Results for “Bayesian experiment” — Page 19

DOE OSTI2021

Bayesian Cross-matching of High Proper-motion Stars in Gaia DR2 and Photometric Metallicities for ∼1.7 million K and M Dwarfs

We present a Bayesian method to cross-match 5,827,988 high proper-motion Gaia sources (μ > 40 mas yr{sup −1}) to various photometric surveys: Two Micron All Sky Survey, AllWISE data release from the Wide-field Infrared Explorer (WISE) mission, Galaxy Evolution Explorer, Radial Velocity Experiment, Sloan Digital Sky Survey, and Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). To efficiently associate these objects across catalogs, we develop a technique that compares the multidimensional distribution of all sources in the vicinity of each Gaia star to a reference distribution of random field stars obtained by extracting all sources in a region on the sky displaced 2′. This offset preserves the local field stellar density and magnitude distribution, allowing us to characterize the frequency of chance alignments. The resulting catalog with Bayesian probabilities >95% has a marginally higher match rate than current internal Gaia data release 2 (DR2) matches for most catalogs. However, a significant improvement is found with Pan-STARRS, where ∼99.8% of the sample within the Pan-STARRS footprint is recovered, as compared to a low ∼20.8% in Gaia DR2. Using these results, we train a Gaussian process regressor to calibrate two photometric metallicity relationships. For dwarfs of 3500 < T{sub eff} < 5280 K, we use metallicity values of 4378 stars from the Apache Point Observatory Galactic Evolution Experiment and Hejazi et al. to calibrate the relationship, producing results with a 1σ precision of 0.12 dex and few systematic errors. We then indirectly infer the metallicity of 4018 stars with 2850 < T{sub eff} < 3500 K, which are wide companions of primaries whose metallicities are estimated with our first regressor, to produce a relationship with a 1σ precision of 0.21 dex and significant systematic errors. Additional work is needed to better remove unresolved binaries from this second sample to reduce these systematic errors.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Investigation of core impurity transport in DIII-D diverted negative triangularity plasmas

Abstract Tokamak operation at negative triangularity has been shown to offer high energy confinement without the typical disadvantages of edge pedestals (Marinoni et al 2021 Nucl. Fusion 61 116010). In this paper, we examine impurity transport in DIII-D diverted negative triangularity experiments. Analysis of charge exchange recombination spectroscopy reveals flat or hollow carbon density profiles in the core, and impurity confinement times consistently shorter than energy confinement times. Bayesian inferences of impurity transport coefficients based on laser blow-off injections and forward modeling via the Aurora package (Sciortino et al 2021 Plasma Phys. Control. Fusion 63 112001) show core cross-field diffusion to be higher in L-mode than in H-mode. Impurity profile shapes remain flat or hollow in all cases. Inferred radial profiles of diffusion and convection are compared to neoclassical, quasilinear gyrofluid, and nonlinear gyrokinetic simulations. Heat transport is observed to be better captured by reduced turbulence models with respect to particle transport. State-of-the-art gyrokinetic modeling compares favorably with measurements across multiple transport channels. Overall, these results suggest that diverted negative triangularity discharges may offer a path to a highly-radiative L-mode scenario with high core performance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1991

Cosmic-structure constraints from a one-degree microwave-background anisotropy experiment

A recent anisotropy experiment with a 30-arcmin beam is close to optimal for testing models in which cosmic structure arose from inflation-generated Gaussian density perturbations. Using a Bayesian analysis to constrain the amplitude of the perturbation spectrum, it is shown that adiabatic hot-dark-matter models are convincingly ruled out and cold-dark-matter models have anisotropies near the derived limits. Theories with broken scale invariance such as isocurvature baryon models are strongly constrained, as are models with extra power crafted to give significant large-scale structures and flows.

