Results for “Function Estimation” — Page 9

DOE OSTI2022

Bootstrap estimation of the effect of instrument response function uncertainty on the reconstruction of fusion neutron sources

Neutron imagers are important diagnostics for the inertial confinement fusion implosions at the National Ignition Facility. They provide two- and three-dimensional reconstructions of the neutron source shape that are key indicators of the overall performance. To interpret the shape results properly, it is critical to estimate the uncertainty in those reconstructions. There are two main sources of uncertainties: limited neutron statistics, leading to random errors in the reconstructed images, and incomplete knowledge of the instrument response function (the pinhole-dependent point spread function). While the statistical errors dominate the uncertainty for lower yield deuterium-tritium (DT) shots, errors due to the instrument response function dominate the uncertainty for DT yields on the order of 10 16 neutrons or higher. In this work, a bootstrapping method estimates the uncertainty in a reconstructed image due to the incomplete knowledge of the instrument response function. The main reconstruction is created from the fixed collection of pinhole images that are best aligned with the neutron source. Additional reconstructions are then built using subsets of that collection of images. Variations in the shapes of these additional reconstructions originate solely from uncertainties in the instrument response function, allowing us to use them to provide an additional systematic uncertainty estimate.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study the interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D weakly asymmetric simple exclusion process. We show that with modest resources, we can capture the features of the susceptibility in large systems that mark the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Characterization and Analysis of the Energy-Reporting Accuracy of Connected Devices

Emerging energy-efficient building systems increasingly exhibit greater functionality, often requiring multiple operating modes (e.g. white-tunability for lighting products and data traffic for devices with networked, integrated sensors). This increased functionality makes energy consumption estimates more complex. Given that these functions consume energy, the energy performance of such building systems is dependent on what operating modes they use and how much time they spend in each mode. Devices and systems that can report their own energy consumption mitigate this energy-performance uncertainty. This study explores the energy-reporting accuracy of market-available connected electrical outlets. The study considers two residential-market products (five units each, one outlet per unit) and three commercial-market products (two units each, 18 to 24 outlets per unit) with the ability to report power drawn and/or energy consumed by devices connected to their receptacles. The products were purchased through typical market channels. Pacific Northwest National Laboratory (PNNL) conducted testing in December 2018 at its Connected Lighting Test Bed (CLTB), using a custom-developed test setup and method adapted from industry standards. The setup collected energy-consumption data reported by the outlet devices under test (DUTs) at one-minute intervals and compared that data with measurements taken by a reference meter over a range of test conditions. The residential products reported power draw but not interval or cumulative energy consumption. The commercial products reported both power draw and cumulative energy consumption. Relative reporting error (RRE) was calculated for all measurements, and analysis of the results revealed variations across devices and test conditions. The total number of measurements (50 for each residential product, 60 for each commercial product) offers an appreciable comparison of performance at the make/model level. The average RRE of the residential products derived from reported power draw was -0.02% and -1.20%. The average RRE for two of the three the commercial products derived from reported power draw was worse than those of the residential products (-2.40%, -2.72%, -0.36%). The internal integration of power over time, used to calculate cumulative energy consumption, typically occurs at current and voltage sampling rates much higher than once per minute. This suggests that the average commercial-product RRE derived from reported energy consumption should be very consistent and better than performance based on reported power draw. However, the RRE derived from reported energy consumption varied significantly across the three makes of commercial-market products and was uniformly less accurate than performance based on reported power draw. Subsequent analysis identified a number of root causes for this decrease in performance, most of which were related to reporting resolution. The goals of this study are to generate awareness of building systems capable of reporting their own energy consumption, further interest in the value of energy data for a variety of uses, draw attention to how the accuracy of reported metrics can be characterized, and quantify the performance variation found in marketavailable products. The results of this study and subsequent related work may be relevant to stakeholders in industry-specification and standards-development organizations. The methods this study employs could inform test and measurement procedures and performance classifications for connected outlets, lighting products, and other building systems capable of reporting their own energy consumption. The study concludes with stakeholder recommendations, including the following: • Energy-reporting device and system manufacturers developing products that report energy consumption should characterize the accuracy of reported metrics using a reference meter calibrated by an independent laboratory that was accredited by an ILAC MRA signatory (and whose scope of accreditation explicitly covers energy measurement), and should include this information on product data sheets. • Standards and specification development organizations should develop application-specific performance classifications that end users can understand and relate to their energy-data use needs (e.g., 2% accuracy class for utility streetlight energy billing needs, or 10% accuracy class for ESCO performance verification needs). • Current or potential owners, operators, and specifiers of energy-reporting building systems should rigorously analyze the dependency of current and planned energy-data use cases on accuracy, noting in particular the dependence (or lack thereof) on relative vs. absolute accuracy, and on trueness vs. precision (i.e., repeatability), and should communicate use-case needs to industry standards and specification organizations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

