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Advances in Kriging-Based Autonomous X-Ray Scattering Experiments

Autonomous experimentation is an emerging paradigm for scientific discovery, wherein measurement instruments are augmented with decision-making algorithms, allowing them to autonomously explore parameter spaces of interest. We have recently demonstrated a generalized approach to autonomous experimental control, based on generating a surrogate model to interpolate experimental data, and a corresponding uncertainty model, which are computed using a Gaussian process regression known as ordinary Kriging (OK). We demonstrated the successful application of this method to exploring materials science problems using x-ray scattering measurements at a synchrotron beamline. Here, we report several improvements to this methodology that overcome limitations of traditional Kriging methods. The variogram underlying OK is global and thus insensitive to local data variation. We augment the Kriging variance with model-based measures, for instance providing local sensitivity by including the gradient of the surrogate model. As with most statistical regression methods, OK minimizes the number of measurements required to achieve a particular model quality. However, in practice this may not be the most stringent experimental constraint; e.g. the goal may instead be to minimize experiment duration or material usage. We define an adaptive cost function, allowing the autonomous method to balance information gain against measured experimental cost. We provide synthetic and experimental demonstrations, validating that this improved algorithm yields more efficient autonomous data collection.

36 MATERIALS SCIENCE↗

Reliability estimation of an advanced nuclear fuel using coupled active learning, multifidelity modeling, and subset simulation

Tristructural isotropic (TRISO)-coated particle fuel is a robust nuclear fuel and determining its reliability is critical for the success of advanced nuclear technologies. However, TRISO failure probabilities are small and the associated computational models are expensive. Here we used coupled active learning, multifidelity modeling, and subset simulation to estimate the failure probabilities of TRISO fuels using several 1D and 2D models. With multifidelity modeling, we replaced expensive high-fidelity (HF) model evaluations with information fusion from two low-fidelity (LF) models. For the 1D TRISO models, we considered three multifidelity modeling strategies: only Kriging, Kriging LF prediction plus Kriging correction, and deep neural network (DNN) LF prediction plus Kriging correction. While the results across these multifidelity modeling strategies compared satisfactorily, strategies employing information fusion from two LF models called the HF model least often. Next, for the 2D TRISO model, we considered two multifidelity modeling strategies: DNN LF prediction plus Kriging correction (data-driven) and 1D TRISO LF prediction plus Kriging correction (physics-based). The physics-based strategy, as expected, consistently required the fewest calls to the HF model. However, the data-driven strategy had a lower overall simulation time since the DNN predictions are instantaneous, and the 1D TRISO model requires a non-negligible simulation time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Physics-Informed Deep Learning for Reconstruction of Spatial Missing Climate Information in the Antarctic

Understanding the influence of the Antarctic on the global climate is crucial for the prediction of global warming. However, due to very few observation sites, it is difficult to reconstruct the rational spatial pattern by filling in the missing values from the limited site observations. To tackle this challenge, regional spatial gap-filling methods, such as Kriging and inverse distance weighted (IDW), are regularly used in geoscience. Nevertheless, the reconstructing credibility of these methods is undesirable when the spatial structure has massive missing pieces. Inspired by image inpainting, we propose a novel deep learning method that demonstrates a good effect by embedding the physics-aware initialization of deep learning methods for rapid learning and capturing the spatial dependence for the high-fidelity imputation of missing areas. We create the benchmark dataset that artificially masks the Antarctic region with ratios of 30%, 50% and 70%. The reconstructing monthly mean surface temperature using the deep learning image inpainting method RFR (Recurrent Feature Reasoning) exhibits an average of 63% and 71% improvement of accuracy over Kriging and IDW under different missing rates. With regard to wind speed, there are still 36% and 50% improvements. In particular, the achieved improvement is even better for the larger missing ratio, such as under the 70% missing rate, where the accuracy of RFR is 68% and 74% higher than Kriging and IDW for temperature and also 38% and 46% higher for wind speed. In addition, the PI-RFR (Physics-Informed Recurrent Feature Reasoning) method we proposed is initialized using the spatial pattern data simulated by the numerical climate model instead of the unified average. Compared with RFR, PI-RFR has an average accuracy improvement of 10% for temperature and 9% for wind speed. When applied to reconstruct the spatial pattern based on the Antarctic site observations, where the missing rate is over 90%, the proposed method exhibits more spatial characteristics than Kriging and IDW.

