL, statistical). Combining temperature and polarization data we obtain ƒ local NL = 0.8 ± 5.0, ƒ equil NL = -4 ± 43, and ƒ ortho NL = -26 ± 21 (68% CL, statistical). The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with estimators based on measuring the Minkowski functionals of the CMB. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and derive constraints on early universe scenarios that generate primordial NG, including general single-field models of inflation, axion inflation, initial state modifications, models producing parity-violating tensor bispectra, and directionally dependent vector models. We present a wide survey of scale-dependent feature and resonance models, accounting for the “look elsewhere” effect in estimating the statistical significance of features. We also look for isocurvature NG, and find no signal, but we obtain constraints that improve significantly with the inclusion of polarization. The primordial trispectrum amplitude in the local model is constrained to be g local NL = (-0.9 ± 7.7 ) X 10 4 (68% CL statistical), and we perform an analysis of trispectrum shapes beyond the local case. The global picture that emerges is one of consistency with the premises of the ΛCDM cosmology, namely that the structure we observe today was sourced by adiabatic, passive, Gaussian, and primordial seed perturbations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Neural Networks to Find the Optimal Forcing for Offsetting the Anthropogenic Climate Change Effects

Abstract Of great relevance to climate engineering is the systematic relationship between the radiative forcing to the climate system and the response of the system, a relationship often represented by the linear response function (LRF) of the system. However, estimating the LRF often becomes an ill-posed inverse problem due to high-dimensionality and nonunique relationships between the forcing and response. Recent advances in machine learning make it possible to address the ill-posed inverse problem through regularization and sparse system fitting. Here, we develop a convolutional neural network (CNN) for regularized inversion. The CNN is trained using the surface temperature responses from a set of Green’s function perturbation experiments as imagery input data together with data sample densification. The resulting CNN model can infer the forcing pattern responsible for the temperature response from out-of-sample forcing scenarios. This promising proof of concept suggests a possible strategy for estimating the optimal forcing to negate certain undesirable effects of climate change. The limited success of this effort underscores the challenges of solving an inverse problem for a climate system with inherent nonlinearity. Significance Statement Predicting the climate response for a given climate forcing is a direct problem, while inferring the forcing for a given desired climate response is often an inverse, ill-posed, problem, posing a new challenge to the climate community. This study makes the first attempt to infer the radiative forcing for a given target pattern of global surface temperature response using a deep learning approach. The resulting deeply trained convolutional neural network inversion model shows promise in capturing the forcing pattern corresponding to a given surface temperature response, with a significant implication on the design of an optimal solar radiation management strategy for curbing global warming. This study also highlights the technical challenges that future research should prioritize in seeking feasible solutions to the inverse climate problem.

Ren, Huiying↗
DOE OSTI2026

Optimization performance, fidelity, and cost: SIAM VQE

This dataset contains files storing results from classically-simulated quantum subroutines within a dynamical mean-field theory workflow, and jupyter notebooks processing the data in these files to generate plots. The files store: (1) Results from variational quantum eigensolver (VQE) simulations searching for optimal parameters allowing parametrized quantum circuits to prepare approximations to ground states of different Anderson impurity models (AIMs) (2) Results from simulations of a quantum Lanczos algorithm (QLA) estimating the Lanczos coefficients defining the continued-fraction representation of an (AIM) Green’s function Description: Any file named vqe_gs_results* stores approximations to the ground state and energy of a given AIM estimated using three different methods: (1) Numerical diagonalization (2) Ideal VQE simulation (3) VQE simulation with sampling noise For each VQE simulations metadata about the optimization (optimization results plus number of quantum circuits that would have been executed on real hardware) is also stored. Any file named qla_dos_results* estimations for the Lanczos coefficients defining the Green’s function of an AIM. The stored estimations are achieved using different methods: (1) Numerical Lanczos algorithm from initial states obtained from numerical diagonalization (2) Simulated quantum Lanczos algorithm from initial states prepared from parametrized quantum circuits yielded by corresponding ideal and noisy VQE subroutines. The dataset is used and described in M. Karabin et al., "Quantum solver for single-impurity Anderson models with particle-hole symmetry", Phys. Rev. Research 8, 033066 (2026). DOI: https://doi.org/10.1103/7ys3-tl4l