Bond, J. R.↗

DOE OSTI2022

Density reconstruction in convergent high-energy-density systems using x-ray radiography and Bayesian inference

X-ray radiography is a technique frequently used to diagnose convergent high-energy-density (HED) systems, such as inertial confinement fusion implosion, and provides unique information that is not available through self-emission measurements. In this work, we investigate the scope and limits of that information using a radiography simulation combined with the Bayesian inference workflow. The accuracy of density reconstruction from simulated radiographs of spherical implosions driven with 27 kJ laser energy is assessed, including the increase or decrease in accuracy due to the addition of Lagrangian marker layers, Poisson noise, and improved prior information. This work is the first to present the full uncertainty distributions inferred from radiography analysis in HED systems and demonstrates the importance of constructing the full posterior probability density, as opposed to a point estimate, due to the modal structure of the likelihood surface introduced by typical experimental noise sources. This general methodology can be used both for robust analysis of radiographic data and for an improved design of radiography experiments by modeling the full experimental system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Technical note: Modeling spatial fields of extreme precipitation – a hierarchical Bayesian approach

Abstract. We introduce a hierarchical Bayesian model for the spatial distribution of rainfall corresponding to an extreme event of a specified duration that could be used with regional hydrologic models to perform a regional hydrologic risk analysis. An extreme event is defined if any gaging site in the watershed experiences an annual maximum rainfall event and the spatial field of rainfall at all sites corresponding to that occurrence is modeled. Applications to data from New York City demonstrate the effectiveness of the model for providing spatial scenarios that could be used for simulating loadings into the urban drainage system. Insights as to the homogeneity in spatial rainfall and its implications for modeling are provided by considering partial pooling in the hierarchical Bayesian framework.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗

DOE OSTI2022

Physics Discovery in Nanoplasmonic Systems via Autonomous Experiments in Scanning Transmission Electron Microscopy

Abstract Physics‐driven discovery in an autonomous experiment has emerged as a dream application of machine learning in physical sciences. Here, this work develops and experimentally implements a deep kernel learning (DKL) workflow combining the correlative prediction of the target functional response and its uncertainty from the structure, and physics‐based selection of acquisition function, which autonomously guides the navigation of the image space. Compared to classical Bayesian optimization (BO) methods, this approach allows to capture the complex spatial features present in the images of realistic materials, and dynamically learn structure–property relationships. In combination with the flexible scalarizer function that allows to ascribe the degree of physical interest to predicted spectra, this enables physical discovery in automated experiment. Here, this approach is illustrated for nanoplasmonic studies of nanoparticles and experimentally implemented in a truly autonomous fashion for bulk‐ and edge plasmon discovery in MnPS 3 , a lesser‐known beam‐sensitive layered 2D material. This approach is universal, can be directly used as‐is with any specimen, and is expected to be applicable to any probe‐based microscopic techniques including other STEM modalities, scanning probe microscopies, chemical, and optical imaging.

42 ENGINEERING↗

NASA NTRSDate not supplied

ARCTRON: A Rapid Experimental Proving Ground for TPS Experiments and Arcjet Technology Development

