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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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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Implementation of a Model Predictive Control Strategy to Regulate Temperature Inside Plug-Flow Solar Reactor With Countercurrent Flow

Abstract Solar-driven thermochemical energy storage systems are proven to be promising energy carriers (solar fuels) to utilize solar energy by using reactive solid-state pellets. However, the production of solar fuel requires a quasi-steady-state process temperature, which represents the main challenge due to the transient nature of solar power. In this work, an adaptive model predictive controller (MPC) is presented to regulate the temperature inside a tubular solar reactor to produce solid-state solar fuel for long-term thermal storage systems. The solar reactor system consists of a vertical tube heated circumferentially over a segment of its length by concentrated solar power, and the reactive pellets (MgMn2O4) are fed from the top end and flow downwards through the heated tube. A countercurrent flowing gas supplied from the lower end interacts with flowing pellets to reduce it thermochemically at a temperature range of 1000—1500 °C. A low-order physical model was developed to simulate the dynamics of the solar reactor including the reaction kinetics, and the proposed model was validated numerically by using a 7-kW electric furnace. The numerical model then was utilized to design the MPC controller, where the control system consists of an MPC code linked to an adaptive system identification code that updates system parameters online to ensure system robustness against external disturbances (sudden change in the flow inside the reactor), model mismatches, and uncertainty. The MPC controller parameters are tuned to enhance the system performance with minimum steady-state error and overshoot. The controller is tested to track different temperature ranges between 500 °C and 1400 °C with different particles/gas mass flowrates and ramping temperature profiles. Results show that the MPC controller successfully regulated the reactor temperature within ± 1 °C of its setpoint and maintained robust performance with minimum input effort when subjected to sudden changes in the amount of flowing media and the presence of chemical reaction.

Engineering↗
DOE OSTI2024

Machine learning-based discovery of molecular descriptors that control polymer gas permeation

While machine learning has found increasing use in predicting the properties of polymeric materials with only a knowledge of chain architecture, determining the molecular factors underpinning properties (“interpretable AI”) has remained less well explored. We show that encoding chain chemistry in commonly employed formats, e.g., binary-valued fingerprints, leads to uniqueness issues during the hashing process to save storage space. This is because the hashing algorithm can map several chemical moieties into the same bit. These issues carry over into the ML algorithms, especially for “inverse” design and interpretable AI, and cannot be avoided by changing the length of the fingerprint. Using MACCS key featurizations of monomer repeats resolves some of these issues, and we show that a few substructures consistently appear in top features for maximizing permeability across several gases and ML models. These are carbon–carbon double bonds (as in polyacetylenes) especially when they are associated with methyl groups (found in branching architectures). Here these results, derived from the limited data set of ~ 500 polymers with experimental gas permeation data, are in agreement with physical insight and thus provide a robust foundation which could further enable study of these material classes through detailed experiments and simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Offline Arterial Signal Timing Optimization based on Virtual Phase Link Model - A Real-world Case Study

Conventional signal timing for arterial usually takes bottom-up approaches. Engineers optimize each individual intersection first and then coordinate them by adjusting the offsets. This work is based on the Virtual Phase-Link (VPL) model, a street traffic model designed for online traffic model predictive control, to obtain a top-down offline arterial signal timing. We Studied the Shallowford Rd. in Chattanooga, TN and found that the inconsistency in intersection capacities along the arterial could lead to some intersections becoming bottlenecks. Signal timing is a significant factor that affect the intersection capacities. We realized that the VPL-based model can guarantee the consistency in intersections along an arterial. We therefore adopted the VPL-based model and developed an offline signal timing optimization approach. The proposed timing derived from the VPL-based offline signal timing optimization showed very good results in simulation. The Chattanooga Department of Transportation adopted the optimized timing obtained from the proposed approach and gave positive feedbacks to the research team. We also collected field experiment data, which demonstrated overall energy reductions and speed improvements on some sections of the Shallowford Rd. arterial. We will continue the experiment when the COVID-19 pandemic impact subsides to have a more robust quantitative evaluation.

