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Results for “Implicit Monte Carlo”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An implicit particle code with exact energy and charge conservation for electromagnetic studies of dense plasmas

A collisional particle code based on implicit energy- and charge-conserving methods is presented. A modified version of the particle-suppressed Jacobian-Free Newton-Krylov method that can enhance the solver efficiency is introduced. Mathematically, it is shown that this new approach can be viewed as a fixed-point iteration method for the particle positions. The model can exactly conserve global energy and local charge and can efficiently use time steps larger than the plasma period. In conclusion, the algorithm's ability to simulate dense plasmas accurately and efficiently is quantified by simulating the dynamic compression of a plasma slab via a magnetic piston in 1D planar geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Monte Carlo Radiation Transport for Astrophysical Transients Powered by Circumstellar Interaction

In this paper, we introduce SuperLite, an open-source Monte Carlo radiation transport code designed to produce synthetic spectra for astrophysical transient phenomena affected by circumstellar interaction. SuperLite utilizes Monte Carlo methods for semi-implicit, semirelativistic radiation transport in high-velocity shocked outflows, employing multigroup structured opacity calculations. The code enables rapid post-processing of hydrodynamic profiles to generate high-quality spectra that can be compared with observations of transient events, including superluminous supernovae, pulsational pair-instability supernovae, and other peculiar transients. We present the methods employed in SuperLite and compare the code's performance to that of other radiative transport codes, such as SuperNu and CMFGEN. We show that SuperLite has successfully passed standard Monte Carlo radiation transport tests and can reproduce spectra of typical supernovae of Type Ia, Type IIP, and Type IIn.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Effect of slip on vortex shedding from a circular cylinder in a gas flow

Most studies of vortex shedding from a circular cylinder in a gas flow have explicitly or implicitly assumed that the no-slip condition applies on the cylinder surface. To investigate the effect of slip, vortex shedding is simulated using molecular gas dynamics (the direct simulation Monte Carlo method) and computational fluid dynamics (the incompressible Navier-Stokes equations with a slip boundary condition). A Reynolds number of 100, a Mach number of 0.3, and a corresponding Knudsen number of 0.0048 are examined. For these conditions, compressibility effects are small, and periodic laminar vortex shedding is obtained. Slip on the cylinder is varied using combinations of diffuse and specular molecular reflections with accommodation coefficients from zero (maximum slip) to unity (minimum slip). Although unrealistic, bounce-back molecular reflections are also examined because they approximate the no-slip boundary condition (zero slip). The results from both methods are in reasonable agreement. The shedding frequency increases slightly as the accommodation coefficient is decreased, and shedding ceases at low accommodation coefficients (large slip). The streamwise and transverse forces decrease as the accommodation coefficient is decreased. Based on the good agreement between the two methods, computational fluid dynamics is used to determine the critical accommodation coefficient below which vortex shedding ceases for Reynolds numbers of 60–100 at a Mach number of 0.3. Finally, conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.

42 ENGINEERING↗
DOE OSTI2024

Avoiding pitfalls in molecular simulation of vapor sorption: Example of propane and isobutane in metal–organic frameworks for adsorption cooling applications

This study introduces recommendations for conducting molecular simulations of vapor adsorption, with an emphasis on enhancing the accuracy, reproducibility, and comparability of results. The first aspect we address is consistency in the implementation of some details of typical molecular models, including tail corrections and cutoff distances, due to their significant influence on generated data. We highlight the importance of explicitly calculating the saturation pressures at relevant temperatures using methods such as Gibbs ensemble Monte Carlo simulations and illustrate some pitfalls in extrapolating saturation pressures using this method. For grand canonical Monte Carlo (GCMC) simulations, the input fugacity is usually calculated using an equation of state, which often requires the critical parameters of the fluid. We show the importance of using critical parameters derived from the simulation with the same model to ensure internal consistency between the simulated explicit adsorbate phase and the implicit bulk phase in GCMC. We show the advantages of presenting isotherms on a relative pressure scale to facilitate easier comparison among models and with experiment. Extending these guidelines to a practical case study, we evaluate the performance of various isoreticular metal–organic frameworks (MOFs) in adsorption cooling applications. This includes examining the advantages of using propane and isobutane as working fluids and identifying MOFs with a superior performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Uncertainty-Informed Volume Visualization using Implicit Neural Representation

