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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Calibration of the Diffusivity Predictions of Centipede Using Approximate Bayesian Computation and Applications in Nyx (Engineering Scale) and Xolotl-MARMOT (Meso-Scale) Simulations

Fission gas evolution and release in UO 2 nuclear fuel are important fuel performance metrics and occur in several distinct stages: 1) nucleation, growth and resolution of intra-granular bubbles, 2) diffusion to grain boundaries and 3) nucleation and growth of bubbles at grain boundaries, which eventually form a connected network (percolation) enabling release of gas from grain boundaries through connections to triple junctions, grain edges or free surfaces. The NE-SciDAC project is developing several computational tools to model this problem, which are connected in a hierarchical multi-scale framework. The information transfer in the multi-scale framework is a critical step that, in addition to best-estimates, should include uncertainty quantification. Despite taking a first-principles multi-scale approach, there is a need to perform parameter calibration to ensure consistency with available experimental data. In the present study, uncertainty quantification (UQ) and parameter calibration is demonstrated for one of the lower length scale codes in the multi-scale framework (Centipede) and then the results, including instances of the propagated uncertainties, are used in other codes within the framework, specifically Nyx and Xolotl-MARMOT. We calibrated the model parameters in Centipede, a computer code used to predict diffusivities of uranium (U) and xenon (Xe) in the context of the simulation of fission gas in uranium oxide (UO 2 ) nuclear fuel. The Centipede code depends on 183 parameters, all of which are subject to uncertainty. The three data sets used in our calibration effort are taken from the literature. This data is available as a set of measurements, including measurement errors. Our goal is to calibrate a statistical model that predicts both the value of the measurement and the uncertainty associated with the measurement. We perform a Bayesian calibration of the model parameters using a dedicated approximate Bayesian computation (ABC) likelihood function. To avoid excessive computational costs, we replace the expensive Centipede simulation code by a higher-order surrogate model, constructed using only the 9 most important parameters. These important parameters are identified by a preliminary global sensitivity analysis (GSA) study. Among the important parameters are T0 (the temperature at which UO 2 is perfectly stoichiometric) and Hf_pO2 (the temperature dependence of the oxygen (O) partial pressure) that should be considered as operating conditions to be estimated along with the other parameters. We consider two different cases: one where we define one set of these operating conditions for all data sets, and one where we define distinct operating condition parameters for each data set. The Xe diffusivities predicted by the latter case show distinct features that could not be observed in the former. Next, we use the diffusivity predictions by Centipede as input to Nyx, a reduced order fuel performance code focused on gas behavior alone, in order to estimate quantities associated with inter-granular bubble formation at conditions specified by the experiments. Finally, the diffusivities obtained from the calibrated Centipede runs were used in coupled Xolotl-MARMOT simulations of intra- and inter-granular gas evolution. The results are compared to simulations using the baseline diffusivities from Turnbull et al.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Bayesian Framework for Bioburden Density Estimation in Planetary Protection

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Coexistent quantum channel characterization using quantum process tomography with spectrally resolved detection

The coexistence of classical and quantum signals over the same optical fiber is critical for quantum networks operating within the existing communications infrastructure. Here, we characterize the quantum channel that results from distributing approximate single-photon polarization-encoded qubits simultaneously with classical light of varying intensities through a 25 km fiber-optic channel. We use spectrally resolved quantum process tomography with a newly developed Bayesian reconstruction method to estimate the quantum channel from experimental data, both with and without classical noise. Furthermore, we show that the coexistent fiber-based quantum channel has high process fidelity with an ideal depolarizing channel if the noise is dominated by Raman scattering. These results aid future development of quantum repeater designs and quantum error-correcting codes which benefit from realistic channel error models.

Chapman, Joseph↗
DOE OSTI2021

Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data

Here, we perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg 2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be ${A}_{\phi }=0.949\,\pm \,0.122$ using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist "bias hardening" or linear bias correction, and reducing the systematic uncertainty on A Φ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A Φ along with A L , the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A Φ and seven times lower effective lensing reconstruction noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Bayesian homodyne and heterodyne tomography

Continuous-variable (CV) photonic states are of increasing interest in quantum information science, bolstered by features such as deterministic resource state generation and error correction via bosonic codes. Data-efficient characterization methods will prove critical in the fine-tuning and maturation of such CV quantum technology. Although Bayesian inference offers appealing properties—including uncertainty quantification and optimality in mean-squared error—Bayesian methods have yet to be demonstrated for the tomography of arbitrary CV states. Here we introduce a complete Bayesian quantum state tomography workflow capable of inferring generic CV states measured by homodyne or heterodyne detection, with no assumption of Gaussianity. As examples, we demonstrate our approach on experimental coherent, thermal, and cat state data, obtaining excellent agreement between our Bayesian estimates and theoretical predictions. Our approach lays the groundwork for Bayesian estimation of highly complex CV quantum states in emerging quantum photonic platforms, such as quantum communications networks and sensors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Human reliability analysis studies from simulator experiments using Bayesian inference