Wang, Qichao↗
DOE OSTI2024

High-yield implosion modeling using the Frustraum: Assessing and controlling the formation of polar jets and enhancing implosion performance with applied magnetization

Frustraums have a higher laser-to-capsule x-ray radiation coupling efficiency and can accommodate a large capsule, thus potentially generating a higher yield with less laser energy than cylindrical Hohlraums for a given Hohlraum volume [Amendt et al., Phys. Plasmas 26, 082707 (2019]. Frustraums are expected to have less m = 4 azimuthal asymmetries arising from the intrinsic inner-laser-beam geometry on the National Ignition Facility. An experimental campaign at Lawrence Livermore National Laboratory to demonstrate the high-coupling efficiency and radiation symmetry tuning of the Frustraum has been under way since 2021. Simulations benchmarked against experimental data show that implosions using Frustraums can achieve more yield with higher ignition margins than cylindrical Hohlraums using the same laser energy. Hydrodynamic jets in capsules along the Hohlraum axis, driven by radiation-flux asymmetries in a Hohlraum with a gold liner on a depleted uranium (DU) wall, are present around stagnation, and these “polar” jets can cause severe yield degradation. The early-time Legendre mode P4<0 radiation-flux asymmetry is a leading cause of these jets, which can be reduced by using an unlined DU Hohlraum because the shape of the shell is predicted to be more prolate. Magnetization can increase the implosion robustness and reduce the required hotspot ρR for ignition; therefore, magnetizing the Frustraum can maintain the same yield while reducing the required laser energy or increase the yield using the same laser energy—all under the constraint that the ignition margin is preserved. Reducing polar jets is particularly important for magnetized implosions because of the intrinsic toroidal hotspot ion temperature topology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Transformational challenge reactor analysis to inform preconceptual core design decisions: Sensitivity study of transient analysis in a hydride-moderated microreactor

The Transformational Challenge Reactor (TCR) program aims to demonstrate a revolutionary design approach enabled by advanced manufacturing and data analytics in the design of nuclear reactors. This article discusses scoping analyses of preconceptual designs to inform TCR design decisions and the evaluation of sensitivities and uncertainties on postulated transient scenarios. The applicability of the systems codes TRACE and RELAP5-3D to TCR transient analysis are examined, and RELAP5-3D models are used to examine the transient response of two candidate core designs at multiple power levels. Then, the uncertainty quantification code RAVEN is used to quantify the effect of several design parameters on reactivity-initiated accident (RIA) progression at hot zero power (HZP) and hot full power (HFP) as well as to assess the impact of uncertainties in transient parameters for the pressurized loss of forced cooling (PLOFC).When results were compared, TRACE and RELAP5-3D showed good agreement in their ability to predict system behavior, but RELAP5-3D calculations were closer to analytical predictions for the RIA. Furthermore, models for a PLOFC accident in two designs (a UO2 and TRISO core) at multiple power levels showed greater temperature margins for the TRISO core at all power levels. Using this information, along with other scoping analyses and constraints, the TCR design team selected a power level of 3 MWth and a TRISO-based core design. For this design RAVEN was applied to vary RIA parameters in RELAP5-3D models at HZP and HFP to understand the effect on figures of merit such as peak power, fuel and coolant temperature, and energy deposition. This sensitivity study found that the inserted reactivity worth was the most important parameter controlling all figures of merit, but for insertion up to 1.5$ no failure of TCR fuel is anticipated. For constant reactivity insertions, the magnitude of the fuel temperature coefficient was found to have the greatest effect on all figures of merit under most circumstances. These results not only demonstrate the anticipated robust safety of the proposed TCR fuel form but also provide a reference for future metal-hydride moderated systems to understand RIA behavior. In the PLOFC, the impact of heat transfer enhancement due to wavy flow channel effects dominated the variance in peak temperatures, and variations in heat exchanger elevation provided the greatest control on natural circulation flow rate. Additionally, no fuel particle failure is anticipated in the PLOFC.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

In-field bioreactors demonstrate dynamic shifts in microbial communities in response to geochemical perturbations

