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DOE OSTI2023

Bayesian uncertainty quantification of tristructural isotropic particle fuel silver release: Decomposing model inadequacy plus experimental noise and parametric uncertainties

Tristructural isotropic (TRISO) particle fuel is one of the most promising fuel concepts enabling high temperature and high burnup reactor operation. One dominant source of radioactivity released from the TRISO particles is silver (Ag), which is subject to a high release fraction and long decay life compared to other fission products. Previous modeling efforts using the fuel performance code BISON indicated nonnegligible uncertainties in modeling the diffusion process of fission products in TRISO compared to the Advanced Gas Reactor experiments. The overall uncertainties observed when modeling the fission product diffusion can result from uncertainties in model parameters, noisy experimental measurements, and deficiencies in the developed models. The three types of underlying uncertainties have not yet been properly quantified in open literature. Here, this paper presents the Bayesian uncertainty quantification (UQ) using massively parallelizable Markov chain Monte Carlo samplers. The uncertainties due to model parameters, model inadequacy, and experimental measurement noise are quantified, with the σ term used to represent the sum of the model inadequacy and measurement noise uncertainties. It is worth noting that this is the first time the σ term is inferred for nuclear fuel experiments, as compared to using prescribed values for uncertainty quantification in previous work. The parallelizable Markov chain Monte Carlo samplers efficiently infer the model parameters and the σ term, giving insight into physical parameters like diffusion coefficients and the combined model discrepancy and measurement noise. A subsequent forward uncertainty quantification (UQ) is also performed based on the calibration results to generate more accurate predictions of the Ag release. The model inadequacy plus experimental noise is the most dominant source of uncertainty compared to the parametric uncertainty. All the UQ analyses presented in this work are based on the second series of the irradiation experiments in the Advanced Gas Reactor program.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Observational implications of mattergenesis during inflation

The observed baryon asymmetry, as well as potentially an asymmetry in the dark matter sector, can be produced through dissipative particle production during inflation. A distinctive feature of this mechanism is the generation of matter isocurvature perturbations that are fully (anti-)correlated with the dominant adiabatic curvature perturbations. We show that chaotic warm inflation models yield anti-correlated isocurvature modes that may partially or even completely screen the contribution of primordial gravity waves to the CMB temperature power spectrum. The tensor-to-scalar ratio inferred from the latter may thus be parametrically smaller than the one deduced from B-mode polarization maps, which is particularly relevant in the light of the recently announced results of the BICEP2 experiment.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Bayesian Inference of the Symmetry Energy of Superdense Neutron-rich Matter from Future Radius Measurements of Massive Neutron Stars

In this work, using as references the posterior probability distribution functions of the equation of state (EOS) parameters inferred from the radii of canonical neutron stars (NSs) reported by the LIGO/VIRGO and NICER Collaborations based on their observations of GW170817 and PSR J0030+0451, we investigate how future radius measurements of more massive NSs will improve our current knowledge about the EOS of superdense neutron-rich nuclear matter, especially its symmetry energy term. Within the Bayesian statistical approach using an explicitly isospin-dependent parametric EOS for the core of NSs, we infer the EOS parameters of superdense neutron-rich nuclear matter from three sets of imagined mass–radius correlation data representing typical predictions by various nuclear many-body theories, that is, the radius stays the same, decreases, or increases with increasing NS mass within ±15% between 1.4 and 2.0 M$_\odot$. The corresponding NS average density increases quickly or slowly or slightly decreases as the NS mass increases from 1.4 to 2.0 M$_\odot$. While the EOSs of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding symmetry energies above about twice the saturation density of nuclear matter are very different, indicating that the radii of massive NSs carry important information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS at suprasaturation densities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

A multishock model for the density variance of anisotropic, highly magnetized, supersonic turbulence

ABSTRACT Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma ^2_{\rho /\rho _0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parametrizes the star formation (SF) rate of a cloud. However, models for $\sigma ^2_{\rho /\rho _0}$ all share a common feature – the variance is assumed to be isotropic. This assumption does not hold when a trans-/sub-Alfvénic mean magnetic field, ${B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma _{\rho /\rho _0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma _{\rho /\rho _0}^2$ in the high Mach number $(\mathcal {M})$ limit as small-scale density fluctuations become suppressed by the strong ${B}_0$. The model reduces to the isotropic $\sigma _{\rho /\rho _0}^2\!-\!\mathcal {M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma _{\rho /\rho _0}^2$ from 12 high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented overdensities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic ${B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

Beattie, James R.↗

DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. DMMs using deep neural networks to parametrize the transition of Markov probability distributions have recently been shown to provide more expressiveness in modeling sequential data and dynamical system responses. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a rigorous analytical method to prove the necessary and sufficient conditions of DMM's stochastic stability. This task is achieved by spectral analysis of the efficiently computed Jacobians of probabilistic maps modeled by deep neural networks. We make theoretical connections between the eigenvalues of neural network's weights and the different activation function types used on the stability and overall dynamic behavior of DMMs with Gaussian distributions. We empirically substantiate our theoretical results on stochastic stability and eigenvalue spectra via several numerical experiments. Formal stability guarantees of DMMs can substantially improve their robustness and trustworthiness, necessary for reliable use in safety-critical real-world applications.

