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DOE OSTI2022

Static and Dynamic Gradient Based Directional Transportation of Neutral Molecules in Swollen Polymer Films

Abstract Materials which selectively transport molecules offer powerful opportunities for concentrating and separating chemical agents. Here, utilizing static and dynamic chemical gradients, transport of molecules within swollen crosslinked polymers is demonstrated. Using an ≈200 μm static hydroxyl to hexyl gradient, the neutral ambipolar nerve agent surrogate diethyl (cyanomethyl)phosphonate (DECP) is directionally transported and concentrated 60‐fold within 4 hours. To accelerate transport kinetics, a dynamic gradient (a “travelling wave”) is utilized. Here, the non‐polar dye pyrene was transported. The dynamic gradient is generated by an ion exchange process triggered by the localized introduction of an aqueous NaCl solution, which converts the gel from hydrophobic to hydrophilic. As the hydrophilic region expands, associated water enters the gel, and pyrene is pushed ahead of the expansion front. The dynamic gradient provides about 10‐fold faster transport kinetics than the static gradient.

Ali, Mohammad A.↗

DOE OSTI2022

Static and Dynamic Gradient Based Directional Transportation of Neutral Molecules in Swollen Polymer Films

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Multi-campaign ship and aircraft observations of marine cloud condensation nuclei and droplet concentrations

In situ marine cloud droplet number concentrations (CDNCs), cloud condensation nuclei (CCN), and CCN proxies, based on particle sizes and optical properties, are accumulated from seven field campaigns: ACTIVATE; NAAMES; CAMP 2 EX; ORACLES; SOCRATES; MARCUS; and CAPRICORN2. Each campaign involves aircraft measurements, ship-based measurements, or both. Measurements collected over the North and Central Atlantic, Indo-Pacific, and Southern Oceans, represent a range of clean to polluted conditions in various climate regimes. With the extensive range of environmental conditions sampled, this data collection is ideal for testing satellite remote detection methods of CDNC and CCN in marine environments. Remote measurement methods are vital to expanding the available data in these difficult-to-reach regions of the Earth and improving our understanding of aerosol-cloud interactions. The data collection includes particle composition and continental tracers to identify potential contributing CCN sources. Several of these campaigns include High Spectral Resolution Lidar (HSRL) and polarimetric imaging measurements and retrievals that will be the basis for the next generation of space-based remote sensors and, thus, can be utilized as satellite surrogates.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in 3D Heterogeneous Porous Media

Physics-based simulators for multiphase flow in porous media emulate nonlinear processes with coupled physics, and usually require extensive computational resources for software development, maintenance and simulation execution. As a result, a huge demand exists for fast modeling of coupled processes in a wide range of subsurface applications including geological sequestration, hydrocarbon recovery and geothermal energy extraction. In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3-Dimensional (3D) heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural networks, specifically U-Net with successive contracting and expansive steps, and is coupled with an efficient continuity-based smoother to predict flow responses that need spatial continuity. Furthermore, the transient regions are penalized to steer the training process such that the model can accurately capture flow in these regions. The model takes inputs including properties of porous media, fluid properties and well controls, and predicts the temporal-spatial evolution of the state variables (pressure and saturation). While maintaining the continuity of fluid flow, the 3D spatial domain is decomposed into 2D images for reducing training cost, and the decomposition results in an increased number of training data samples and better training efficiency. Additionally, a surrogate model is separately constructed as a postprocessor to calculate well flow rate based on the predictions of state variables from the deep learning model. We use the example of CO 2 injection into saline aquifers, and apply the physics-constrained deep learning model that is trained from physics-based simulation data and emulates the physics process. The model performs prediction with a speedup of ~ 1400 times compared to physics-based simulations, and the average temporal errors of predicted pressure and saturation plumes are 0.27% and 0.099% respectively. Furthermore, water production rate is efficiently predicted by a surrogate model for well flow rate, with a mean error less than 5%. Therefore, with its unique scheme to cope with the fidelity in fluid flow in porous media, the physics-constrained deep learning model can become an efficient predictive model for computationally demanding inverse problems or other coupled processes.