Subsurface microbial communities mediate the transformation and fate of redox sensitive materials including organic matter, metals and radionuclides. Few studies have explored how changing geochemical conditions influence the composition of groundwater microbial communities over time. We temporally monitored alterations in abiotic forces on microbial community structure using 1L in-field bioreactors receiving background and contaminated groundwater at the Oak Ridge Reservation, TN. Planktonic and biofilm microbial communities were initialized with background water for 4 days to establish communities in triplicate control reactors and triplicate test reactors and then fed filtered water for 14 days. On day 18, three reactors were switched to receive filtered groundwater from a contaminated well, enriched in total dissolved solids relative to the background site, particularly chloride, nitrate, uranium, and sulfate. Biological and geochemical data were collected throughout the experiment, including planktonic and biofilm DNA for 16S rRNA amplicon sequencing, cell counts, total protein, anions, cations, trace metals, organic acids, bicarbonate, pH, Eh, DO, and conductivity. We observed significant shifts in both planktonic and biofilm microbial communities receiving contaminated water. This included a loss of rare taxa, especially amongst members of the Bacteroidetes, Acidobacteria, Chloroflexi, and Betaproteobacteria, but enrichment in the Fe- and nitrate- reducing Ferribacterium and parasitic Bdellovibrio. These shifted communities were more similar to the contaminated well community, suggesting that geochemical forces substantially influence microbial community diversity and structure. These influences can only be captured through such comprehensive temporal studies, which also enable more robust and accurate predictive models to be developed.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Wind turbine gearbox fault prognosis using high-frequency SCADA data

Condition-based maintenance using routinely collected Supervisory Control and Data Acquisition (SCADA) data is a promising strategy to reduce downtime and costs associated with wind farm operations and maintenance. New approaches are continuously being developed to improve the condition monitoring for wind turbines. Development of normal behaviour models is a popular approach in studies using SCADA data. This paper first presents a data-driven framework to apply normal behaviour models using an artificial neural network approach for wind turbine gearbox prognostics. A one-class support vector machine classifier, combining different error parameters, is used to analyse the normal behaviour model error to develop a robust threshold to distinguish anomalous wind turbine operation. A detailed sensitivity study is then conducted to evaluate the potential of using high-frequency SCADA data for wind turbine gearbox prognostics. The results based on operational data from one wind turbine show that, compared to the conventionally used 10-min averaged SCADA data, the use of high-frequency data is valuable as it leads to improved prognostic predictions. High-frequency data provides more insights into the dynamics of the condition of the wind turbine components and can aid in earlier detection of faults.

17 WIND ENERGY↗
DOE OSTI2026

Anomaly Detection for Online Monitoring of Thermocouple Sensors in the Advanced Test Reactor

This study explores data-driven anomaly detection methods to analyze sensor fail- ures in the Advanced Gas Reactor (AGR) nuclear fuel irradiation experiments. Specifically, we examine failures of thermocouples (TCs), which are critical for mon- itoring and controlling in-reactor temperatures during operation. Failures were pri- marily observed during abrupt power transitions and manifested as sensor drop-outs, drifts, or unexplained behavior. We applied three time-series analysis techniques— rolling mean smoothing, matrix profile, and vector auto-regression (VAR)—to de- tect anomalies in TC data prior to failure events. The rolling mean method effec- tively highlighted deviations aligned with reported failures, while the matrix profile provided partial early warning but sometimes flagged normal fluctuations during power-down periods. VAR shows potential in capturing multivariate dependencies but requires further calibration. A rare case of TC drift was also documented, which did not result in failure, underscoring the challenge of building predictive models with sparse positive examples. Our findings demonstrate that traditional statistical tools can aid anomaly detection but have limited predictive power without richer training data. We propose future directions including synthetic data generation, real- time surrogate modeling, and multi-modal feature integration. This work provides a foundation for applying robust anomaly detection frameworks to mission-critical sensor systems in experimental settings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

MFNets: Multifidelity data-driven networks for Bayesian learning and prediction

This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Statistical Uncertainty in Paleoclimate Proxy Reconstructions

A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data-forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.

58 GEOSCIENCES↗
DOE OSTI2026

Instant folded strings, dark energy and a cyclic bouncing universe

We present a wholly self-consistent, complete cyclic bouncing cosmology based on components drawn from string theory and constructed in a way that is under perturbative control throughout (e.g., with temperature much less than the string scale and string coupling g s ≪ 1 at all times). The cyclic evolution is governed by standard dilaton-gravity in (3+1)-dimensions with a perturbatively generated potential and a coupling between the dilaton and a second field that becomes massless at ϕ = ϕ ESP , resulting in an enhanced symmetry point (ESP) that prevents the dilaton from running all the way to zero coupling. A central role is played by instant folded strings (IFSs) — fundamental strings with the unusual property of being much lighter than the string mass while extending far beyond the string length, and violating the Null Energy Condition (NEC). IFSs are produced classically when the string coupling grows with time, which occurs at two critical points in each cycle. In turn, they fulfill a dual function: Enabling cosmological bounces and initiating transient epochs of dark-energy domination that naturally transition into slow contraction. The resulting cosmology eliminates the cosmic singularity and multiverse problems of big bang inflationary models and robustly predicts time-varying IFS-induced dark energy and the absence of primordial B-mode polarization in the cosmic microwave background.

