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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Bayesian inference for plasmonic nanometrology

Here, we introduce a Bayesian method for the characterization of plasmonic nanoparticles, which is applicable to both near- and far-field problems. Designed to combine data generated from any photon-plasmon interaction experiment with physically motivated theoretical models, our approach leverages state-of-the-art Markov chain Monte Carlo sampling techniques and returns parameter estimates on nanometric scales. Simulated spectral data sets, describing resonant scattering of photons from ellipsoidal and toroidal nanoparticles, are explored as concrete examples of our approach, with the resulting Bayesian estimates showing excellent agreement with the ground truth, even under conditions of high statistical noise. By incorporating Bayes factors into the method as well, we reveal how model selection can determine which one of competing geometric shapes better explains the observed data. Our comprehensive nanometrology procedure can be tailored to a variety of light-particle interaction models, and its reliance on Bayesian inference furnishes automatic uncertainty quantification. In addition to applicability to a host of plasmonic configurations such as nanoparticle dimers, trimers, and array studies, it is proposed that the presented analysis can be extended to the quantum regime, where nonclassical photon statistics may provide additional insight for inference of scatterer properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge L 1 and L 2 regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing methodologies are limited to maximum a posteriori estimation. The potential to perform uncertainty quantification has not yet been realized. This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement. In addition, it lends itself naturally to conduct model selection for the choice of hyperparameters. Here, we illustrate the performance of our methodology in several computed examples, including a deconvolution problem and sparse identification of dynamical systems from time series data.

Bayesian shrinkage↗
DOE OSTI2016

Graphical models for optimal power flow

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

wa-hls4ml and lui-gnn: A benchmark and GNN-based surrogate model for hls4ml resource and latency estimation

As machine learning (ML) increasingly serves as a tool for addressing real-time challenges in scientific applications, the development of advanced tooling has significantly reduced the time required to iterate on various designs. These advancements have solved major obstacles, but also exposed new challenges. For example, processes that were not previously considered bottlenecks, such as model synthesis, are now becoming limiting factors in the rapid iteration of designs. To reduce these emerging constraints, multiple efforts are being launched toward designing an ML-based surrogate model that estimates resource usage of synthesized accelerator architectures. This model would reduce the design iteration time, especially when designing within a set of given hardware constraints. This approach shows considerable potential, but as it stands, the effort is early and would benefit from coordination and standardization to assist future work as it emerges. We introduce wa-hls4ml, a benchmark for ML accelerator resource and latency estimation, and its corresponding initial dataset of more than 100,000 fully connected neural networks, all synthesized using hls4ml and targeting Xilinx FPGAs. In addition to the resource utilization and latency data provided, the dataset includes generated artifacts and log files for many of the synthesized neural networks, in order to support future research in ML-based code generation. The benchmark evaluates the performance of resource and latency predictors against several common ML model architectures, primarily originating from scientific domains, as exemplar models, as well as the average performance across a subset of the dataset. We measure the performance of a given predictor model through multiple metrics, including $R^2$ score and SMAPE on regression tasks, as well as inference time to further characterize the estimator under test. Additionally, we introduce the latency/utilization inference graph neural network (lui-gnn), a surrogate model that uses a graph neural network to represent input architectures in the form of a directed graph. This graph representation allows for a diverse set of model architectures to all be effectively handled by a surrogate model. We present the architecture and performance of the model, as evaluated by the new proposed benchmark, including SMAPE, $R^2$ score, and inference times, and find that lui-gnn generally predicts latency and utilization for the 75\% quantile within several percent of the synthesized resources on the synthetic test dataset, indicating that this approach of estimating resource and latency via a surrogate models has promise and warrants further research.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations

Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high- delity simulations of radiation transport within an urban domain. The model is constructed to employ a source location (x, y, z) as input and return the estimated count rate for a set of speci ed detector locations. Because MCNP simulations are computationally expensive, we develop e cient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes (GP) and neural networks (NN) that we train and verify using the MCNP simulations. The trained surrogate models provide an e cient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo (MCMC) algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source's location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Measuring the giant radio galaxy length distribution with the LoTSS