Drgona, Jan↗

DOE OSTI2025

Discriminative versus generative approaches to simulation-based inference

Most of the fundamental, emergent, and phenomenological parameters of particle and nuclear physics are determined through parametric template fits. Simulations are used to populate histograms which are then matched to data. This approach is inherently lossy, since histograms are binned and low-dimensional. Deep learning has enabled unbinned and high-dimensional parameter estimation through neural likelihood(-ratio) estimation. We compare two approaches for neural simulation-based inference (NSBI): one based on discriminative learning (classification) and one based on generative modeling. These two approaches are directly evaluated on the same datasets, with a similar level of hyperparameter optimization in both cases. In addition to a Gaussian dataset, we study NSBI using a Higgs boson dataset from the FAIR Universe Challenge. We find that both the direct likelihood and likelihood ratio estimation are able to effectively extract parameters with reasonable uncertainties. For the numerical examples and within the set of hyperparameters studied, we found that the likelihood ratio method is more accurate and/or precise. Both methods have a significant spread from the network training and would require ensembling or other mitigation strategies in practice.

high energy physics↗

DOE OSTI2020

Turbulence model reduction by deep learning

A defining problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce an alternative, data-driven method for parametrizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local gradient of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Application of Sequential Design of Experiments (SDoE) to Large Pilot-Scale Solvent-Based CO2 Capture Process at Technology Centre Mongstad (TCM)

The United States Department of Energy’s Carbon Capture Simulation for Industry Impact (CCSI2) program has developed a framework for sequential design of experiments (SDoE) that aims to maximize knowledge gained from budget- and schedule-limited pilot scale testing. SDoE was applied to the planning and execution of campaigns for testing CO2 capture systems at pilot-scale in order to optimally allocate resources available for the testing. In this methodology, a stochastic process model is developed by quantifying the parametric uncertainty in submodels of interest; for a solvent-based CO2 capture system, these may include physical properties and equipment performance submodels (e.g., mass transfer, interfacial area). This uncertainty is propagated through the full process model, over variable operating conditions, for estimating the resulting uncertainty in key model outputs (e.g., percentage of CO2 capture, solvent regeneration energy requirement). In developing a data collection plan, the predicted output uncertainty is incorporated into an algorithm that seeks simultaneously to select process operating conditions for which the predicted uncertainty is relatively high and to ensure that the entire space of operation is well represented. This test plan is then used to guide operation of the pilot plant at varying steady-state conditions, with resulting process data incorporated into the existing model using Bayesian inference to refine parameter distributions. The updated stochastic model, with reduced parametric uncertainty from data collected, is then used to guide additional data collection, thus the sequential nature of the experimental design. The SDoE process was implemented at the pilot test unit (12 MWe in scale) at Norway’s Technology Centre Mongstad (TCM) in a summer 2018 test campaign with aqueous monoethanolamine (MEA). During the test campaign, the varied operating conditions included the flowrates of circulated solvent, flue gas, and reboiler steam and the CO2 concentration in the flue gas. The process data were used to update probability distributions of mass transfer and interfacial area parameters of a stochastic process model developed by the CCSI2 team. Two iterations of the SDoE process were executed, resulting in the uncertainty in model predicted CO2 capture percentage decreasing by an average of 58.0 ± 4.7% over the full input space of interest. This work demonstrates the potential of the SDoE process for model refinement through reduction in process model parametric uncertainty, and ultimately risk in scale-up, in CO2 capture technology performance.

carbon capture↗

DOE OSTI2023

Imaging electron angular distributions to assess a full-power petawatt-class laser focus

Here we present a technique to assess the focal volume of petawatt-class lasers at full power. Our approach exploits quantitative measurement of the angular distribution of electrons born in the focus via ionization of rarefied gas, which are accelerated forward and ejected ponderomotively by the field. We show that a bivariate (θ,Φ) angular distribution, which was obtained with image plates, not only enables the peak intensity to be extracted, but also reflects nonideality of the focal-spot intensity distribution. In our prototype demonstration at intensities of a few ×10 19 to a few ×10 20 W/cm 2 , an f/10 optic produced a focal spot in the paraxial regime. This allows a plane-wave parametrization of the peak intensity given by tanθ c =2/a 0 (a 0 being the normalized vector potential and θ c the minimum ejection angle) to be compared with our measurements. Qualitative agreement was found using an a 0 inferred from the pulse energy, pulse duration, and focal spot distribution with a modified parametrization, tanθ c =2η/a 0 ($η=2.02^{+0.26}_{–0.22}$). This highlights the need for (i) better understanding of intensity degradation due to focal-spot distortions and (ii) more robust modeling of the ejection dynamics. Using single-shot detection of electrons, we showed that while there is significant shot-to-shot variation in the number of electrons ejected at a given angular position, the average distribution scales with the pulse energy in a way that is consistent with that seen with the image plates. Finally, we note that the asymptotic behavior as θ→0° limits the usability of angular measurement. For 800 nm, this limit is at an intensity ~10 21 W/cm 2 .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