alternatives to inflation↗
DOE OSTI2020

Defect Kinetics and Control for Module Reliability

Potential induced degradation is currently one of the most important module degradation mechanisms. It has been suggested that stacking faults decorated with sodium from the module glass are responsible for this effect and authors have also shown the reversibility of this effect upon reverse biasing of the module. The importance of sodium in the failure mechanism is clear, however, little is known regarding the factors that control its diffusion into the wafer, making it nearly impossible to predict the performance of a given module and engineer it to be better. Sodium migration from module glass into silicon cells and the resulting module degradation is a clear example of how defect kinetics can determine overall module performance and long-term reliability. To the detriment of the industry and its bankability, no quantitative models yet exist to predict defect-assisted module degradation, limiting the progress in improving reliability. In particular, the understanding of defect behavior under high electric fields, under stresses imparted by encapsulation or temperature, and under real operating conditions over long periods of time is a crucial gap in the current state-of-the-art. In this work we developed a Defect-Device-Degradation model to predict defect behavior and its impact on device performance over the module operational lifetime using experimentally-determined defect parameterizations. The validated model will provide a platform for manufacturing process optimization across input materials and architectures to avoid deleterious defects upstream and enable enhanced module robustness.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Instant Folded Strings, Dark Energy and a Cyclic Bouncing Universe

We present a wholly self-consistent, complete cyclic bouncing cosmology based on components drawn from string theory and constructed in a way that is under perturbative control throughout (e.g., with temperature much less than the string scale and string coupling $g_s \ll 1$ at all times). The cyclic evolution is governed by standard dilaton-gravity in $(3+1)$-dimensions with a perturbatively generated potential and a coupling between the dilaton and a second field that becomes massless at $ϕ= ϕ_{ESP}$, resulting in an enhanced symmetry point (ESP) that prevents the dilaton from running all the way to zero coupling. A central role is played by instant folded strings (IFSs) - fundamental strings with the unusual property of being much lighter than the string mass while extending far beyond the string length, and violating the Null Energy Condition (NEC). IFSs are produced classically when the string coupling grows with time, which occurs at two critical points in each cycle. In turn, they fulfill a dual function: enabling cosmological bounces and initiating transient epochs of dark-energy domination that naturally transition into slow contraction. The resulting cosmology eliminates the cosmic singularity and multiverse problems of big bang inflationary models and robustly predicts time-varying IFS-induced dark energy and the absence of primordial B-mode polarization in the cosmic microwave background.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗
DOE OSTI2025

Controlled Enzyme Cargo Loading in Engineered Bacterial Microcompartment Shells

Bacterial microcompartments (BMCs) are nanometer-scale organelles with a protein-based shell that serve to colocalize and encapsulate metabolic enzymes. They may provide a range of benefits to improve pathway catalysis, including substrate channeling and selective permeability. Several groups are working toward using BMC shells as a platform for enhancing engineered metabolic pathways. The microcompartment shell of Haliangium ochraceum (HO) has emerged as a versatile and modular shell system that can be expressed and assembled outside its native host and with non-native cargo. Further, the HO shell has been modified to use the engineered protein conjugation system SpyCatcher–SpyTag for non-native cargo loading. Here, we used a model enzyme, triose phosphate isomerase (Tpi), to study non-native cargo loading into four HO shell variants and begin to understand maximal shell loading levels. We also measured activity of Tpi encapsulated in the HO shell variants and found that activity was determined by the amount of cargo loaded and was not strongly impacted by the predicted permeability of the shell variant to large molecules. All shell variants tested could be used to generate active, Tpi-loaded versions, but the simplest variants assembled most robustly. We propose that the simple variant is the most promising for continued development as a metabolic engineering platform.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Machine learning assisted phase and size-controlled synthesis of iron oxide particles