54 ENVIRONMENTAL SCIENCES↗

Estimating basis functions in massive fields under the spatial mixed effects model

Abstract Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.

Pazdernik, Karl↗

GIS-Based Modeling of Contaminated Soil Volumes at Multiple Sites in the Formerly Utilized Sites Remedial Action Program - 20149

The remediation of hazardous, toxic, and radioactive waste (HTRW) sites produces cost-related risks associated with the estimation of contaminated soil or debris volumes. Historical risk-management techniques include cost contingencies to cover volume uncertainties that affect project budgeting and decision-making. The Buffalo District teamed with project partners to lessen volume uncertainty and reduce project risks at multiple HTRW sites managed under the Formerly Utilized Sites Remedial Action Program (FUSRAP). Historical remedial investigations under FUSRAP commonly identified the presence of radiological material in site media, the associated human health risk, and then areas of remediation. To manage remedial execution and reduce risk, pre-design or remediation-phase sampling essentially 'chased' contamination, which was not conducive to efficient predictive budgeting derived from Feasibility Study (FS) cost analyses. The Buffalo District first optimized their approach to better understand volume uncertainty by utilizing the Argonne National Laboratory's Bayesian Approaches for Adaptive Spatial Sampling (BAASS) software [1]. BAASS processed soft data (e.g., gamma walk-over data) and spatial sampling data to estimate the lateral extent of contaminated soil irrespective of depth (i.e., gross contamination extent) and define areas of contaminant uncertainty. The software performed a binary transformation of contaminant concentrations at all sampling points based upon remedial action goals or a sum of ratios approach (i.e., clean, impacted, or range of impacts in soil). The model produced two-dimensional (horizontal) contaminant probability contours and statistical uncertainty in the sampling coverage and resulting contaminant extents. This method was translated vertically by partitioning the sampling data into depth brackets that produced a stacked representation of contaminant extents and uncertainty in the subsurface (i.e., similar to construction lifts). The results commonly led to a better understanding of project uncertainty and the need for sampling strategies that produce high-confidence soil volumes, which control costs. The BAASS-based delineations were eventually replaced by Empirical Bayesian Kriging (EBK) methods available in ArcGIS Spatial or 3D Analysts [2]. The EBK method calculates contaminant probability zones derived from user-controlled semivariograms of the spatial datasets. The resulting probability zones (e.g., 50% or 80% of contaminant probability) represent the two-dimensional surface delineation of the overall horizontal remedial area, similarly to BAASS. However, unlike BAASS, the vertical sampling data within these probability zones became vertical control points to contour a subterranean surface that connects subsurface points to the land-surface delineations of contamination. The resulting representation of horizontal and vertical impacts within an enclosed envelop (volume) of soil included uncertainty distributions that are used to plan uncertainty-reduction sampling. These data-driven and math-based models of three-dimensional sampling results produced well-bounded remedial volumes for project planning and better uncertainty predictions during project budgeting. The EBK method was applied to several FUSRAP sites managed by the Buffalo District and compared to less rigorously modeled sites previously remediated by the District. The comparison of modeled to actual remediated volumes provide a basis for validating the volume-estimation method. This comparison is important to ensure modeled volumes match physical boundaries of site remediation. FUSRAP sites with denser investigative sampling and lesser volume uncertainty proved useful in remedial planning and contracting. The Buffalo District noted that historical sites with sparser sampling arrays had greater disparity between estimated volumes and final remedial volumes. The benefit achieved over the cost of detailed soil sampling appears positive for FUSRAP projects, especially where impacts vary widely and appear unbounded by investigation-phase sampling. The subsequent Empirical Bayesian Kriging of contamination coupled with vertical contouring for soil estimations reduces uncertainty in soil volumes or indicates where sampling is required to reduce uncertainty, which together optimize remedial planning and budgeting. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Dynamic PRA-Based Estimation of PWR Coping Time Using a Surrogate Model for Accident Tolerant Fuel