Many massive galaxies launch jets from the accretion disk of their central black hole, but only ~10 3 instances are known in which the associated outflows form giant radio galaxies (GRGs, or giants): luminous structures of megaparsec extent that consist of atomic nuclei, relativistic electrons, and magnetic fields. Large samples are imperative to understanding the enigmatic growth of giants, and recent systematic searches in homogeneous surveys constitute a promising development. For the first time, it is possible to perform meaningful precision statistics with GRG lengths, but a framework to do so is missing. We measured the intrinsic GRG length distribution by combining a novel statistical framework with a LOFAR Two-metre Sky Survey (LoTSS) sample of freshly discovered giants. In turn, this allowed us to answer an array of questions on giants. For example, we can now assess how rare a 5 Mpc giant is compared with one of 1 Mpc, and how much larger – given a projected length – the corresponding intrinsic length is expected to be. Notably, we can now also infer the GRG number density in the Local Universe. We assumed the intrinsic GRG length distribution to be Paretian (i.e. of power-law form) with tail index ξ, and predicted the observed distribution by modelling projection and selection effects. To infer ξ, we also systematically searched the LoTSS for hitherto unknown giants and compiled the largest catalogue of giants to date. We show that if intrinsic GRG lengths are Pareto distributed with index ξ, then projected GRG lengths are also Pareto distributed with index ξ. Selection effects induce curvature in the observed projected GRG length distribution: angular length selection flattens it towards the lower end, while surface brightness selection steepens it towards the higher end. We explicitly derived a GRG’s posterior over intrinsic lengths given its projected length, laying bare the ξ dependence. We also discovered 2060 giants within LoTSS DR2 pipeline products; our sample more than doubles the known population. Spectacular discoveries include the largest, second-largest, and fourth-largest GRG known (l p = 5.1 Mpc, l p = 5.0 Mpc, and l p = 4.8 Mpc), the largest GRG known hosted by a spiral galaxy (l p = 2.5 Mpc), and the largest secure GRG known beyond redshift 1 (l p = 3.9 Mpc). We increase the number of known giants whose angular length exceeds that of the Moon from 10 to 23; among the discoveries is the angularly largest known radio galaxy in the Northern Sky, which is also the angularly largest known GRG ($\phi$ = 2°). Combining theory and data, we determined that intrinsic GRG lengths are well described by a Pareto distribution, and measured the index ξ = –3.5 ± 0.5. This implies that, given its projected length, a GRG’s intrinsic length is expected to be just 15% larger. Finally, we determined the comoving number density of giants in the Local Universe to be n GRG = 5 ± 2(100 Mpc) –3 . We developed a practical mathematical framework that elucidates the statistics of giant radio galaxy lengths. Through a LoTSS search, we also discovered 2060 new giants. By combining both advances, we determined that intrinsic GRG lengths are well described by a Pareto distribution with index ξ = –3.5 ± 0.5, and that giants are truly rare in a cosmological sense: most clusters and filaments of the Cosmic Web are not currently home to a giant. Thus, our work yields new observational constraints for analytical models and simulations featuring radio galaxy growth.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Bayesian Approach to the Eagar–Tsai Model for Melt Pool Geometry Prediction with Implications in Additive Manufacturing of Metals

Here, this paper focuses on improving the melt pool geometry predictions and quantifying uncertainties using an adapted version of the Eagar–Tsai (E–T) model that incorporates temperature-dependent properties of the material as well as powder conditions. Additionally, Bayesian inference is employed to predict distributions for the E–T model input parameters of laser absorptivity and powder bed porosity by incorporating experimental results into the analysis. Monte Carlo uncertainty propagation is then used with these parameter distributions to estimate the melt pool depth and associated uncertainty. Our results for the 316L stainless steel suggest that both the absorptivity and powder bed porosity are strongly influenced by the laser power. In contrast, the scanning speed has only a marginal effect on both the absorptivity and powder bed porosity. We constructed a printability map using the Bayesian E–T model based on power-dependent input parameter values to demonstrate the merit of the approach. The Bayesian approach improved the accuracy in predicting the keyhole regions in the laser power-scan speed parameter space for the 316L stainless steel. Although applied to a specific adaptation of the E–T model, the method put forth can be extended to quantify uncertainties in other numerical models as well as in the estimation of unknown parameters.

316L Stainless Steel (SS).↗
DOE OSTI2016

SOLAR MODELS WITH NEW LOW METAL ABUNDANCES

In the past decade, the photospheric abundances of the Sun had been revised several times by many observers. The standard solar models constructed with the new low-metal abundances disagree with helioseismic results and detected neutrino fluxes. The solar model problem has puzzled some stellar physicists for more than 10 years. Rotation, enhanced diffusion, convection overshoot, and magnetic fields are used to reconcile the new abundances with helioseismology. The too low helium subsurface abundance in enhanced diffusion models can be improved by the mixing caused by rotation and magnetic fields. The problem of the depth of the convective zone in rotating models can be resolved by convection overshoot. Consequently, the Asplund–Grevesse–Sauval rotation model including overshooting (AGSR) reproduces the seismically inferred sound-speed and density profiles and the convection zone depth as well as the Grevesse and Sauval model computed before. But this model fails to reproduce the surface helium abundance, which is 0.2393 (2.6 σ away from the seismic value), and neutrino fluxes. The magnetic model called AGSM keeps the agreement of the AGSR and improves the prediction of the surface helium abundance. The observed separation ratios r {sub 02} and r {sub 13} are reasonably reproduced by AGSM. Moreover, neutrino fluxes calculated by this model are not far from the detected neutrino fluxes and the predictions of previous works.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Data–driven model reduction for the Bayesian solution of inverse problems