58 GEOSCIENCES↗

DOE OSTI2021

Dual-Purpose Canister Filling Demonstration Project Progress Report

This report discusses the progress made at the Oak Ridge National Laboratory to support direct disposal of dual-purpose canisters (DPCs). Acceptable filler materials should demonstrate that the probability of criticality in DPCs during the disposal timeframe is below the probability threshold for inclusion in a repository performance assessment. This effort, which will ultimately result in a full-scale demonstration, includes computational fluid dynamics (CFD) modelling developed to gauge the filling process and to uncover any unforeseen issues. Filling simulations of the lower region (mouse holes) of a prototypic DPC show successfully simulate filling of the void space inside the canister and a smooth, even progression of the liquid level. Flow through a pipe that is similar to the drainpipe in a DPC is being investigated separately to gain valuable insight of the flow regime inside a pipe. Three physical experiments validating the computational filling model have been completed using surrogate liquids. One experiment using molten metal has been completed and the results demonstrate adequate filling of the canister void spaces. Although the scale experiment observed some void spaces related to shrinkage of the metal during cooling, the volume filled is expected to be sufficient to meet the purpose of moderator exclusion. Further experiments will scale up the geometry, moving towards a full-sized DPC demonstration, and provide a more rigorous investigation of candidate filler materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2022

Compression Analysis of Materials via in situ X-ray Computed Tomography

X-ray computed tomography (X-ray CT) is an analytical technique used in materials science to non– destructively characterize features in a variety of materials like polymers, metals, composites, and explosives. The non-destructive imaging allows for the analysis of features (voids and cracks), which give a fundamental understanding of material characteristics.This is more effective when combinedwith a load cell to expose the material to realworld stimuli to understand material characteristics and morphological behavior in situ. This study focused on using in situ X-ray CT to understand the material characteristics and morphological changes of sugar prills and a lattice under a compressive load. Sugar prills are used as a surrogate to analyze explosives in a safer and less expensiveway. The sugar prills were found to be brittle and shattered when compressed via the CT renderings and the stress/strain information. The lattices are used as both the basis and ground truth comparison for the development of models to predict the morphological and material characteristic changes that occur as a result of loading. The lattice was found to have weak regions due to low polymer interlayer fusion in these regions during the printing process. It was also found that under the initial compression the lattice demonstrated elastic behavior as its cellular structure was intact until the cellular structure started to collapse causing yielding in the lattice. Additionally, the analysis of the sugar prills and lattice demonstrate the information that can be gleaned from in situ X-ray CT experiments that would be lost in traditional pre- and post-mortem X-rayCT analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Plasma production and ion heating systems for the Material Plasma Exposure eXperiment

Plasma production and ion heating in the Material Plasma Exposure eXperiment (MPEX), whose design is nearing completion, is accomplished using continuous wave RF power with average power density up to 1.6 MW/m2 at the plasma interface. Plasma is produced using helicon waves coupled through a single helical antenna at 13.56 MHz with power supplied by three 100 kW fixed-frequency RF generators feeding a power combiner network followed by the matching network and launcher. The helicon source can utilize various gasses including hydrogen, deuterium, and helium, with a magnetic field strength in the source region up to 0.2 T, and maximum device |B| of 2.5 T. Power is coupled to ions via ion cyclotron heating at the fundamental resonance using a pair of phased helical antennas operating in the frequency range 4-9 MHz, that launch waves towards the resonance from the antenna region where ω > ωci. ICH power is supplied by a single 500 kW tunable RF transmitter through a 90° power splitter and matching/decoupling network. In the case of both the helicon and ICH systems the antennas are located external to the vacuum, with power transferred through novel water-cooled coaxial vacuum windows consisting of fused quartz outer cylinders and silicon nitride inner cylinders with forced convection water cooling between them. The antenna enclosures are pressurized with dry air to 3 bar absolute for voltage standoff.Several 3-D COMSOL models have been created to simulate the two systems. A model of the helicon region utilizing a cold plasma dielectric tensor with accurate magnetic field and realistic plasma density profiles has been used to calculate the plasma loading/complex antenna input impedance at the launcher feed for various ne and |B| values, for the purpose of estimating power handling. It also incorporates the geometry of all launcher structures relevant to this determination. A still more detailed model of the launcher together with a lossy dielectric plasma surrogate has been used to determine RF electric field values and power losses in the device components.Similar models have been produced to predict the performance and power handling of the ICH launcher. For this device the impedance matrix of the two-element antenna array is calculated using a warm plasma model, necessary to properly determine the wave propagation and absorption.