The increasing adoption of Deep Neural Networks (DNNs) has led to their application in many challenging scientific visualization tasks. While advanced DNNs offer impressive generalization capabilities, understanding factors such as model prediction quality, robustness, and uncertainty is crucial. These insights can enable domain scientists to make informed decisions about their data. However, DNNs inherently lack ability to estimate prediction uncertainty, necessitating new research to construct robust uncertainty-aware visualization techniques tailored for various visualization tasks. In this work, we propose uncertainty-aware implicit neural representations to model scalar field data sets effectively and comprehensively study the efficacy and benefits of estimated uncertainty information for volume visualization tasks. We evaluate the effectiveness of two principled deep uncertainty estimation techniques: (1) Deep Ensemble and (2) Monte Carlo Dropout (MC-Dropout). These techniques enable uncertainty-informed volume visualization in scalar field data sets. Our extensive exploration across multiple data sets demonstrates that uncertainty-aware models produce informative volume visualization results. Moreover, integrating prediction uncertainty enhances the trustworthiness of our DNN model, making it suitable for robustly analyzing and visualizing real-world scientific volumetric data sets.

Saklani, Shanu↗
DOE OSTI2023

Fully Implicit Conjugate Heat Transfer Analysis of the ARC-Class Vacuum Vessel

The coupled simulation of fusion reactor blankets including neutronics, thermal-hydraulics and thermo-mechanics is expected to speed up the design cycle of fusion reactor design concepts. In this work we demonstrate tight implicit coupling of conjugate heat transfer using the open-source Computational Fluid Dynamics software OpenFOAM for thermo-fluid mechanics and Diablo for thermo-solid mechanics. The heat transfer analysis is augmented by volumetric energy deposition from neutronic calculations using the Monte Carlo N-particle code on both solid and fluid parts of the vacuum vessel. An additional heat flux is imposed on the first wall estimated from the design power of the reactor. The tight coupling is realized through the open-source coupling library, preCICE, and tested on the vacuum vessel of the affordable, robust, compact reactor design by Commonwealth Fusion Systems. The features of the coupling and the influence of different coupling parameters such as coupling schemes, acceleration techniques and convergence criterion are discussed. The coupled simulation results are compared to a thermal-hydraulics simulation which includes only the fluid domains (the liquid immersion molten salt blanket and cooling channel) to demonstrate usefulness of a coupled simulation. Further analysis is performed to identify regions of hot spots for subsequent design improvement. This introduces the outline for integrating conjugate electromagnetics and fluid/solid mechanics (e.g., allow for deformation of the cooling channel walls) with our present approach for future analysis.

Sircar, Arpan↗
DOE OSTI2023

Concepts of association between cancer and ionising radiation: accounting for specific biological mechanisms

The probability that an observed cancer was caused by radiation exposure is usually estimated using cancer rates and risk models from radioepidemiological cohorts and is called assigned share (AS). This definition implicitly assumes that an ongoing carcinogenic process is unaffected by the studied radiation exposure. However, there is strong evidence that radiation can also accelerate an existing clonal development towards cancer. In this work, we define different association measures that an observed cancer was newly induced, accelerated, or retarded. The measures were quantified exemplarily by Monte Carlo simulations that track the development of individual cells. Three biologically based two-stage clonal expansion (TSCE) models were applied. In the first model, radiation initiates cancer development, while in the other two, radiation has a promoting effect, i.e. radiation accelerates the clonal expansion of pre-cancerous cells. The parameters of the TSCE models were derived from breast cancer data from the atomic bomb survivors of Hiroshima and Nagasaki. For exposure at age 30, all three models resulted in similar estimates of AS at age 60. For the initiation model, estimates of association were nearly identical to AS. However, for the promotion models, the cancerous clonal development was frequently accelerated towards younger ages, resulting in associations substantially higher than AS. This work shows that the association between a given cancer and exposure in an affected person depends on the underlying biological mechanism and can be substantially larger than the AS derived from classic radioepidemiology.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Development of CTF modeling of interfacial drag, wall shear, and interfacial heat transfer for bubbly and annular-mist flow regimes

This milestone report discusses improvements to CTF closure models for modeling of bubbly and annular mist two-phase flow conditions, which are important for accurate modeling and simulation for boiling water reactor (BWR) conditions. Models that were improved include the two-phase wall shear, wall boiling, and phase mass and heat transfer. A new flow regime map was implemented to improve on the prediction of transition to annular flow, which was generally largely over-predicted by the legacy CTF flow regime map. The annular mist interfacial drag models were also reviewed and new models were proposed for implementation into the code. In addition to implementing new models, an activity was performed to calibrate these new models to experimental data using a Markov Chain Monte Carlo technique, thus further improving their accuracy. Finally, new experiments were implemented into the CTF validation matrix which add more two-phase pressure drop and void measurements for the assessment of CTF for modeling of BWRs. The results show that the Chisholm model, which was implemented and then calibrated, results in significantly improved comparison against the Riso two-phase pressure drop data. Furthermore, improvements in the implicit heat transfer and wall boiling models resulted in good agreement with the void measurement data.