In this study, we propose an interpolation-based response surface surrogate methodology to manage a large number of scenarios in dynamic probabilistic risk assessment. It adopts the shape Dynamic Time Warping algorithm to cluster the interpolation neighborhood from time series sample data. The interpolation method was adapted from Taylor Kriging to allow a reduced-order model of the Taylor series. In order to demonstrate its applicability to complex issues in risk assessment for nuclear engineering, an example risk response surface to estimate emergency core cooling system (ECCS) criteria for triplex silicon carbide (SiC) accident-tolerant fuel was constructed. The response surface was exploited to estimate the cumulative failure probability of the fuel cladding structure due to the uncertainties in operator actions and safety systems. The functional failures were assessed based on a combination of individual layer failures computed by coupling Risk Analysis Virtual Environment software with a pressurized water reactor 1000-MW(electric) RELAP5 model and the in-house fuel performance assessment module. Results showed that SiC cladding failure probability spiked less than 1 min after a large-break loss-of- coolant accident whenever the current ECCS criteria for Zircaloy-4 (Zr-4) cladding was used. However, it still provides an increased safety margin of three orders of magnitude compared to Zr-4. This positive margin could be utilized to relax active ECCS requirements by allowing deviations of up to 450 s in its actuation time. The proposed surrogate methodology generated a response surface of SiC cladding failure probability reasonably well, with a significant savings of computation time. This methodology is expected to be useful in the analysis of system response with complex uncertainty sources.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Feedback on Forty-year Long Clean-up Operations of a Contaminated Soil for Environmental Purpose - 20026

One of the CEA facilities in France is the place of miscellaneous mapping and clean-up operations since the 1980's. The final purpose of the conducted work deals with the environmental remediation of the building. In France, the absence of a regulatory framework for the management of sites polluted by radioactive substances, especially as the lack of release thresholds, has led to develop different approaches of soil radiological characterization. The geostatistical approach is part of them. Preliminary investigations are an unavoidable step prior to clearance and remediation. First, historical analysis enables to define site perimeters to investigate as well as to precisely locate expected contaminated parts. For radioactive pollutants, the media (water, soil, air) and transfer routes participate in the definition of the investigation perimeter and thus also need to be identified through a geological study. At the same time, functional analysis leads to choose the best measurement means which could provide useful information when combined with visual inspection. An equipment well adapted to easy-to-measure radionuclides as gamma emitters, such as gamma probe or on-site gamma spectrometry, is usually selected as a non-destructive assay. Coupled with spatial positions, processed on-site radiological data can be mapped. Data processing consists in mapping and kriging before a geostatistical analysis in order to identify the zones of interest to be targeted. Selected zones are not only linked to high level count rates but also to low level ones so that a pollution-free reference is known in the area. This data processing also enables to categorize waste types according to their origin and contamination levels. An expected volume of different waste then follows as well as the waste characterization equipments. In-depth investigations, e.g. core drillings and samplings, naturally ensue to aim at remediation optimization through the assessment of environmental impact. After clean-up operations, non-destructive assays as well as destructive samplings enable to check the effective clearance. Following this methodology in the present remediation work, results of the first non-destructive assay campaign highlighted a long-lived transuranic radionuclides contamination in the concrete flagstone. Successive non-destructive assays were then performed in the defined zones of interest. Count rates measured with a surface probe were first mapped. The best localization of destructive assays, i.e. core drillings at a 1 meter depth, came from this surface mapping followed by a geostatistical analysis. The concrete flagstone was totally removed. Then, the depth of soil to remove under the flagstone was optimized from the results of radiological activities measured in core drillings samples. A new surface mapping was then drawn after this partial soil excavation. The sand and demolition rubble samples, homogeneously constituted from the flagstone fragments, were analyzed by gamma spectrometry. Meanwhile, waste drums and other containers were also measured by gamma spectrometry and passive neutron measurement devices. All these results have brought miscellaneous pieces of information. In this context, major issues appear in terms of physical constraints such as the premises tininess as well as of soil sampling techniques and in terms of measurement performances assessment and the representativeness of homogeneous samples. The choice of radiological soil and waste characterization devices is described in the light of enhanced performances by keeping in mind radiation protection requirements and a willing to always optimize waste categories (very low level waste) and volume. The improvement of the characterization methods appears through this forty-year long work while sharing the feedback of encountered difficulties. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Special Issue: Geostatistics and Machine Learning