Goulding, Richard↗

DOE OSTI2021

Pre- and post-treatment image-based dosimetry in 90 Y-microsphere radioembolization using the TOPAS Monte Carlo toolkit

Objective.To evaluate the pre-treatment and post-treatment imaging-based dosimetry of patients treated with 90Y-microspheres, including accurate estimations of dose to tumor, healthy liver and lung. To do so, the Monte Carlo (MC) TOPAS platform is in this work extended towards its utilization in radionuclide therapy. Approach. In this study, five patients treated at the Massachusetts General Hospital were selected for this study. All patients had data for both pre-treatment SPECT-CT imaging using 99mTc-MAA as a surrogate of the 90Y-microspheres treatment and SPECT-CT imaging immediately after the 90Y activity administration. Pre- and post-treatment doses were computed with TOPAS using the SPECT images to localize the source positions and the CT images to account for tissue inhomoegeneities. We compared our results with analytical calculations following the voxel-based MIRD scheme. Main results. TOPAS results largely agreed with the MIRD-based calculations in soft tissue regions: the average difference in mean dose to the liver was 0.14 Gy GBq -1 (2.6%). However, dose distributions in the lung differed considerably: absolute differences in mean doses to the lung ranged from 1.2 to 6.3 Gy GBq -1 and relative differences from 153% to 231%. We also found large differences in the intra-hepatic dose distributions between pre- and post-treatment imaging, but only limited differences in the pulmonary dose. Significance. Doses to lung were found to be higher using TOPAS with respect to analytical calculations which may significantly underestimate dose to the lung, suggesting the use of MC methods for 90Y dosimetry. According to our results, pre-treatment imaging may still be representative of dose to lung in these treatments.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2026

Neural Posterior Estimation for Scalable and Accurate Inverse Parameter Inference in Li-Ion Batteries

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE can infer parameters equally or more accurately than Bayesian calibration, even if it leads to higher voltage reconstruction errors. We also demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters). The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).

25 ENERGY STORAGE↗

DOE OSTI2024

In-cylinder spray evolution in a motored central-injection gasoline engine: Imaging and simulating the effects of flash-boiling and intake crossflow

Accurate predictions of fuel spray behavior and mixture formation in simulations of direct-injection spark-ignition (DISI) engines are fundamental to ensure proper description of all subsequent processes including ignition, combustion, and emissions. In this work, the spray evolution in a single-cylinder optical DISI engine was studied experimentally and numerically with the goal of enabling predictive computational fluid dynamics (CFD) modeling of in-cylinder sprays. The authors explored a wide range of operating conditions characterized by several fuel injection temperatures and engine speeds, using a well-characterized nine-component gasoline surrogate known as PACE-20. The effect of flash boiling and intake crossflow on the spray is discussed, with a focus on evaluating the ability of the spray models to capture highly transient spray behavior. In the experiments, the fuel temperature was varied between 20°C and 80°C, allowing for non-flash- to flash-boiling transition to emerge with enhanced flashing intensity at the highest temperatures. Spray collapse resulted in vapor-rich regions, owing to the locally lower inertia of the fluid. Varying the engine speed from 650 to 1950 rpm promoted increasingly more turbulent in-cylinder crossflow which interacted with the spray during the injection event and resulted in enhanced spray dispersion. The CFD model was able to capture the spray morphology transition at different fuel temperatures and engine speeds adequately. Further, it is shown that the spray breakup model could capture the transitional spray behavior induced by flash boiling atomization and intake flow via proper initialization of the spray cone angle and calibration of the spray models’ constants.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Bulk Spray and Individual Plume Characterization of LPG and Iso-Octane Sprays at Engine-Like Conditions