42 ENGINEERING↗
DOE OSTI2025

Understanding Differences in Water Adsorption Isotherms: Structural Variations, Force Fields, and Monte Carlo Simulation Approaches

Accurate prediction of water adsorption in micro- and mesoporous materials with hydrophobic pores is essential for the design and characterization of advanced adsorbent materials for separation and energy applications. Here, we assess the reproducibility and consistency of water adsorption isotherms in two microporous all-silica MFI zeolite structures (MFI-K and MFI-O) using two different zeolite force fields and three simulation approaches: grand canonical Monte Carlo (GCMC), Gibbs ensemble Monte Carlo (GEMC), and transition matrix Monte Carlo (TMMC). We demonstrate that consistent treatment of the bulk fluid phase in GCMC and TMMC simulations is critical for reconciling isotherms across methods, and we construct simulation-based equations of state for the TIP4P water model to enable rigorous fugacity-to-pressure conversions. Large shifts in the isotherms are observed for two zeolite force fields developed using different parametrization strategies, with the GCS force field representing implicitly a defect-containing all-silica zeolite, whereas the TraPPE-zeo force field accurately represents an essentially defect-free all-silica zeolite. While water in the van Koningsveld structure of MFI exhibits a first-order phase transition and condensation-like step for adsorption near room temperature, water in the Olson structure of MFI displays continuous adsorption, attributed to differences in the adsorption free energy landscapes. Structural analysis reveals that small geometric variations, particularly Si–O–Si bond angles near the strongest adsorption sites, lead to these substantial differences in adsorption behavior. Furthermore, our results highlight the sensitivity of simulated water adsorption isotherms in hydrophobic frameworks to seemingly small differences in the framework structures, force field parametrization, and simulation approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Capabilities of multivariate Bayesian inference toward seismic hazard assessment

Multivariate Bayesian analysis can bring significant benefits to seismic hazard analysis: Its multivariate feature enables computing scalar and vector hazard without making any approximations; Correlations between intensity measures are implicitly modeled, permitting direct simulation of ground motion selection tools such as the conditional mean spectrum and the generalized conditioning intensity measure; and Its updating feature enables a seamless integration of new ground motion data into the hazard results. Here, we first develop a multivariate Bayesian ground motion model through the NGA-West2 database. The model functional form considers fault-type, magnitude, and distance dependencies, and also the linear and the rock intensity dependent site response. We use a hybrid Markov Chain Monte Carlo sampling to perform Bayesian inference consisting of Gibbs step and a multilevel Metropolis-Hastings step. We then perform several checks on the model and note that its performance is satisfactory. Finally, we illustrate the merits of this multivariate Bayesian analysis, which include: ground motion model updating with ground motion data recorded in the last four years not part of the NGA-West2 database; computation of scalar and vector seismic hazard using the un-updated and updated ground motion models for Los Angeles, CA; and simulation of the conditional mean spectrum under scalar and vector IM conditioning while accounting for different sources of aleatoric and epistemic uncertainties.

58 GEOSCIENCES↗
DOE OSTI2020

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

In this work, we present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress–energy tensor is evolved in flux-conservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Furthermore, radiation four-forces are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency-dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that Method of Characteristics Moment Closure converges at least as ~N -1 , rather than the canonical Monte Carlo N -1/2 , where N is the number of samples per zone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates

Abstract A reliable estimate of the redshift distribution n ( z ) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo- z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo- z point estimation. The established stacked estimator of n ( z ) avoids reducing photo- z PDFs to point estimates but yields a systematically biased estimate of n ( z ) that worsens with a decreasing signal-to-noise ratio, the very regime where photo- z PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts ( CHIPPR ), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator of n ( z ) produced by traditional procedures and is provably the only self-consistent way to recover n ( z ) from photo- z PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo- z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo- z community focus on developing methodologies that enable the recovery of photo- z likelihoods with support over all redshifts, either directly or via a known prior probability density.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Liquid Phase Modeling in Porous Media: Adsorption of Methanol and Ethanol in H-MFI in Condensed Water