Innovation in high-enthalpy facilities is fundamentally limited by the cost and risk of experimentation. New concepts for plasma control, diagnostics, facility components, and plasma-material interaction often require repeated iterations that are impractical to perform in production arcjets. As a result, promising ideas may remain unexplored or reach operational facilities only after significant development effort. ARCTRON is being developed as a rapid experimental proving ground where new ideas in plasma science, arcjet engineering, diagnostics, and material response can be conceived, tested, and quantitatively evaluated before transition to large-scale facilities. The platform combines radio-frequency (RF) and DC arc plasma generation, externally applied magnetic fields, configurable gas composition, reduced-pressure operation, laser heating, electrical biasing, and modular diagnostic access. These capabilities permit the plasma source, applied forcing, test article, and measurement configuration to be modified independently, allowing individual physical mechanisms to be isolated more readily than in a traditional test environment. One class of investigations addresses fundamental plasma-surface interaction physics. Conventional material tests often expose a specimen simultaneously to convective heating, reactive species, pressure, shear, radiation, and surface-current effects. The resulting material response may be measured accurately, while the contribution of each mechanism remains difficult to identify. ARCTRON is designed to vary these effects selectively. Plasma chemistry can be changed independently through configurable gas mixtures; magnetic fields and electrical biasing can modify charged-particle transport; laser heating can provide a non-plasma thermal input; and pressure, flow, and discharge mode can be varied over a broad operating space. This enables controlled tests of hypotheses involving surface catalycity, reactive-species transport, plasma-assisted oxidation, electromagnetic effects, shear, and the relative contributions of thermal and chemical loading. A second class of investigations enabled by this approach concerns the engineering of high-enthalpy facilities themselves. Arc-heated facilities are limited by electrode erosion, unstable arc attachment, localized heating, and damage to nozzles and other plasma-facing components. ARCTRON provides a lower-cost environment for testing concepts intended to mitigate these limitations. Candidate investigations include the use of applied magnetic fields to alter current paths and reduce plasma interaction with nozzle walls, ExB forcing to introduce controlled plasma rotation, magnetic or geometric approaches for distributing arc attachment, and alternative electrode or discharge configurations intended to reduce erosion and improve stability. Because the platform is reconfigurable, these concepts can be evaluated through repeated design--build--test cycles before they are considered for implementation in operational facilities. The platform also supports the development and validation of diagnostics that may be difficult to introduce initially into a large arcjet. Current and planned measurements include spatially resolved optical emission spectroscopy, electrostatic probes, fast imaging, pyrometry, calorimetry, laser-induced fluorescence, and absorption spectroscopy. These diagnostics are intended not merely to document a nominal operating condition, but to constrain the local plasma state and its relationship to component or material response. The modular facility geometry allows diagnostic concepts to be tested, calibrated, and compared under repeatable conditions before deployment in more demanding environments. ARCTRON is also supported by an integrated software suite. Automated control and data acquisition allow discharge parameters, gas composition, magnetic fields, diagnostic timing, and test configuration to be recorded as part of each experiment (STARDAC - Software for Testing, Analysis, Research Data, and Control). The Backend for Experiment Analysis, Storage, and Traceability (BEAST) is a database that provides the infrastructure needed to associate heterogeneous measurements with facility configuration, specimen identity, calibration state, geometry, and analysis provenance. This backend is particularly important for exploratory campaigns, in which many related configurations may be tested, and the value of an individual experiment depends on its connection to earlier and subsequent iterations. Complementary analysis capabilities, including computer-vision-based transient response measurements (arcjetCV), three-dimensional surface reconstruction (STARSCAN), and model-based Bayesian inference (SHIELD), and tomography data analysis (TOMATO, PuMA) can be incorporated when required by a specific hypothesis without becoming the focus of every campaign. The central objective of ARCTRON is therefore not to maximize heat flux or reproduce a complete flight environment. Its purpose is to reduce the cost and time required to ask consequential questions about plasma behavior, plasma-facing materials, diagnostics, and arcjet technology. By providing a controlled environment for rapid reconfiguration, mechanism isolation, quantitative measurement, and iterative engineering, ARCTRON can help mature concepts that would otherwise remain too speculative or too risky for evaluation in production facilities. The resulting knowledge can then guide the design of material models, focus test objectives in larger arcjets, reduce facility-development risk, and improve the physical basis of high-enthalpy ground testing. This work will present the ARCTRON architecture, operating modes, diagnostic suite, and digital experimental workflow. Initial experimental results from the first integrated operation of the facility will be presented, including flow characterization, power limitations, and deployment of the initial diagnostic suite. Ongoing development efforts aimed at catalycity characterization, magnetic plasma control, and advanced optical diagnostics will also be discussed, illustrating how the platform supports rapid iteration from concept to experiment.

experimental diagnostics↗

NASA NTRSDate not supplied

ARCTRON: A Rapid Experimental Proving Ground for TPS Experiments and Arcjet Technology Development