Abstract Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different origins, machine learning and geostatistics share concepts and methods. For example, the kriging formalism can be cast in the machine learning framework of Gaussian process regression. Machine learning, with its focus on algorithms and ability to seek, identify, and exploit hidden structures in big data sets, is providing new tools for exploration and prediction in the earth sciences. Geostatistics, on the other hand, offers interpretable models of spatial (and spatiotemporal) dependence. This special issue on Geostatistics and Machine Learning aims to investigate applications of machine learning methods as well as hybrid approaches combining machine learning and geostatistics which advance our understanding and predictive ability of spatial processes.

58 GEOSCIENCES↗

Accelerating geostatistical modeling using geostatistics-informed machine Learning

Ordinary Kriging (OK) is a popular geostatistical algorithm for spatial interpolation and estimation. The computational complexity of OK changes quadratically and cubically for memory and speed, respectively, given the number of data. Therefore, it is computationally intensive and also challenging to process a large set of data, especially in three-dimensional (3D) cases. This paper develops a geostatistics-informed machine learning (GIML) model to improve the efficiency of OK by reducing the number of points required to be estimated using OK. Specifically, only a very few of the unknown points are estimated by OK to get the weights and estimations, which are used as the training dataset. Moreover, the governing equations of OK are used to guide our proposed machine learning to better reproduce the spatial distributions. Our results show that the proposed GIML can reduce the computational time of OK by at least one order of magnitude. The effectiveness of the GIML is evaluated and compared using a 2D case. Furthermore, we demonstrate its efficiency and robustness by considering a different number of training samples on various 3D simulation grids.

58 GEOSCIENCES↗

Gaussian process regression constrained by boundary value problems

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

42 ENGINEERING↗

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Comparison of fiber-optic distributed temperature sensing and high-sensitivity sensor spatial surveying of stream temperature

Measuring surface water temperature spatial variability is needed to estimate the interaction between surface water and groundwater, evaluate fish habitat and thermal inertia, and to estimate streamflow frequency and duration. Fiber optic distributed temperature sensing (FO-DTS) has been used in rivers and lakes, providing high-resolution and sensitive temperature monitoring over large temporal and spatial scales. However, in streams with cobbly or bedrock-lined streambeds and variable bathymetry, use of FO-DTS to measure temperature close to the surface water and groundwater interface can be challenging if even feasible. FO-DTS can also be costly, involve difficult installations, and require an advanced understanding of the technology, calibration, and data processing. In this study, we compared FO-DTS stream temperature survey results to an alternative temperature survey method employing a towed transect of high-resolution temperature loggers spaced at 1-m and transported in the stream along the study reach, to measure the spatial distribution of stream-water temperature in East Fork Poplar Creek near Oak Ridge, Tennessee, USA. We assessed the applicability and limitations of the two methods, and quantitatively compared in-situ temperature survey results measured simultaneously with each method. Regression results showed strong temporal and spatial correlation between the two methods. Differences were only elevated near the stream banks in areas that were coincident with correlation slope deviations from unity, which was attributed to shallower water and lower data density. Kriging standard errors were also low at channel center with minor increases near the stream banks. Furthermore, the results suggested that the array of the individual temperature sensors can provide a practical alternative to FO-DTS for thermal characterization of surface water, providing slightly lower spatial and temporal resolution, but with higher accuracy of temperature measurement, with greater simplicity, and with a broader range of conditions where it may be applied.