Synthesis of iron oxides with specific phases and particle sizes is a crucial challenge in various fields, including materials science, energy storage, biomedical applications, environmental science, and earth science. However, despite significant advances in this area, much of the current palette of particle outcomes has been based on time-consuming trial-and-error exploration of synthesis conditions. The present study was designed to explore a very different approach to 1) predict the outcome of synthesis from specified reaction parameters based on using machine learning (ML) techniques, and 2) correlate sets of parameters to obtain products with desired outcomes by a newly designed recommendation algorithm. To achieve this, four ML algorithms were tested, namely random forest, logistic regression, support vector machine, and k-nearest neighbor. Among the models, random forest outperformed the others, attaining 96% and 81% accuracy when predicting the phase and size of iron oxide particles in the test dataset. Surprisingly, the permutation feature importance analysis revealed that volume, which may strongly relate to pressure, was one of the important features, along with precursor concentration, pH, temperature, and time, influencing the phase and size of iron oxide particles during synthesis. To verify the robustness of the random forest models, prediction and experimental results were compared based on 24 randomly generated methods in additive and non-additive systems not included in the datasets. The predictions of product phase and particle size from the models agreed well with the experimental results. Furthermore, a searching and ranking algorithm was developed to recommend potential synthesis parameters for obtaining iron oxide products with the desired phase and particle size from previous studies in the dataset. Furthermore, this study lays the foundation for a closed-loop approach in materials synthesis and preparation, beginning with suggesting potential reaction parameters from the dataset and predicting potential outcomes, followed by conducting experiments and analyses, and ultimately enriching the dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Performance of Fire Danger Indices and Their Utility in Predicting Future Wildfire Danger Over the Conterminous United States

Abstract Predicting current and future wildfire frequency and size is central to wildfire control and management. Multiple fire danger indices (FDIs) that incorporate weather and fuel conditions have been developed and utilized to support wildfire predictions and risk assessment. However, the scale‐dependent performance of individual FDIs remains poorly understood, which leads to large uncertainty in the estimated fire sizes under climate change. Here, we calculate four commonly used FDIs over the conterminous United States using high‐resolution (4 km) climate and fuel data sets for the 1984–2019 period. The relationships of these four FDIs to the observed wildfire sizes show that higher values of FDIs correlate to larger total fire sizes; this correlation is more robust at larger spatial scales. Sensitivity analysis indicates that the daily minimum relative humidity and precipitation are the most important drivers of the annual mean fire danger. In the instances of extreme fire danger, wind speed becomes a critical factor and should be considered in the calculation of the FDI. To assess the impact of climate change on future fire size, we calculate the present‐day and end‐of‐century FDIs using the 12 km regional climate model simulations. The four FDIs generally predict consistent changes in future fire potential, suggesting an overall higher fire potential in conjunction with a prolonged wildfire season in future climate. Regionally, the four FDIs also reveal similar seasonal patterns as the enhancement arises mostly in spring and summer over the southwest US while in summer and fall over the northern and eastern US.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

CyBERT: Cybersecurity Claim Classification by Fine-Tuning the BERT Language Model

We introduce CyBERT, a cybersecurity feature claims classifier based on bidirectional encoder representations from transformers and a key component in our semi-automated cybersecurity vetting for industrial control systems (ICS). To train CyBERT, we created a corpus of labeled sequences from ICS device documentation collected across a wide range of vendors and devices. This corpus provides the foundation for fine-tuning BERT’s language model, including a prediction-guided relabeling process. We propose an approach to obtain optimal hyperparameters, including the learning rate, the number of dense layers, and their configuration, to increase the accuracy of our classifier. Fine-tuning all hyperparameters of the resulting model led to an increase in classification accuracy from 76% obtained with BertForSequenceClassification’s original architecture to 94.4% obtained with CyBERT. Furthermore, we evaluated CyBERT for the impact of randomness in the initialization, training, and data-sampling phases. CyBERT demonstrated a standard deviation of ±0.6% during validation across 100 random seed values. Finally, we also compared the performance of CyBERT to other well-established language models including GPT2, ULMFiT, and ELMo, as well as neural network models such as CNN, LSTM, and BiLSTM. The results showed that CyBERT outperforms these models on the validation accuracy and the F1 score, validating CyBERT’s robustness and accuracy as a cybersecurity feature claims classifier.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