Innovation in high-enthalpy facilities is fundamentally limited by the cost and risk of experimentation. New concepts for plasma control, diagnostics, facility components, and plasma-material interaction often require repeated iterations that are impractical to perform in production arcjets. As a result, promising ideas may remain unexplored or reach operational facilities only after significant development effort. ARCTRON is being developed as a rapid experimental proving ground where new ideas in plasma science, arcjet engineering, diagnostics, and material response can be conceived, tested, and quantitatively evaluated before transition to large-scale facilities. The platform combines radio-frequency (RF) and DC arc plasma generation, externally applied magnetic fields, configurable gas composition, reduced-pressure operation, laser heating, electrical biasing, and modular diagnostic access. These capabilities permit the plasma source, applied forcing, test article, and measurement configuration to be modified independently, allowing individual physical mechanisms to be isolated more readily than in a traditional test environment. One class of investigations addresses fundamental plasma-surface interaction physics. Conventional material tests often expose a specimen simultaneously to convective heating, reactive species, pressure, shear, radiation, and surface-current effects. The resulting material response may be measured accurately, while the contribution of each mechanism remains difficult to identify. ARCTRON is designed to vary these effects selectively. Plasma chemistry can be changed independently through configurable gas mixtures; magnetic fields and electrical biasing can modify charged-particle transport; laser heating can provide a non-plasma thermal input; and pressure, flow, and discharge mode can be varied over a broad operating space. This enables controlled tests of hypotheses involving surface catalycity, reactive-species transport, plasma-assisted oxidation, electromagnetic effects, shear, and the relative contributions of thermal and chemical loading. A second class of investigations enabled by this approach concerns the engineering of high-enthalpy facilities themselves. Arc-heated facilities are limited by electrode erosion, unstable arc attachment, localized heating, and damage to nozzles and other plasma-facing components. ARCTRON provides a lower-cost environment for testing concepts intended to mitigate these limitations. Candidate investigations include the use of applied magnetic fields to alter current paths and reduce plasma interaction with nozzle walls, ExB forcing to introduce controlled plasma rotation, magnetic or geometric approaches for distributing arc attachment, and alternative electrode or discharge configurations intended to reduce erosion and improve stability. Because the platform is reconfigurable, these concepts can be evaluated through repeated design--build--test cycles before they are considered for implementation in operational facilities. The platform also supports the development and validation of diagnostics that may be difficult to introduce initially into a large arcjet. Current and planned measurements include spatially resolved optical emission spectroscopy, electrostatic probes, fast imaging, pyrometry, calorimetry, laser-induced fluorescence, and absorption spectroscopy. These diagnostics are intended not merely to document a nominal operating condition, but to constrain the local plasma state and its relationship to component or material response. The modular facility geometry allows diagnostic concepts to be tested, calibrated, and compared under repeatable conditions before deployment in more demanding environments. ARCTRON is also supported by an integrated software suite. Automated control and data acquisition allow discharge parameters, gas composition, magnetic fields, diagnostic timing, and test configuration to be recorded as part of each experiment (STARDAC - Software for Testing, Analysis, Research Data, and Control). The Backend for Experiment Analysis, Storage, and Traceability (BEAST) is a database that provides the infrastructure needed to associate heterogeneous measurements with facility configuration, specimen identity, calibration state, geometry, and analysis provenance. This backend is particularly important for exploratory campaigns, in which many related configurations may be tested, and the value of an individual experiment depends on its connection to earlier and subsequent iterations. Complementary analysis capabilities, including computer-vision-based transient response measurements (arcjetCV), three-dimensional surface reconstruction (STARSCAN), and model-based Bayesian inference (SHIELD), and tomography data analysis (TOMATO, PuMA) can be incorporated when required by a specific hypothesis without becoming the focus of every campaign. The central objective of ARCTRON is therefore not to maximize heat flux or reproduce a complete flight environment. Its purpose is to reduce the cost and time required to ask consequential questions about plasma behavior, plasma-facing materials, diagnostics, and arcjet technology. By providing a controlled environment for rapid reconfiguration, mechanism isolation, quantitative measurement, and iterative engineering, ARCTRON can help mature concepts that would otherwise remain too speculative or too risky for evaluation in production facilities. The resulting knowledge can then guide the design of material models, focus test objectives in larger arcjets, reduce facility-development risk, and improve the physical basis of high-enthalpy ground testing. This work will present the ARCTRON architecture, operating modes, diagnostic suite, and digital experimental workflow. Initial experimental results from the first integrated operation of the facility will be presented, including flow characterization, power limitations, and deployment of the initial diagnostic suite. Ongoing development efforts aimed at catalycity characterization, magnetic plasma control, and advanced optical diagnostics will also be discussed, illustrating how the platform supports rapid iteration from concept to experiment.