Zeolites are used in the chemical and separation industries for their exceptional selectivity, adsorption capacity, regenerability, and stability in gas and liquid phase processing. Here, we developed an explicit solvation method for predicting solvent/condensed phase effects on adsorption free energies in microporous media such as zeolites based on the hybrid quantum mechanical/molecular mechanical free energy perturbation (QM/MM-FEP) technique. Our explicit solvation method for zeolite systems, called eSZS, aims to capture site-specific interactions during the adsorption process at the Brønsted acid sites of H-MFI zeolite while still considering the diverse configuration space of the solvent molecules. This strategy is ideal for chemical reactions or adsorbates that interact with the microporous medium in few distinct adsorbate/transition state configurations, i.e., the harmonic or similar approximations are acceptable for the adsorbate/transition state while such approximations break down for the solvent molecules that require extensive configuration space sampling. In this way, our approach effectively overcomes the limitations of implicit solvation models and classical force field methods for describing solvation effects on chemical reactions within porous materials such as zeolites. Specifically, in this study, we investigated various aspects of our hybrid QM/MM approach, including QM cluster size dependencies in a periodic electrostatically embedded cluster model (PEECM), rules for link atoms at the QM/MM boundary, and functional and basis set considerations for converged and reasonably accurate gas and aqueous phase methanol and ethanol adsorption free energy predictions in H-MFI. For gas phase adsorption of methanol and ethanol in H-MFI at a Brønsted acid site in T12 position, we compute adsorption free energies at 298 K of −0.61 and −0.75 eV, respectively, using a PEECM containing 50 Si and 1 Al atom with ωB97x-D/def2-TZVP level of theory. For solvent effect calculations, we sample the aqueous phase using grand canonical Monte Carlo (GCMC) simulations to (1) obtain a mean field of electrostatic interactions in the reaction system and (2) perform a rigorous free energy perturbation calculation. Similar to the experimentally and computationally observed endergonic solvation effects observed for hydrocarbon adsorption on metal surfaces, we also observe that a condensed aqueous environment destabilizes methanol and ethanol at these acid sites in H-MFI at 298 K. Specifically, the computed solvation free energies of adsorption (ΔΔG solv ) for methanol and ethanol are +0.44 and +0.54 eV, respectively. From this study, it is evident that adsorbates (methanol and ethanol) are competing with water for adsorption space inside the H-MFI zeolite, leading to an endergonic solvation effect. Here, we expect that the endergonic, aqueous solvent effect during adsorption in microporous zeolites is highly tunable by changing the pore size and hydrophobicity of the microporous material as this will affect the water density inside the pore structure.

Adsorption↗
DOE OSTI2024

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C 60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Divergence Reduction in Monte Carlo Neutron Transport with On-GPU Asynchronous Scheduling

While Monte Carlo Neutron Transport (MCNT) is near-embarrasingly parallel, the effectively unpredictable lifetime of neutrons can lead to divergence when MCNT is evaluated on GPUs. Divergence is the phenomenon of adjacent threads in a warp executing different control flow paths; on GPUS, it reduces performance because each work group may only execute one path at a time. The process of Thread Data Remapping (TDR) resolves these discrepancies by moving data across hardware such that data in the same warp will be processed through similar paths. A common issue among prior implementations of TDR is the synchronous nature of its remapping and processing cycles, which exhaustively sort data produced by prior processing passes and exhaustively evaluate the sorted data. In another work, we defined a method of remapping data through an asynchronous scheduler which allows for work to be stored in shared memory and deferred arbitrarily until that work is a viable option for low-divergence evaluation. This article surveys a wider set of cases, with the goal of characterizing performance trends across a more comprehensive set of parameters. These parameters include cross sections of scattering/capturing/fission, use of implicit capture, source neutron counts, simulation time spans, and tuned memory allocations. Across these cases, we have recorded minimum and average execution times, as well as a heuristically tuned near-optimal memory allocation size for both synchronous and asynchronous scheduling. Across the collected data, it is shown that the asynchronous method is faster and more memory efficient in the majority of cases, and that it requires less tuning to achieve competitive performance.

Computer Science↗
DOE OSTI2021

Volumetric recombination in EMC3-EIRENE: Implementation and first application to the pre-fusion power operation phase in ITER

An upgrade to the 3D plasma boundary model EMC3-EIRENE for detached divertor plasmas is introduced and evaluated. Stabilization of the iterative approximation of a self-consistent plasma–neutral gas solution is required at low divertor plasma temperatures, and this has been achieved by linearization of the energy loss term associated with the electron–neutral gas interaction. An implicit method for volumetric recombination has been implemented, which improves agreement with SOLPS-ITER results for the pre-fusion power operation phase in ITER. Resonant magnetic perturbations for control of edge localized modes are found to result in a partially detached divertor plasma with a significantly broader reduction of particle loads in the traditional strike zone, which is attributed to volumetric recombination. The additional non-axisymmetric far scrape-off layer strike points, on the other hand, remain attached at relatively high temperature so that volumetric recombination is not effective there.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bayesian Optimization Framework for Imperfect Data or Models

Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.

97 MATHEMATICS AND COMPUTING↗