A Nonparametric Method for the Inference of Halo Occupation Distributions

The galaxy–halo connection traces processes by which galaxies form and evolve. The halo occupation distribution (HOD) describes the relationship between galaxies and their host dark matter haloes. Measurements of the galaxy two-point correlation function (2PCF) allow us to extract information about the HODs of observed galaxy samples. Several parametric HOD models have been proposed in the literature, but the choice of parameterization restricts the space of possible HODs. To resolve this issue, we introduce a nonparametric HOD fitting method in which we train an emulator to learn the mappings among the galaxy 2PCF, physical properties used to select galaxy samples, and the HOD, all obtained from simulated past light cones constructed with the Santa Cruz semianalytic model. Implementing this emulator within a likelihood analysis framework, we derive constraints on the HOD of a galaxy sample when provided with a measurement of its 2PCF. Using the emulator to accelerate likelihood evaluations, we test the nonparametric HOD approach on a set of 2PCFs for mock galaxy samples drawn from the TNG100-1 simulation and selected above threshold values of stellar mass and star formation rate. Our framework is able to recover TNG100-1 HODs within 0.2 dex. We use the TNG100-1 mocks to tune the reported uncertainties to estimate those expected in the analysis of observations. Comparing to parametric HOD modelling routines applied to the same mock galaxy samples, our approach consistently infers the HOD with comparable or greater precision and accuracy.

Kennedy, Jacob [Rutgers Univ., Piscataway, NJ (Uni↗

DOE OSTI2012

GCG parametrization for growth function and current constraints

We study the linear growth function f for large scale structures in a cosmological scenario where Generalised Chaplygin Gas (GCG) serves as dark energy candidate. We parametrize the growth index parameter as a function of redshift and do a comparative study between the theoretical growth rate and the proposed parametrization. Moreover, we demonstrate that growth rates for a wide range of dark energy models can be modeled accurately by our proposed parametrization. Finally, we compile a data set consisting of 28 data points within redshift range (0.15,3.8) to constrain the growth rate. It includes direct growth data from various projects/surveys including the latest data from the Wiggle-Z measurements. It also includes data constraining growth indirectly through the rms mass fluctuation σ{sub 8}(z) inferred from Ly-α measurements at various redshifts. By fitting our proposed parametrization for f to these data, we show that growth history of large scale structures of the universe although allows a transient acceleration, one cannot distinguish it at present with an eternally accelerating universe.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Systematic parameter inference in stochastic mesoscopic modeling

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. These include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 10 5 structural models and 10 6 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable “shape envelope” among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles’ shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Quality Quandaries: Predicting a Population of Curves

We present a random effects spline regression model based on splines that provides an integrated approach for analyzing functional data, i.e., curves, when the shape of the curves is not parametrically specified. An analysis using this model is presented that makes inferences about a population of curves as well as features of the curves.

42 ENGINEERING↗

DOE OSTI2024

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗

DOE OSTI2015

Bayesian inference on the sphere beyond statistical isotropy

We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the inference of the parameters of a Doppler boosted sky map. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Comprehensive characterization of irradiation induced defects in ceria: Impact of point defects on vibrational and optical properties

Validation of multiscale microstructure evolution models can be improved when standard microstructure characterization tools are coupled with methods sensitive to individual point defects. We demonstrate how electronic and vibrational properties of defects revealed by optical absorption and Raman spectroscopies can be used to compliment transmission electron microscopy (TEM) and x-ray diffraction (XRD) in the characterization of microstructure evolution in ceria under non-equilibrium conditions. Experimental manifestation of non-equilibrium conditions was realized by exposing cerium dioxide (CeO2) to energetic protons at elevated temperature. Two sintered polycrystalline CeO2 samples were bombarded with protons accelerated to a few MeVs. These irradiation conditions produced a microstructure with resolvable extended defects and a significant concentration of point defects. A rate theory (RT) model was parametrized using the results of TEM, XRD, and thermal conductivity measurements to infer point defect concentrations. An abundance of cerium sublattice defects suggested by the RT model is supported by Raman spectroscopy measurements, which show peak shift and broadening of the intrinsic T2g peak and emergence of new defect peaks. Additionally, spectroscopic ellipsometry measurements performed in lieu of optical absorption reveals the presence of Ce3+ ions associated with oxygen vacancies. This work lays the foundation for a coupled approach that considers a multimodal characterization of microstructures to guide and validate complex defect evolution models.

Chauhan, Vinay S.↗