experimental diagnostics↗

DOE OSTI2022

Posterior Regularized Bayesian Neural Network incorporating soft and hard knowledge constraints

Neural Networks (NNs) have been widely used in supervised learning due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. Furthermore, the experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

14 SOLAR ENERGY↗

NASA NTRSDate not supplied

Quantifying radiation quality for space relevant radiation types: Fitting excess risk models to three combined HZE-irradiated mouse datasets

Radiation health risks are predominantly derived from low linear energy transfer (LET) terrestrial exposures; however, space radiation includes exposure to high-LET and high-charge, high-energy (HZE) particles. Accurately quantifying the differences in radiation quality between the space and terrestrial radiation environments is important for assessing and predicting health risks for astronauts. Weil et al. 2009 and 2014 used two different inbred mouse strains to study differences in hepatocellular carcinoma (HCC) tumorigenesis after exposures to low- and high- LET radiation. More recently, Edmundson et al. 2020 provided valuable new tumor data in outbred mice that were exposed to low- and high-LET radiation. The present study aims to rigorously investigate a relative biological effectiveness (RBE) factor by leveraging the HCC tumor data from Weil et al. 2009, Weil et al. 2014, and Edmundson et al. 2020. The three experiments were similarly designed, allowing the raw data to be combined into a pooled dataset to estimate excess relative risk (ERR) and excess absolute risk (EAR) models using Bayesian Poisson regression. These effect estimates from the pooled data provide greater power to calculate a data driven RBE. Extensive sensitivity analyses test the robustness of RBE estimates to various model assumptions. The following questions will be explored through the sensitivity analyses: • Is the shape of the dose response different for low-LET radiation and HZE radiation, indicating that RBE is a function of dose? • Does attained age modify the effect estimates differently for low-LET radiation and HZE radiation, indicating RBE is a function of attained age? • Are the effect estimates and RBE estimates different for inbred mouse strains and outbred mouse strains? • Do assumptions about differences in ERR models and EAR models change the estimated RBE? Additional studies would be needed to validate the findings from these exploratory analyses.

Lori J. Chappell↗

NASA NTRSDate not supplied

Quantifying radiation quality for space relevant radiation types: Fitting excess risk models to three combined HZE-irradiated mouse datasets

Radiation health risks are predominantly derived from low linear energy transfer (LET) terrestrial exposures; however, space radiation includes exposure to high-LET and high-charge, high-energy (HZE) particles. Accurately quantifying the differences in radiation quality between the space and terrestrial radiation environments is important for assessing and predicting health risks for astronauts. Weil et al. 2009 and 2014 used two different inbred mouse strains to study differences in hepatocellular carcinoma (HCC) tumorigenesis after exposures to low- and high- LET radiation[1-2]. More recently, Edmondson et al. 2020 provided valuable new tumor data in outbred mice that were exposed to low- and high-LET radiation[3]. The present study aims to rigorously investigate a relative biological effectiveness (RBE) factor by leveraging the HCC tumor data from the three datasets[1-3]. The three experiments were similarly designed, allowing the raw data to be combined into a pooled dataset to estimate excess relative risk (ERR) and excess absolute risk (EAR) models using Bayesian Poisson regression.

Lori J. Chappell↗

DOE OSTI2025

DESI Spectroscopy of HETDEX Emission-line Candidates. I. Line Discrimination Validation

