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All sources NASA NTRS DOE OSTI

DOE OSTI2022

Scalable deep learning for watershed model calibration

Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters often need to be estimated/calibrated through inverse modeling to produce reliable predictions on hydrological fluxes and states. Existing parameter estimation methods can be time consuming, inefficient, and computationally expensive for high-dimensional problems. In this paper, we present an accurate and robust method to calibrate the SWAT model (i.e., 20 parameters) using scalable deep learning (DL). We developed inverse models based on convolutional neural networks (CNN) to assimilate observed streamflow data and estimate the SWAT model parameters. Scalable hyperparameter tuning is performed using high-performance computing resources to identify the top 50 optimal neural network architectures. We used ensemble SWAT simulations to train, validate, and test the CNN models. We estimated the parameters of the SWAT model using observed streamflow data and assessed the impact of measurement errors on SWAT model calibration. We tested and validated the proposed scalable DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the CNN-based calibration is better than two popular parameter estimation methods (i.e., the generalized likelihood uncertainty estimation [GLUE] and the dynamically dimensioned search [DDS], which is a global optimization algorithm). For the set of parameters that are sensitive to the observations, our proposed method yields narrower ranges than the GLUE method but broader ranges than values produced using the DDS method within the sampling range even under high relative observational errors. The SWAT model calibration performance using the CNNs, GLUE, and DDS methods are compared using R 2 and a set of efficiency metrics, including Nash-Sutcliffe, logarithmic Nash-Sutcliffe, Kling-Gupta, modified Kling-Gupta, and non-parametric Kling-Gupta scores, computed on the observed and simulated watershed responses. The best CNN-based calibrated set has scores of 0.71, 0.75, 0.85, 0.85, 0.86, and 0.91. The best DDS-based calibrated set has scores of 0.62, 0.69, 0.8, 0.77, 0.79, and 0.82. The best GLUE-based calibrated set has scores of 0.56, 0.58, 0.71, 0.7, 0.71, and 0.8. The scores above show that the CNN-based calibration leads to more accurate low and high streamflow predictions than the GLUE and DDS sets. Our research demonstrates that the proposed method has high potential to improve our current practice in calibrating large-scale integrated hydrologic models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The impact of hurricane disturbances on a tropical forest: implementing a palm plant functional type and hurricane disturbance module in ED2-HuDi V1.0

Hurricanes commonly disturb and damage tropical forests. Hurricane frequency and intensity are predicted to change under the changing climate. The short-term impacts of hurricane disturbances to tropical forests have been widely studied, but the long-term impacts are rarely investigated. Modeling is critical to investigate the potential response of forests to future disturbances, particularly if the nature of the disturbances is changing with climate. Unfortunately, existing models of forest dynamics are not presently able to account for hurricane disturbances. Therefore, we implement the Hurricane Disturbance in the Ecosystem Demography model (ED2) (ED2-HuDi). The hurricane disturbance includes hurricane-induced immediate mortality and subsequent recovery modules. The parameterizations are based on observations at the Bisley Experimental Watersheds (BEW) in the Luquillo Experimental Forest in Puerto Rico. We add one new plant functional type (PFT) to the model – Palm, as palms cannot be categorized into one of the current existing PFTs and are known to be an abundant component of tropical forests worldwide. The model is calibrated with observations at BEW using the generalized likelihood uncertainty estimation (GLUE) approach. The optimal simulation obtained from GLUE has a mean relative error of –21 %, –12 %, and –15 % for stem density, basal area, and aboveground biomass, respectively. The optimal simulation also agrees well with the observation in terms of PFT composition (+1 %, –8 %, –2 %, and +9 % differences in the percentages of “Early”, “Mid”, “Late”, and “Palm” PFTs, respectively) and size structure of the forest (+0.8 % differences in the percentage of large stems). Lastly, using the optimal parameter set, we study the impact of forest initial condition on the recovery of the forest from a single hurricane disturbance. The results indicate that, compared to a no-hurricane scenario, a single hurricane disturbance has little impact on forest structure (+1 % change in the percentage of large stems) and composition (<1 % change in the percentage of each of the four PFTs) but leads to 5 % higher aboveground biomass after 80 years of succession. The assumption of a less severe hurricane disturbance leads to a 4 % increase in aboveground biomass.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