Probabilistic Safety Assessment (PSA) of complex facilities is performed to arrive at the risk posed by them. PSA also accounts for the contribution of the human errors towards the overall risk through Human Reliability Analysis (HRA) in terms of Human Error Probability (HEP). Human operators are part of the system and do not work in isolation. Their performance is influenced by the context in which the actions are performed. As a result, quantification of HEP requires operator performance data under the given context. Some good sources of operator performance data are plant‘s operation data, simulator data and expert judgement. The plant operation data pertaining to HRA is generally sparse. In this situation, a full scope plant simulator provides a good alternative for operator performance data generation. Many of the currently practiced HRA methods have been developed by combining the empirical evidence with expert judgement and contain a lot of uncertainty in their estimates. Bayesian inference is suitable for updating the prior HRA estimates with the simulator evidence to obtain the posterior HEP. Here, posterior HEP has been calculated for postulated accident scenarios in advanced reactor (first of its kind) at design stage, using plant simulator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

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

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

Bayesian inference↗
DOE OSTI2023

Fusion of Multiple Models for Improving Gross Primary Production Estimation With Eddy Covariance Data Based on Machine Learning

Abstract Terrestrial gross primary production (GPP) represents the magnitude of CO 2 uptake through vegetation photosynthesis, and is a key variable for carbon cycles between the biosphere and atmosphere. Light use efficiency (LUE) models have been widely used to estimate GPP for its physiological mechanisms and availability of data acquisition and implementation, yet each individual GPP model has exhibited large uncertainties due to input errors and model structure, and further studies of systematic validation, comparison, and fusion of those models with eddy covariance (EC) site data across diverse ecosystem types are still needed in order to further improve GPP estimation. We here compared and fused five GPP models (VPM, EC‐LUE, GOL‐PEM, CHJ, and C‐Fix) across eight ecosystems based on FLUXNET2015 data set using the ensemble methods of Bayesian Model Averaging (BMA), Support Vector Machine (SVM), and Random Forest (RF) separately. Our results showed that for individual models, EC‐LUE gave a better performance to capture interannual variability of GPP than other models, followed by VPM and GLO‐PEM, while CHJ and C‐Fix were more limited in their estimation performance. We found RF and SVM were superior to BMA on merging individual models at various plant functional types (PFTs) and at the scale of individual sites. On the basis of individual models, the fusion methods of BMA, SVM, and RF were examined by a five‐fold cross validation for each ecosystem type, and each method successfully improved the average accuracy of estimation by 8%, 18%, and 19%, respectively.

Environmental Sciences & Ecology↗
DOE OSTI2024

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

In this work we present a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

42 ENGINEERING↗
DOE OSTI2026

Active operator learning with predictive uncertainty quantification for partial differential equations

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. Here, we propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework’s uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Quantifying Uncertainties In Neutron-Alpha Scattering With Chiral Nucleon-Nucleon And Three-Nucleon Forces

We report that modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations. Starting from NN potentials up to fifth order (N 4 LO) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confidence intervals for the 3N contact and contact-plus-one-pion-exchange low-energy constants (c E and c D ) contribute to the overall uncertainty budget of many-body calculations of neutron- 4 He (n-α) elastic scattering. We compute structure and reaction observables for three-, four-, and five-nucleon systems within the ab initio frameworks of the no-core shell model and no-core shell model with continuum. Using a small set of design runs, we construct a Gaussian process model (GPM) that acts as a statistical emulator for the theory. With this, we gain insight into how uncertainties in the 3N low-energy constants propagate throughout the calculation and determine the Bayesian posterior distribution of these parameters with Markov-Chain Monte Carlo. We find rapidly converging n-α phase shifts with respect to the chiral order. With the adopted leading-order 3N force, calculations based on the NN interaction at N 4 LO of Entem, Machleidt, and Nosyk are unable to reproduce the experimental phase shifts in the 3/2 - channel within the estimated chiral truncation errors. Closer agreement with empirical data is found when using an older parametrization of the NN interaction at order N 3 LO, and the position and width of the P-wave resonances can be used to reduce the uncertainty of the 3N low-energy constants. The present results point to a lack of spin-orbit strength when the newer parametrization of the chiral NN force up to fifth order is combined with the leading-order 3N force. The inclusion of higher-order 3N-force terms may be required to recover the missing strength. GPMs can act as fast and accurate emulators of ab initio many-body calculations of low-energy scattering and reactions of light nuclei, opening the way to a robust quantification of theoretical uncertainties grounded in the description of the underlying chiral Hamiltonian.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

BEYONDPLANCK II. CMB mapmaking through Gibbs sampling

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning

Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.