One of the prime challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper presents a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. To begin, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced-order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full-scale numerical model as in a standard MCMC method, we couple the full-scale model and the reduced-order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady-state flow in a porous medium, the data-driven reduced-order model achieves better accuracy than a reduced-order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared with a standard MCMC method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Midplane neutral density profiles in the National Spherical Torus Experiment

Atomic and molecular density data in the outer midplane of NSTX [Ono et al., Nucl. Fusion 40, 557 (2000)] are inferred from tangential camera data via a forward modeling procedure using the DEGAS 2 Monte Carlo neutral transport code. The observed Balmer-β light emission data from 17 shots during the 2010 NSTX campaign display no obvious trends with discharge parameters such as the divertor Balmer-α emission level or edge deuterium ion density. Simulations of 12 time slices in 7 of these discharges produce molecular densities near the vacuum vessel wall of 2–8 × 10{sup 17 }m{sup −3} and atomic densities ranging from 1 to 7 × 10{sup 16 }m{sup −3}; neither has a clear correlation with other parameters. Validation of the technique, begun in an earlier publication, is continued with an assessment of the sensitivity of the simulated camera image and neutral densities to uncertainties in the data input to the model. The simulated camera image is sensitive to the plasma profiles and virtually nothing else. The neutral densities at the vessel wall depend most strongly on the spatial distribution of the source; simulations with a localized neutral source yield densities within a factor of two of the baseline, uniform source, case. The uncertainties in the neutral densities associated with other model inputs and assumptions are ≤50%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Disk radii and grain sizes in Herschel-resolved debris disks

The radii of debris disks and the sizes of their dust grains are important tracers of the planetesimal formation mechanisms and physical processes operating in these systems. Here we use a representative sample of 34 debris disks resolved in various Herschel Space Observatory (Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA) programs to constrain the disk radii and the size distribution of their dust. While we modeled disks with both warm and cold components, and identified warm inner disks around about two-thirds of the stars, we focus our analysis only on the cold outer disks, i.e., Kuiper-belt analogs. We derive the disk radii from the resolved images and find a large dispersion for host stars of any spectral class, but no significant trend with the stellar luminosity. This argues against ice lines as a dominant player in setting the debris disk sizes, since the ice line location varies with the luminosity of the central star. Fixing the disk radii to those inferred from the resolved images, we model the spectral energy distribution to determine the dust temperature and the grain size distribution for each target. While the dust temperature systematically increases toward earlier spectral types, the ratio of the dust temperature to the blackbody temperature at the disk radius decreases with the stellar luminosity. This is explained by a clear trend of typical sizes increasing toward more luminous stars. The typical grain sizes are compared to the radiation pressure blowout limit s {sub blow} that is proportional to the stellar luminosity-to-mass ratio and thus also increases toward earlier spectral classes. The grain sizes in the disks of G- to A-stars are inferred to be several times s {sub blow} at all stellar luminosities, in agreement with collisional models of debris disks. The sizes, measured in the units of s {sub blow}, appear to decrease with the luminosity, which may be suggestive of the disk's stirring level increasing toward earlier-type stars. The dust opacity index β ranges between zero and two, and the size distribution index q varies between three and five for all the disks in the sample.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Low-latency Jet Tagging for HL-LHC Using Transformer Architectures

Transformers are the state-of-the-art model architectures and widely used in application areas of machine learning. However the performance of such architectures is less well explored in the ultra-low latency domains where deployment on FPGAs or ASICs is required. Such domains include the trigger and data acquisition systems of the LHC experiments. We present a transformer-based algorithm for jet tagging built with the HGQ2 framework, which is able to produce a model with heterogeneous bitwidths for fast inference on FPGAs, as required in the trigger systems at the LHC experiments. The bitwidths are acquired during training by minimizing the total bit operations as an additional parameter. By allowing a bitwidth of zero, the model is pruned in-situ during training. Using this quantization-aware approach, our algorithm achieves state-of-the-art performance while also retaining permutation invariance which is a key property for particle physics applications. Due to the strength of transformers in representation learning, our work also serves as a stepping stone for the development of a larger foundation model for trigger applications.