A Novel Modeling Framework for Computationally Efficient and Accurate Real-Time Ensemble Flood Forecasting With Uncertainty Quantification

A novel modeling framework that simultaneously improves accuracy, predictability, and computational efficiency is presented. It embraces the benefits of three modeling techniques integrated together for the first time: surrogate modeling, parameter inference, and data assimilation. The use of polynomial chaos expansion (PCE) surrogates significantly decreases computational time. Parameter inference allows for model faster convergence, reduced uncertainty, and superior accuracy of simulated results. Ensemble Kalman filters assimilate errors that occur during forecasting. To examine the applicability and effectiveness of the integrated framework, we developed 18 approaches according to how surrogate models are constructed, what type of parameter distributions are used as model inputs, and whether model parameters are updated during the data assimilation procedure. We conclude that (1) PCE must be built over various forcing and flow conditions, and in contrast to previous studies, it does not need to be rebuilt at each time step; (2) model parameter specification that relies on constrained, posterior information of parameters (so-called Selected specification) can significantly improve forecasting performance and reduce uncertainty bounds compared to Random specification using prior information of parameters; and (3) no substantial differences in results exist between single and dual ensemble Kalman filters, but the latter better simulates flood peaks. The use of PCE effectively compensates for the computational load added by the parameter inference and data assimilation (up to ~80 times faster). Therefore, the presented approach contributes to a shift in modeling paradigm arguing that complex, high-fidelity hydrologic and hydraulic models should be increasingly adopted for real-time and ensemble flood forecasting.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Analysis of Polarimetry Data with Angular Uncertainties

For a track based polarimeter, such as the Imaging X-ray Polarimetry Explorer (IXPE), the sensitivity to polarization depends on the modulation factor, which is a strong function of energy. In previous work, a likelihood method was developed that would account for this variation in order to estimate the minimum detectable polarization (MDP). That method essentially required that the position angles of individual events should be known precisely. In a separate work, however, it was shown that using a machine-learning method for measuring event tracks can generate track angle uncertainties, which can be used in the analysis. Here, the maximum likelihood method is used as a basis for revising the estimate of the MDP in a general way that can include uncertainties in event track position angles. The resultant MDP depends solely upon the distribution of track angle uncertainties present in the input data. Due to the physics of the IXPE detectors, it is possible to derive a simple relationship between these angular uncertainties and the energy-dependent modulation function as a step in the process.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

On the uncertainty of long-period return values of extreme daily precipitation

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2009

Reliability Analysis of Systems Subject to First-Passage Failure

An obvious goal of reliability analysis is the avoidance of system failure. However, it is generally recognized that it is often not feasible to design a practical or useful system for which failure is impossible. Thus it is necessary to use techniques that estimate the likelihood of failure based on modeling the uncertainty about such items as the demands on and capacities of various elements in the system. This usually involves the use of probability theory, and a design is considered acceptable if it has a sufficiently small probability of failure. This report contains findings of analyses of systems subject to first-passage failure.

Lutes, Loren D.↗

DOE OSTI2022

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

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

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A Compound Poisson Generator Approach to Point-source Inference in Astrophysics

Abstract The identification and description of point sources is one of the oldest problems in astronomy, yet even today the correct statistical treatment for point sources remains one of the field’s hardest problems. For dim or crowded sources, likelihood-based inference methods are required to estimate the uncertainty on the characteristics of the source population. In this work, a new parametric likelihood is constructed for this problem using compound Poisson generator (CPG) functionals that incorporate instrumental effects from first principles. We demonstrate that the CPG approach exhibits a number of advantages over non-Poissonian template fitting (NPTF)—an existing method—in a series of test scenarios in the context of X-ray astronomy. These demonstrations show that the effect of the point-spread function, effective area, and choice of point-source spatial distribution cannot, generally, be factorized as they are in NPTF, while the new CPG construction is validated in these scenarios. Separately, an examination of the diffuse-flux emission limit is used to show that most simple choices of priors on the standard parameterization of the population model can result in unexpected biases: when a model comprising both a point-source population and diffuse component is applied to this limit, nearly all observed flux will be assigned to either the population or to the diffuse component. A new parameterization is presented for these priors that properly estimates the uncertainties in this limit. In this choice of priors, CPG correctly identifies that the fraction of flux assigned to the population model cannot be constrained by the data.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