Characterization and Analysis of the Energy-Reporting Accuracy of Connected Devices

Emerging energy-efficient building systems increasingly exhibit greater functionality, often requiring multiple operating modes (e.g. white-tunability for lighting products and data traffic for devices with networked, integrated sensors). This increased functionality makes energy consumption estimates more complex. Given that these functions consume energy, the energy performance of such building systems is dependent on what operating modes they use and how much time they spend in each mode. Devices and systems that can report their own energy consumption mitigate this energy-performance uncertainty. This study explores the energy-reporting accuracy of market-available connected electrical outlets. The study considers two residential-market products (five units each, one outlet per unit) and three commercial-market products (two units each, 18 to 24 outlets per unit) with the ability to report power drawn and/or energy consumed by devices connected to their receptacles. The products were purchased through typical market channels. Pacific Northwest National Laboratory (PNNL) conducted testing in December 2018 at its Connected Lighting Test Bed (CLTB), using a custom-developed test setup and method adapted from industry standards. The setup collected energy-consumption data reported by the outlet devices under test (DUTs) at one-minute intervals and compared that data with measurements taken by a reference meter over a range of test conditions. The residential products reported power draw but not interval or cumulative energy consumption. The commercial products reported both power draw and cumulative energy consumption. Relative reporting error (RRE) was calculated for all measurements, and analysis of the results revealed variations across devices and test conditions. The total number of measurements (50 for each residential product, 60 for each commercial product) offers an appreciable comparison of performance at the make/model level. The average RRE of the residential products derived from reported power draw was -0.02% and -1.20%. The average RRE for two of the three the commercial products derived from reported power draw was worse than those of the residential products (-2.40%, -2.72%, -0.36%). The internal integration of power over time, used to calculate cumulative energy consumption, typically occurs at current and voltage sampling rates much higher than once per minute. This suggests that the average commercial-product RRE derived from reported energy consumption should be very consistent and better than performance based on reported power draw. However, the RRE derived from reported energy consumption varied significantly across the three makes of commercial-market products and was uniformly less accurate than performance based on reported power draw. Subsequent analysis identified a number of root causes for this decrease in performance, most of which were related to reporting resolution. The goals of this study are to generate awareness of building systems capable of reporting their own energy consumption, further interest in the value of energy data for a variety of uses, draw attention to how the accuracy of reported metrics can be characterized, and quantify the performance variation found in marketavailable products. The results of this study and subsequent related work may be relevant to stakeholders in industry-specification and standards-development organizations. The methods this study employs could inform test and measurement procedures and performance classifications for connected outlets, lighting products, and other building systems capable of reporting their own energy consumption. The study concludes with stakeholder recommendations, including the following: • Energy-reporting device and system manufacturers developing products that report energy consumption should characterize the accuracy of reported metrics using a reference meter calibrated by an independent laboratory that was accredited by an ILAC MRA signatory (and whose scope of accreditation explicitly covers energy measurement), and should include this information on product data sheets. • Standards and specification development organizations should develop application-specific performance classifications that end users can understand and relate to their energy-data use needs (e.g., 2% accuracy class for utility streetlight energy billing needs, or 10% accuracy class for ESCO performance verification needs). • Current or potential owners, operators, and specifiers of energy-reporting building systems should rigorously analyze the dependency of current and planned energy-data use cases on accuracy, noting in particular the dependence (or lack thereof) on relative vs. absolute accuracy, and on trueness vs. precision (i.e., repeatability), and should communicate use-case needs to industry standards and specification organizations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗

DOE OSTI2019

Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries

ABSTRACT We present configuration-space estimators for the auto- and cross-covariance of two- and three-point correlation functions (2PCF and 3PCF) in general survey geometries. These are derived in the Gaussian limit (setting higher order correlation functions to zero), but for arbitrary non-linear 2PCFs (which may be estimated from the survey itself), with a shot-noise rescaling parameter included to capture non-Gaussianity. We generalize previous approaches to include Legendre moments via a geometry-correction function calibrated from measured pair and triple counts. Making use of importance sampling and random particle catalogues, we can estimate model covariances in fractions of the time required to do so with mocks, obtaining estimates with negligible sampling noise in ∼10 (∼100) CPU-hours for the 2PCF (3PCF) autocovariance. We compare results to sample covariances from a suite of BOSS DR12 mocks and find the matrices to be in good agreement, assuming a shot-noise rescaling parameter of 1.03 (1.20) for the 2PCF (3PCF). To obtain strongest constraints on cosmological parameters, we must use multiple statistics in concert; having robust methods to measure their covariances at low computational cost is thus of great relevance to upcoming surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Graphite Characterization: Baseline Variability Analysis Report