This study presents experimental and numerical examination of directly injected (DI) propane and iso-octane, surrogates for liquified petroleum gas (LPG) and gasoline, respectively, at various engine like conditions with the overall objective to establish the baseline with regards to fuel delivery required for future high efficiency DI-LPG fueled heavy-duty engines. Sprays for both iso-octane and propane were characterized and the results from the optical diagnostic techniques including high-speed Schlieren and planar Mie scattering imaging were applied to differentiate the liquid-phase regions and the bulk spray phenomenon from single plume behaviors. The experimental results, coupled with high-fidelity internal nozzle-flow simulations were then used to define best practices in CFD Lagrangian spray models. Optical imaging revealed that unlike iso-octane, propane’s spray propagation was fed by its flash boiling, spray collapse, and high degree of vaporization, resulting in a direct proportionality of propane’s penetration length to temperature. These unique features of propane and its variation from iso-octane’s spray pattern, contributed to its classification as an unconventional spray. Appropriate corrections to the injection and breakup models were developed to reproduce the under-expanded jet dynamics and to mimic the flash boiling-driven spray development observed with propane sprays. The simulation results were found to be sensitive to cone and inclusion angles of the blob injector. The current work represents a first assessment of the capability of the commonly available models for engine-spray simulations and highlights the fact that, despite the reasonable agreement obtained in the fuel vapor morphology, the representation of the liquid phase lacks accuracy and requires further model development.

02 PETROLEUM↗

DOE OSTI2025

Examples of Mission-driven Data Science from Jefferson Lab and ACES

This presentation details mission-driven data science initiatives at Jefferson Lab and the Joint Institute for Advanced Computing on Environmental Studies (ACES). JLab, a U.S. Department of Energy Office of Science national laboratory, operates the Continuous Electron Beam Accelerator Facility (CEBAF), and is the lead institute for the new High Performance Data Facility (HPDF) Hub. The Joint Institute for ACES brings together interdisciplinary teams in health informatics, climate modeling, computer science, and physics to address environmental challenges, including flood modeling. The Hampton Roads region, particularly Norfolk and Virginia Beach, faces increasing flood risks, motivating the need for rapid, reliable, and risk-aware decision support. ACES’s flooding work has a focus on uncertainty quantification (UQ) and machine learning (ML) for coastal flood management. The work is motivated by the increasing vulnerability of communities such as Norfolk and Virginia Beach, Virginia, to frequent coastal flooding events, and the need for rapid, reliable decision support. The research develops computationally efficient ML surrogate models to forecast water levels and flooding risk. A central theme is the quantification and calibration of predictive uncertainty, especially for out-of-distribution (OOD) scenarios, using techniques such as Monte Carlo Dropout, Deep Ensembles, Gaussian Processes, and Deep Quantile Regression (DQR). The study demonstrates that distance-aware UQ is critical for reliable scientific AI, particularly in high-dimensional, safety-critical, and real-time applications.

McSpadden, Diana [Thomas Jefferson National Accele↗

DOE OSTI2021

Embedding Sensors in 3D Printed Metal Structures

The Transformational Challenge Reactor (TCR) program is leveraging recent advances in modeling and simulation, materials, and additive manufacturing (AM) technologies to design a modern nuclear reactor. Some of the main TCR technologies include in situ monitoring and the integration of sensors during the manufacturing of quality-significant nuclear reactor components. This report describes the general procedure and process optimization for embedding sensors within generic stainless steel 316 (SS316) components using laser powder bed fusion (LPBF). A more detailed, quality-significant test plan and supporting procedures are available upon request (ORNL/TM-2021/2127). LPBF involves the use of a scanning laser to selectively melt regions of a powder bed, additively building a part layer by layer. This report describes the LPBF processing technique and discusses the effects of LPBF processing parameters on the success of the sensor embedding process. Experiments used machined cavities in the form of channels in an SS316 base for the sensors to lay in while material is additively built over the top, thereby embedding them in an SS316 matrix. A preliminary investigation involved using empty SS316 sheaths as surrogates to explore the effects of various LPBF processing parameters and the dimensional requirements of the machined channels. Microstructural investigations showed that a smaller channel width/depth combination closer to the sensor’s diameter was best for the embedding process. After the desired parameters were selected, Type-K thermocouples were embedded and evaluated post-embedding using nondestructive thermal testing, as well as destructive sectioning and microscopy. Post-build characterization showed that the thermocouples were well-bonded to the SS316 matrix and were fully functional after embedding. During thermal testing to temperatures up to 500 °C, the embedded thermocouples read consistently with one another and deviated only slightly from the readings of a nonembedded thermocouple located within the furnace. This slight discrepancy was most likely due to differences in the thermal time constants for a nonembedded thermocouple vs. a thermocouple embedded in a solid SS316 block. The results presented in this report will serve as the foundation for future work that will focus on embedding sensors in relevant TCR reactor components and eventually testing those components under neutron irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2026