TDRS orbit determination by radio interferometry

In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometry tracking accuracy. The Orbit Determination Accuracy Estimator (ODAE) models the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with the group and phase delay measurements from radio interferometry. ODAE models the statistical properties of tracking error sources, including inherent observable imprecision, atmospheric delays, clock offsets, station location uncertainty, and measurement biases, and through Monte Carlo simulation, ODAE calculates the statistical properties of errors in the predicted satellites state vector. This paper presents results from ODAE application to orbit determination of the Tracking and Data Relay Satellite (TDRS) by radio interferometry. Conclusions about optimal ground station locations for interferometric tracking of TDRS are presented, along with a discussion of operational advantages of radio interferometry.

Pavloff, Michael S.↗

DOE OSTI2023

Uncertain of uncertainties? A comparison of uncertainty quantification metrics for chemical data sets

Abstract With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet to be established and different studies on uncertainties generally uses different metrics to evaluate them. We compare three of the most popular validation metrics (Spearman’s rank correlation coefficient, the negative log likelihood (NLL) and the miscalibration area) to the error-based calibration introduced by Levi et al. ( Sensors 2022 , 22 , 5540). Importantly, metrics such as the negative log likelihood (NLL) and Spearman’s rank correlation coefficient bear little information in themselves. We therefore introduce reference values obtained through errors simulated directly from the uncertainty distribution. The different metrics target different properties and we show how to interpret them, but we generally find the best overall validation to be done based on the error-based calibration plot introduced by Levi et al. Finally, we illustrate the sensitivity of ranking-based methods (e.g. Spearman’s rank correlation coefficient) towards test set design by using the same toy model ferent test sets and obtaining vastly different metrics (0.05 vs. 0.65).

Rasmussen, Maria H.↗

NASA NTRS1994

Application of a Monte Carlo accuracy assessment tool to TDRS and GPS

In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometric tracking accuracy. Initially, the tool was applied to the problem of determining optimal interferometric station siting for orbit determination of the Tracking and Data Relay Satellite (TDRS). Subsequently, the Orbit Determination Accuracy Estimator (ODAE) was expanded to model the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with measurement types including not only group and phase delay from radio interferometry, but also range, range rate, angular measurements, and satellite-to-satellite measurements. The user of ODAE specifies the statistical properties of error sources, including inherent observable imprecision, atmospheric delays, station location uncertainty, and measurement biases. Upon Monte Carlo simulation of the orbit determination process, ODAE calculates the statistical properties of the error in the satellite state vector and any other parameters for which a solution was obtained in the orbit determination. This paper presents results from ODAE application to two different problems: (1)determination of optimal geometry for interferometirc tracking of TDRS, and (2) expected orbit determination accuracy for Global Positioning System (GPS) tracking of low-earth orbit (LEO) satellites. Conclusions about optimal ground station locations for TDRS orbit determination by radio interferometry are presented, and the feasibility of GPS-based tracking for IRIDIUM, a LEO mobile satellite communications (MOBILSATCOM) system, is demonstrated.

Pavloff, Michael S.↗

DOE OSTI2024

Multivariate degradation modeling using generalized cauchy process and application in life prediction of dye-sensitized solar cells

Recently, the Generalized Cauchy (GC) process has been applied to capture a Long Memory (LM) phenomenon in product degradation modeling and life prediction. Compared with the traditional fractional Brownian motion that captures the LM using a single Hurst parameter, the GC process has two free parameters (Hurst and fractal dimension parameters) that flexibly capture both global LM and local irregularity. However, all existing GC-based degradation models are for a single Degradation Characteristic (DC). In this article, motivated by a real degradation problem of dye-sensitized solar cells that jointly exhibits multiple DCs, global LM, local irregularity and DC-wise cross-correlation, we propose a novel GC-based Multivariate Degradation Model (GC-MDM) to simultaneously capture the aforementioned effects. A maximum likelihood estimation approach is developed to estimate parameters of the GC-MDM. Subsequently, product life prediction based on the GC-MDM is developed. The proposed GC-MDM is validated through a simulation study and a physical experiment of dye-sensitized solar cells. Furthermore, results show that the proposed GC-MDM fundamentally improves the life prediction accuracy in comparison with conventional degradation models which significantly misestimate the uncertainty of product life.