42 ENGINEERING↗
DOE OSTI2025

Physics-based hybrid machine learning for critical heat flux prediction with uncertainty quantification

Critical heat flux (CHF) is a key quantity in nuclear system modeling due to its impact on heat transfer, safety margins, and reactor performance. This study develops and validates an uncertainty-aware hybrid modeling approach that combines machine learning with physics-based models to predict CHF in cases of dryout. The Biasi and Bowring empirical correlations were paired with three ML uncertainty quantification (UQ) techniques: deep neural network (DNN) ensembles, Bayesian neural networks (BNNs), and deep Gaussian processes (DGPs). A pure ML model without a base model was evaluated for comparison. Model performance was assessed under plentiful (7,350 points) and limited (9 points) training data scenarios using parity, uncertainty distributions, and calibration curves. Results show that the Biasi hybrid DNN ensemble achieved the best overall performance, with a mean absolute relative error of 1.846%, and well-calibrated uncertainty estimates. The BNN-based hybrids showed slightly higher error (2.14%) but superior uncertainty calibration. DGP models underperformed, with over 6% error and poor uncertainty calibration. All hybrid models outperformed pure machine learning configurations, demonstrating resistance against data scarcity. These findings indicate that hybrid modeling significantly improves predictive accuracy, interpretability, and resilience to data scarcity. The integration of uncertainty awareness provides actionable confidence in CHF predictions, which is vital for safety-critical decisions in nuclear applications. This hybrid approach offers a viable pathway for deploying ML models in reactor analysis tools while preserving domain knowledge and physical consistency.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Cluster characterization in atom probe tomography: Machine learning using multiple summary functions

In this work, we develop a machine learning-based method to characterize intracluster concentration (ρ c ), background concentration (ρ b ), clustering radius (r̄), and radius dispersity (δ r ) in simulated atom probe tomography data using multiple spatial statistics summary functions to train a Bayesian regularized neural network. Here, we build upon previous work that utilized Ripley’s K-function by incorporating additional features from nearest-neighbor spatial statistics summary functions to better characterize concentration-based metrics. The addition of nearest-neighbor based features allows for highly accurate estimates of ρ c and ρ b , both with 90% of the predictions within 4.0% of the real value; the root-mean-square errors are reduced by 81.5% and 92.8% from predictions using only K-function based features, respectively. Additionally, including these nearest-neighbor based features improves the ability to differentiate between r̄ and δ r .

36 MATERIALS SCIENCE↗
DOE OSTI2020

How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties

Here, we introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (𝜒⁢EFT ). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as 𝜒⁢EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the 𝜒⁢EFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Bayesian Approach to Estimation of Water Table Elevations Using Historical Rasters as Prior Information 2019 - 20430

In cases of complex but only partially known geology and a lack of spatial control in observation well locations, water table elevation estimation is very challenging. In some cases, auxiliary information, such as observations of the movement of tracers, operation of injection and extraction wells, and calibration of groundwater models against the historical elevation data, can be combined with expert judgement to estimate flow directions in areas of sparse data and to aid in the production of more reliable contour maps (and associated rasters) than could be produced by relying on sparse well elevation data alone. Given a historical sequence of these raster maps, the question arises how to automate, to the extent possible, the process of producing new raster maps to reflect data from previous times, the current data and the operation of expert judgement. One solution is to adopt a Bayesian point of view and to regard the historical well elevation data, auxiliary information and historical raster maps as prior information. The well elevations for water table wells, as well as those for injection/extraction wells and the data associated with other relevant variables, can be viewed as predictors for the raster surface. From this prior information, we can, conditional on the values of these predictors for a new time period, compute an expected value map and a standard deviation map for the new raster. These then can be taken to specify a prior predictive distribution for the pixels in the new raster map. Then we condition the pixels, corresponding to water level observation wells within the raster, on the observed values in those wells (which in general will differ from the regression estimate) for the new time period. Given the smoothness of the water table surface, we then smooth the surface of deviations from the mean surface, based on the variograms of the historical rasters, and add this smoothed surface to the regression mean surface. The error structure of the produced raster map is defined by the regression error structure and the error due to smoothing based on the estimated variograms. This methodology has been developed and is being further refined for groundwater monitoring and remediation at LANL. It is a very flexible method that can also be applied with a variety of other predictors applied to model the water level wells in the area of interest over the historical record. The smoothness of the spatial process and its possible evolution over time can then be estimated from the residuals from this regression. This can be augmented by expert hydrogeological opinion based on site topography and hydrogeology. (authors)

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