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Change-point Detection and Image Segmentation for Time Series of Astrophysical Images

Many astrophysical phenomena are time-varying, in the sense that their intensity, energy spectrum, and/or the spatial distribution of the emission suddenly change. This paper develops a method for modeling a time series of images. Under the assumption that the arrival times of the photons follow a Poisson process, the data are binned into 4D grids of voxels (time, energy band, and x-y coordinates), and viewed as a time series of non-homogeneous Poisson images. The method assumes that at each time point, the corresponding multiband image stack is an unknown 3D piecewise constant function including Poisson noise. It also assumes that all image stacks between any two adjacent change points (in time domain) share the same unknown piecewise constant function. The proposed method is designed to estimate the number and the locations of all of the change points (in time domain), as well as all of the unknown piecewise constant functions between any pairs of the change points. The method applies the minimum description length principle to perform this task. A practical algorithm is also developed to solve the corresponding complicated optimization problem. Simulation experiments and applications to real data sets show that the proposed method enjoys very promising empirical properties. Applications to two real data sets, the XMM observation of a flaring star and an emerging solar coronal loop, illustrate the usage of the proposed method and the scientific insight gained from it.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Uncertainty Quantification and Error Propagation in the Enthalpy and Entropy of Surface Reactions Arising from a Single DFT Functional

Accounting for parametric uncertainty in models is essential for quantifying the models’ predictive ability. Recently, approaches have been introduced to estimate parametric uncertainty in kinetic models while accounting for correlations among energy parameters. However, correlations have been estimated indirectly and correlations in entropies have not been accounted for. For surface-catalyzed microkinetic models of >C2 (more than two carbon-containing) molecules, which consist of thousands of reaction steps and intermediate surface species, first-principles density functional theory (DFT) is costly, and thus, estimation of thermochemistry and reaction barriers requires surrogate methods of DFT, such as group additivity and Brønsted–Evans–Polanyi relationships, respectively. For such parametrization, model uncertainty is unclear. This work develops a framework to overcome these gaps using group additivity and a single DFT functional. We estimate correlations in parameters of kinetic models and quantify uncertainty for thermochemistry, reaction barriers, reaction paths, and ultimately reaction rates, accounting also for the contribution of entropic uncertainty. Furthermore, the approach is illustrated on propane combustion and ethane oxidative dehydrogenation reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Performance of density functionals for modeling vapor liquid equilibria of CO 2 and SO 2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE-D3, BLYP-D3,PBE0-D3, M062X-D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal vander Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP-D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Altogether, theBLYP-D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO 2 and SO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Extreme metrics from large ensembles: investigating the effects of ensemble size on their estimates

Abstract. We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a number of extreme metrics. While we exploit existing large ensembles, our perspective is that of a modeling center wanting to estimate a priori such sizes on the basis of an existing small ensemble (we assume the availability of only five members here). We therefore ask if such a small-size ensemble is sufficient to estimate accurately the population variance (i.e., the ensemble internal variability) and then apply a well-established formula that quantifies the expected error in the estimation of the population mean (i.e., the forced component) as a function of the sample size n, here taken to mean the ensemble size. We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extremes as a function of n by plugging into the formula an estimate of the population variance derived on the basis of five members. For a range of spatial and temporal scales, forcing levels (we use simulations under Representative Concentration Pathway 8.5) and two models considered here as our proof of concept, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, and this remains true when statistical inference through extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation and – importantly – about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. Using the F test, we find that estimates on the basis of only 5 or 10 ensemble members accurately represent the full ensemble variance even when the analysis is conducted at the grid-point scale. The detection of changes in the variance when comparing different times along the simulation, especially for the precipitation-based metrics, requires larger sizes but not larger than 15 or 20 members. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, such as physics parameter settings, when designing ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Quantifying the effect of interannual ocean variability on the attribution of extreme climate events to human influence