14 SOLAR ENERGY↗

NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗

NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗

NASA NTRS1996

Uncertainty and Intelligence in Computational Stochastic Mechanics

Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.

Ayyub, Bilal M.↗

DOE OSTI2021

METHODOLOGY AND APPLICATION OF PHYSICAL SECURITY EFFECTIVENESS BASED ON DYNAMIC FORCE-ON-FORCE MODELING

This paper describes ongoing work within the Light Water Reactor Sustainability (LWRS) Program at Idaho National Laboratory (INL) to optimize security and cost of nuclear power plants (NPPs). It reviews the conservatisms in conventional physical security posture and regulations. It introduces the dynamic risk assessment tool developed at INL, Event Modeling Risk Assessment using Linked Diagrams (EMRALD). The dynamic assessment methodology leverages EMRALD to process results of force-on-force (FOF) simulations and crediting safety mitigation actions from probabilistic risk assessment (PRA) models as well as diverse and flexible coping strategies (FLEX) mitigation strategies. Timing information from these simulations are compared against the available time to perform mitigations obtained from Reactor Excursion and Leak Analysis Program (RELAP5) simulations. To illustrate the methodology, a station blackout (SBO) attack scenario was modeled in commercially available FOF simulation tools. The simulation results provide valuable insights into possible attack outcomes and as the probabilistic risk of a core damage event given these outcomes. Safety mitigation procedures were modeled in EMRALD, and were dependent on the attack outcomes by considering human operator uncertainties. RELAP5 simulations incorporating human and hardware uncertainties were performed to estimate the distribution of time-to-core damage. The results demonstrate that, even in the extreme case of a successful adversarial attack, plant mitigation strategies provide significantly high-likelihood of preventing radiological release. The proposed modeling and simulation framework of integrating FLEX equipment with FOF models enables the NPPs to credit FLEX portable equipment in the plant security posture, resulting in an efficient and optimized physical security.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

MultiPEM Toolbox: User Manual [Rev. 2]

This document explains use of the Multi-Phenomenology Explosion Monitoring (Multi PEM) Toolbox, a collection of R scripts for estimating the unknown device parameters of a new event with uncertainty quantification. The methodology and application used for illustration in this user manual are fully documented in a Los Alamos National Laboratory technical report hereafter designated “WPA” for reference. Additional details on the application are found in a recent journal article. Two assessment types are available: rapid and complete. Rapid assessments are conducted in two stages, as described in Section 2. In the first stage, calibration data are used to estimate forward and error model parameters (WPA, §5.1) and (if relevant) errors-in-variables yield values for calibration sources (WPA, §3, Equation (3)). In the second stage, new event data are used to estimate the unknown new event device parameters (WPA, §5.2) with uncertainty quantification. Two options for treating the inferred first stage parameters in second stage Bayesian analysis are available: fixing them at their maximum likelihood estimate (default), or multiple imputation. Multiple imputation involves utilizing several posterior samples (imputations) of the first stage parameters as fixed values in the second stage posterior sampling of the new event device parameters. Second stage sampling is conducted across imputations in parallel to improve computational efficiency. This method produces improved uncertainty quantification of the new event device parameters compared with the default treatment of the first stage parameters, at the expense of additional computation. Complete assessments are conducted in a single stage, as described in Section 3. Calibration and (if relevant) new event data are used simultaneously to estimate all forward model, error model, and (if relevant) new event device parameters with uncertainty quantification on the latter. As the name suggests, rapid assessments generally run substantially faster than complete assessments (even with multiple imputation), because the results of first stage analysis can be stored and incorporated into estimating a relatively low-dimensional space of new event device parameters whenever relevant new event data becomes available. On the other hand, complete assessments must be run on the full set of model and device parameters with calibration and new event data every time the latter becomes available.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A practical and efficient approach for Bayesian quantum state estimation

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