A Comprehensive Comparative Study of Active Learning Schemes for Nanophotonics Design

We present a benchmarking study of active learning (AL) schemes for designing planar multilayer nanophotonic metamaterials, where the design tasks are formulated as binary optimization problems. Different surrogate models, including factorization machine (FM), Gaussian process regression (GPR), and convolutional neural network (CNN), combined with different optimization methods, including exhaustive enumeration, discrete particle swarm optimization (DPSO), quantum annealing (QA), hybrid QA, and simulated annealing are studied. The benchmark cases investigated range from small problems with short binary lengths (N = 25) to large problems with N up to 100, focusing on the design of two classes of photonic structures, including antireflective coatings for the long-wavelength infrared region and transparent radiative coolers. For small problems, CNN coupled with DPSO in AL achieves the best performance. As N increases, FM with QA outperforms GPR and CNN. For FM-based AL, hybrid QA yields the best optimization results, particularly in high-dimensional cases (N = 100). These results demonstrate that the optimization method can significantly affect in AL performance as N increases, and that QA-based optimization can provide practical routes for mitigating the optimization bottleneck in high-dimensional problems.

Jung, Serang [Kyung Hee University, Korea]↗

DOE OSTI2024

Uncertainty Quantification and Sensitivity Analysis of Non-Nuclear Advanced Controls Testbed Reactor Mockup

The research presented in this report describes our progress in applying stochastic methods and uncertainty quantification, parametric study, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated with Griffin, with the goal of developing a reduced order (surrogate) model which can be rapidly sampled while perturbing multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums, which are controlled by a hybrid proportional, integral and derivative (PID) controller, actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time and $\beta$ from a transient Griffin simulation executed with the improved quasi-static method to provide the kinetic parameters) as inputs to functions which control the CD rotation angle. Using a number of stochastic method approaches, we developed a dual purpose training-surrogate model of the NTP system using polynomial regression. The trained model can be rapidly sampled while simultaneously perturbing various input parameters of the model, such as coefficients on the PID control, or temperature (directly affect the neutron cross section). The surrogate model delivers accurate results orders-of-magnitude faster (minutes, not days) than the base model. Once the base model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs and their effect on the output. For example, coefficients used in the PID control system may vary due to some physical interference, or there may be uncertainty in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters and operational boundaries can be determined. The goal of this work is to support development of an advanced control system to operate CDs in a functioning NTP system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

High-Fidelity Accelerated Design of High-performance Electrochemical Systems

Large-scale electrification is vital to addressing the climate crisis, but several scientific and technological challenges remain to fully electrify both the chemical industry and transportation. In both of these areas, new electrochemical materials will be critical, but their development currently relies heavily on human-time-intensive experimental trial and error and computationally expensive first-principles, meso-scale and continuum simulations. To accelerate this process, our team has developed the AutoMat platform. AutoMat can accelerate development of new electrochemical materials along two avenues: first, automated input generation and management of simulations at multiple lengthscales as well as “handoff” of outputs from one lengthscale as inputs to the next; and second, replacement of the most computationally intensive simulation processes with machine-learned surrogate models. The crux of our team’s effort was not “reinventing the wheel” by developing entirely new techniques, but rather building a “superhighway” that allows existing state-of-the-art techniques to run faster and more smoothly than before. AutoMat can utilize tools spanning from first-principles quantum chemistry computations to automated robotic experimentation, and is driven by design space search techniques to reduce the number of iterations through the full simulation loop by rapidly targeting promising regions of design spaces such as single-atom alloy catalysts or blends of liquid electrolytes.

25 ENERGY STORAGE↗

DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