In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed “event attribution.” Limitations in the observational record and in computational resources motivate the use of uncoupled, atmosphere/land-only climate models with prescribed ocean conditions run over a short period, leading up to and including an event of interest. In this approach, large ensembles of high-resolution simulations can be generated under factual observed conditions and counterfactual conditions that might have been observed in the absence of human interference; these can be used to estimate the change in probability of the given event due to anthropogenic influence. However, using a prescribed ocean state ignores the possibility that estimates of attributable risk might be a function of the ocean state. Thus, the uncertainty in attributable risk is likely underestimated, implying an over-confidence in anthropogenic influence. In this work, we estimate the year-to-year variability in calculations of the anthropogenic contribution to extreme weather based on large ensembles of atmospheric model simulations. Our results both quantify the magnitude of year-to-year variability and categorize the degree to which conclusions of attributable risk are qualitatively affected. The methodology is illustrated by exploring extreme temperature and precipitation events for the northwest coast of South America and northern-central Siberia; we also provides results for regions around the globe. While it remains preferable to perform a full multi-year analysis, these results can serve as an indication of where and when attribution researchers should be concerned about the use of atmosphere-only simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Polarized and unpolarized gluon PDFs: Generative machine learning applications for lattice QCD matrix elements at short distance and large momentum

Lattice quantum chromodynamics (QCD) calculations share a defining challenge by requiring a small finite range of spatial separation z between quark/gluon bilinears for controllable power corrections in the perturbative QCD factorization, and a large hadron boost p z for a successful determination of collinear parton distribution functions (PDFs). However, these two requirements make the determination of PDFs from lattice data very challenging. We present the application of generative machine learning algorithms to estimate the polarized and unpolarized gluon correlation functions utilizing short-distance data and extending the correlation up to z p z ≲ 14 , surpassing the current capabilities of lattice QCD calculations. We train physics-informed machine learning algorithms to learn from the short-distance correlation at z ≲ 0.36 fm and take the limit, p z → ∞ , thereby minimizing possible contamination from the higher-twist effects for a successful reconstruction of the polarized gluon PDF. We also expose the bias and problems with underestimating uncertainties associated with the use of model-dependent and overly constrained functional forms, such as x α ( 1 − x ) β and its variants to extract PDFs from the lattice data. We propose the use of generative machine learning algorithms to mitigate these issues and present our determination of the polarized and unpolarized gluon PDFs in the nucleon. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Joint inference of multiplicative and additive systematics in galaxy density fluctuations and clustering measurements

Galaxy clustering measurements are a key probe of the matter density field in the Universe. With the era of precision cosmology upon us, surveys rely on precise measurements of the clustering signal for meaningful cosmological analysis. However, the presence of systematic contaminants can bias the observed galaxy number density, and thereby bias the galaxy two-point statistics. As the statistical uncertainties get smaller, correcting for these systematic contaminants becomes increasingly important for unbiased cosmological analysis. We present and validate a new method for understanding and mitigating both additive and multiplicative systematics in galaxy clustering measurements (two-point function) by joint inference of contaminants in the galaxy overdensity field (one-point function) using a maximum-likelihood estimator (MLE). We test this methodology with Kilo-Degree Survey-like mock galaxy catalogues and synthetic systematic template maps. We estimate the cosmological impact of such mitigation by quantifying uncertainties and possible biases in the inferred relationship between the observed and the true galaxy clustering signal. Our method robustly corrects the clustering signal to the sub-percent level and reduces numerous additive and multiplicative systematics from 1.5σ to less than 0.1σ for the scenarios we tested. In addition, we provide an empirical approach to identifying the functional form (additive, multiplicative, or other) by which specific systematics contaminate the galaxy number density. Even though this approach is tested and geared towards systematics contaminating the galaxy number density, the methods can be extended to systematics mitigation for other two-point correlation measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Statistical Properties for Flows with Unbounded Roof Function, Including the Lorenz Attractor

For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We also obtain the functional central limit theorem and moment estimates, as well as iterated versions of these results. A consequence is deterministic homogenisation (convergence to a stochastic differential equation) for fast-slow dynamical systems whenever the fast dynamics is singularly hyperbolic of codimension two.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

Here, we present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

97 MATHEMATICS AND COMPUTING↗