Laatu, Lauri [Imperial Coll., London]↗
DOE OSTI2014

Bayesian inference of substrate properties from film behavior

We demonstrate that by observing the behavior of a film deposited on a substrate, certain features of the substrate may be inferred with quantified uncertainty using Bayesian methods. We carry out this demonstration on an illustrative film/substrate model where the substrate is a Gaussian random field and the film is a two-component mixture that obeys the Cahn–Hilliard equation. We construct a stochastic reduced order model to describe the film/substrate interaction and use it to infer substrate properties from film behavior. This quantitative inference strategy may be adapted to other film/substrate systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Veridical data science

Building and expanding on principles of statistics, machine learning, and scientific inquiry, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework, composed of both a workflow and documentation, aims to provide responsible, reliable, reproducible, and transparent results across the data science life cycle. The PCS workflow uses predictability as a reality check and considers the importance of computation in data collection/storage and algorithm design. It augments predictability and computability with an overarching stability principle. Stability expands on statistical uncertainty considerations to assess how human judgment calls impact data results through data and model/algorithm perturbations. As part of the PCS workflow, we develop PCS inference procedures, namely PCS perturbation intervals and PCS hypothesis testing, to investigate the stability of data results relative to problem formulation, data cleaning, modeling decisions, and interpretations. We illustrate PCS inference through neuroscience and genomics projects of our own and others. Moreover, we demonstrate its favorable performance over existing methods in terms of receiver operating characteristic (ROC) curves in high-dimensional, sparse linear model simulations, including a wide range of misspecified models. Finally, we propose PCS documentation based on R Markdown or Jupyter Notebook, with publicly available, reproducible codes and narratives to back up human choices made throughout an analysis. The PCS workflow and documentation are demonstrated in a genomics case study available on Zenodo.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗
DOE OSTI2018

Notos - a galaxy tool to analyze CpN observed expected ratios for inferring DNA methylation types

Background: DNA methylation patterns store epigenetic information in the vast majority of eukaryotic species. The relatively high costs and technical challenges associated with the detection of DNA methylation however have created a bias in the number of methylation studies towards model organisms. Consequently, it remains challenging to infer kingdom-wide general rules about the functions and evolutionary conservation of DNA methylation. Methylated cytosine is often found in specific CpN dinucleotides, and the frequency distributions of, for instance, CpG observed/expected (CpG o/e) ratios have been used to infer DNA methylation types based on higher mutability of methylated CpG. Results: Predominantly model-based approaches essentially founded on mixtures of Gaussian distributions are currently used to investigate questions related to the number and position of modes of CpG o/e ratios. These approaches require the selection of an appropriate criterion for determining the best model and will fail if empirical distributions are complex or even merely moderately skewed. We use a kernel density estimation (KDE) based technique for robust and precise characterization of complex CpN o/e distributions without a priori assumptions about the underlying distributions. Conclusions: We show that KDE delivers robust descriptions of CpN o/e distributions. For straightforward processing, we have developed a Galaxy tool, called Notos and available at the ToolShed, that calculates these ratios of input FASTA files and fits a density to their empirical distribution. Based on the estimated density the number and shape of modes of the distribution is determined, providing a rational for the prediction of the number and the types of different methylation classes. Notos is written in R and Perl.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Parameter inference with deep jointly informed neural networks

Abstract A common challenge in modeling inertial confinement fusion (ICF) experiments with computer simulations is that many of the simulation inputs are unknown and cannot be directly measured. Often, parameters that are measured in the experiment are used to infer the unknown inputs by solving the inverse problem: finding the set of simulation inputs that result in outputs consistent with the experimental observations. In ICF, this process is often referred to as a “post‐shot analysis.” Post‐shot analyses are challenging as the inverse problem is often highly degenerate, the input parameter space is vast, and simulations are computationally expensive. In this work, deep neural network models equipped with model uncertainty estimates are used to train inverse models, which map directly from output to input space, to find the distribution of post‐shot simulations that are consistent with experimental observations. The inverse model approach is compared to Markov chain Monte Carlo (MCMC) sampling of the forward model, which maps from input to output space, for parameter inference tasks of varying complexity. The inverse models perform best when searching vast parameter spaces for post‐shot simulations that are consistent with a large number of observables, where MCMC sampling can be prohibitively expensive. We demonstrate how augmenting inverse models with autoencoders enable the inclusion of several dozen observables in the inverse mapping, reducing the degeneracy of the model and improving the accuracy of the post‐shot analysis.

Humbird, Kelli D.↗
DOE OSTI2020

Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model – Application to realistic N -body simulations

ABSTRACT Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z’s tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $\Delta \bar{z} \approx 0.05,$ the final biases in the posterior are $\Delta \bar{z} \lesssim 0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.

79 ASTRONOMY AND ASTROPHYSICS↗