The Hobby–Eberly Dark Energy Experiment (HETDEX) is an untargeted spectroscopic galaxy survey that uses Lyα-emitting galaxies (LAEs) as tracers of 1.9 < z < 3.5 large-scale structure. Most detections consist of a single emission line, whose identity is inferred via a Bayesian analysis of ancillary data. To determine the accuracy of these line identifications, HETDEX detections were observed with the Dark Energy Spectroscopic Instrument (DESI). In two DESI pointings, high-confidence spectroscopic redshifts are obtained for 1157 sources, including 982 LAEs. The DESI spectra are used to evaluate the accuracy of the HETDEX object classifications and tune the methodology to achieve the HETDEX science requirement of ≲2% contamination of the LAE sample by low-redshift emission-line galaxies, while still assigning 96% of the true Lyα emission sample with the correct spectroscopic redshift. We compare emission-line measurements between the two experiments assuming a simple Gaussian line fitting model. Fitted values for the central wavelength of the emission line, the measured line flux, and line widths are consistent between the surveys within uncertainties. Derived spectroscopic redshifts, from the two classification pipelines, when both agree as an LAE classification, are consistent to within $\langle$Δz/(1 + z)$\rangle$ = 6.9 × 10 −5 with an rms scatter of 3.3 × 10 −4 . Data are available at https://data.desi.lbl.gov/desi/public/dr1/vac/dr1/hetdex.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Machine Learning Accelerates Innovation in Perovskite Manufacturing Scale-up (Final Technical Report (FTR))

We propose to address the challenge of the vast parameter space associated with perovskite manufacturing optimization, by developing a machine learning (ML)-assisted optimization framework for a scalable perovskite PV manufacturing tool. This framework will be interpretable, sequential, and rapidly adaptable to upgraded systems (e.g., via transfer learning). The tool is an open-air rapid spray plasma process (RSPP) of perovskite films, which has already been established at Stanford and is a unique platform to test and deploy the proposed ML-guided framework because the RSPP technique is able to conduct optimization experiments with a high throughput, and easily adjust a wide range of process variables.

14 SOLAR ENERGY↗

DOE OSTI2024

Sequential Selection for Minimizing the Variance with Application to Crystallization Experiments

For many crystal-based products (e.g., pharmaceuticals, energy storage), the size uniformity is not only a key quality attribute, but sometimes also an indicator of other attributes such as solid purity. This article proposes a sequential selection approach to find a proper experimental setting that leads to high uniformity, or equivalently, small variance for crystal sizes, from the advanced slug flow reaction crystallization process of a model crystal, called manganese oxalate hydrate. The proposed sequential selection approach contains a Bayesian adaptive method to incorporate new uniformity measurements in each step and two design acquisition functions to improve the selection of the most promising experimental setting in terms of minimizing the variance. We study the performance of the proposed approach through multiple synthetic numerical studies, as well as a case study based on data from slug flow crystallization experiments. Throughout these studies, the proposed approach shows competitive performance in identifying the best experimental setting.

Expected improvement↗

DOE OSTI2023

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗

DOE OSTI2023

BEYONDPLANCK XI. Bayesian CMB analysis with sample-based end-to-end error propagation

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the BeyondPlanck framework. We first use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, although with notably higher noise due to our exclusion of HFI data. We find a best-fit CMB dipole amplitude of 3362.7 ± 1.4 µK, in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of ${σ}_{2}^{TT}$ = 229 ± 97 µK 2 , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the naive diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between the quadrupole and octopole than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, but also by our more conservative analysis mask required to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600, and it now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation, and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination

Post-training model compression can reduce the inference costs of deep neural networks, but uncompressed training still consumes enormous hardware resources and energy. To enable low-energy training on edge devices, it is highly desirable to directly train a compact neural network from scratch with a low memory cost. Low-rank tensor decomposition is an effective approach to reduce the memory and computing costs of large neural networks. However, directly training low-rank tensorized neural networks is a very challenging task because it is hard to determine a proper tensor rank a priori, and the tensor rank controls both model complexity and accuracy. Here, this paper presents a novel end-to-end framework for low-rank tensorized training. We first develop a Bayesian model that supports various low-rank tensor formats (e.g., CANDECOMP/PARAFAC, Tucker, tensor-train, and tensor-train matrix) and reduces neural network parameters with automatic rank determination during training. Then we develop a customized Bayesian solver to train large-scale tensorized neural networks. Our training methods shows orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the experiments. On a very large deep learning recommendation system with over 4.2 ×10 9 model parameters, our method can reduce the parameter number to 1.6 ×10 5 automatically in the training process (i.e., by 2.6 ×10 4 times) while achieving almost the same accuracy. Code is available at https://github.com/colehawkins/bayesian-tensor-rank-determination.

compact neural networks↗