54 ENVIRONMENTAL SCIENCES↗

Deep-learning-based workflow for boundary and small target segmentation in digital rock images using UNet++ and IK-EBM

We report three-dimensional (3D) X-ray micro-computed tomography (μCT) has been widely used in petroleum engineering because it can provide detailed pore structural information for a reservoir rock, which can be imported into a pore-scale numerical model to simulate the transport and distribution of multiple fluids in the pore space. The partial volume blurring (PVB) problem is a major challenge in segmenting raw μCT images of rock samples, which impacts boundaries and small targets near the resolution limit. We developed a deep-learning (DL)-based workflow for accurate and fast partial volume segmentation. The DL model's performance depends primarily on the training data quality and model architecture. This study employed the entropy-based-masking indicator kriging (IK-EBM) to segment 3D Berea sandstone images as training datasets. The comparison between IK-EBM and manual segmentation using a 3D synthetic sphere pack, which had a known ground truth, showed that IK-EBM had higher accuracy on partial volume segmentation. We then trained and tested the UNet++ model, a state-of-the-art supervised encoder-decoder model, for binary (i.e., void and solid) and four-class segmentation. We compared the UNet++ with the commonly used U-Net and wide U-Net models and showed that the UNet++ had the best performance in terms of pixel-wise and physics-based evaluation metrics. Specifically, boundary-scaled accuracy demonstrated that the UNet++ architecture outperformed the regular U-Net architecture in the segmentation of pixels near boundaries and small targets, which were subjected to the PVB effect. Feature map visualization illustrated that the UNet++ bridged the semantic gaps between the feature maps extracted at different depths of the network, thereby enabling faster convergence and more accurate extraction of fine-scale features. The developed workflow significantly enhances the performance of supervised encoder-decoder models in partial volume segmentation, which has extensive applications in fundamental studies of subsurface energy, water, and environmental systems.

02 PETROLEUM↗

Machine Learning Reduced Order Model for Cost and Emission Assessment of a Pyrolysis System

Biomass pyrolysis is a promising approach for producing economic and environmentally-friendly fuels and bioproducts. Biomass pyrolysis experiments show that feedstock properties have a significant impact on product yields and composition. Scientists are developing detailed chemical reaction mechanisms to capture the relationships between biomass composition and pyrolysis yields. These mechanisms can be computationally intensive. In this study, we investigate the use of a machine learning reduced order model (ROM) for assessing the costs and emissions of a pyrolysis biorefinery. Here, we developed a Kriging-based ROM to predict pyrolysis yields of 314 feedstock samples based on the results of a detailed chemical kinetic pyrolysis mechanism. The ROM is integrated into a chemical process model for calculating mass and energy yields in a commercial-scale (2000 tonne/day) biorefinery. The ROM estimated biofuel yields of 65 to 130 gallons per ton of dry biomass. This results in biofuel minimum fuel-selling prices of $2.62 to $5.43 per gallon and emissions of -13.62 to 145 kg of CO 2 per MJ. The ROM achieved an average mean square error of 1.8e-20 and a mean absolute error of 0.53%. These results suggest that ROMs can facilitate rapid feedstock screening for biorefinery systems.

09 BIOMASS FUELS↗

Data-Driven Global Sensitivity Analysis of Three-Phase Distribution System with PVs

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV variations plays an important role in designing optimal voltage control schemes. This paper proposes a Kriging, i.e., Gaussian process modeling enabled data-driven GSA method. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol index can be conveniently calculated to assess the global sensitivity of voltage to various power injection variations. Comparison results with other model-based GSA methods on the IEEE 37-bus feeder, such as the polynomial chaos expansion and the Monte Carlo approaches demonstrate that the proposed method can achieve accurate GSA outcomes while maintaining high computational efficiency.

distribution system analysis↗