The Idaho National INL’s Baseline Material Property program provides many measurements of different material properties on a variety of nuclear graphite grades being investigated for irradiation-induced changes in material properties. The baseline material properties provide an unirradiated reference for comparison with measurements of those properties after irradiation. This study describes how uncertainty, or variance, in estimates of important material properties, like compressive strength, may depend on sample size, sample distribution and parameter estimation methods. Compressive strength data from two large collections of specimens from a billet of PCEA graphite (sample size = 230) and a billet of IG-110 graphite (sample size = 48) are used to illustrate these dependencies. The grades of graphite used represent approximate end members in terms of relative variability in strength measurements. Monte Carlo simulation and bootstrapping methods were used to examine variance in Weibull-parameter estimates as a function of sample size. Results were consistent with what previous statistical analyses have shown about the relationship between sample size and width of the confidence interval for maximum likelihood (ML) estimated parameters when samples are repeatedly drawn from a Weibull distribution. As a function of sample size, the precision of the modulus estimate increases faster than that of the characteristic strength. The modulus maximum likelihood estimates (MLEs) are biased for low sample sizes. The American Society for Testing and Materials document ASTM D7846-16 provides equations that describe the dependence of the variance of parameter MLEs on sample size. Using the same methodology, we show that the polynomials provided for variance dependence on sample size are inaccurate for sample sizes greater than ~120. We provide approximations to that relationship that illustrate relative constancy for sample size > ~10, in the logspace relationship of the modulus variance and the log transformed characteristic strength variance. Bootstrapping provided a means of comparing Weibull parameters obtained using ASME’s guidance for specimen collection to those obtained using different weighting in a case where strength is related to position in a billet and to grain orientation and a single distribution is used to characterize the billet. ASME specifies that samples be collected with equal representation in all locations and grain orientations. Parameter values obtained using ASME’s method were different from those obtained using random sampling of the complete data sets, and this was particularly true for the PCEA data. In addition, while the ASME approach yielded more conservative parameters for the PCEA data, the opposite was true for the IG-110 data. The difference observed for the PCEA data set likely reflects the larger number of against-grain specimens collected, which had generally higher strength than the with-grain specimens. This emphasizes the importance of the dependence of strength on location or grain orientation and suggests that it may be prudent to weight specimen collection toward the weaker subgroups if a conservative estimate as desired, as the equal weighting method recommended by ASME would will not always provide the most conservative Weibull parameters. Because spatial correlations commonly exist in certain grades of graphite, future work may involve developing a methodology for parameter inference that relaxes the assumption of independent specimens. ASTM and ASME codes recommend different parameter estimation methods and models of the Weibull distribution in different situations. Descriptions of the effects on parameter estimates for the example billets used in this study provide an example of how the method may affect the parameter estimate, and how—in this case—that compares to differences due to other factors, such as sample size and dependence on grain orientation or sample location.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Approximating and incorporating model uncertainty in an inversion for seismic source functions: Preliminary results

We present preliminary work on propagating model uncertainty into the estimation of the time domain source time functions of the seismic source. Our method is based on an estimated model covariance function, which we estimate from the data. The model covariance function is then used to construct a suite of surrogate Greens functions which we use in a Monte Carlo type inversion scheme. The result is a probability density function of the six independent source time functions, each of which corresponds to an individual component of the seismic moment tensor. We compare the results of our method with those obtained using a computationally expensive finite difference Monte Carlo method and find that our new method produces results that are deficient in low frequencies. The advantage of our new method, which we term the Karhunen-Loeve Monte Carlo (KLMC) method, is that is several orders of magnitude faster than our current method, which uses a finite difference scheme to produce the suite of forward models.

42 ENGINEERING↗

DOE OSTI2022

Towards mapping biodiversity from above: Can fusing lidar and hyperspectral remote sensing predict taxonomic, functional, and phylogenetic tree diversity in temperate forests?

Abstract Aim Rapid global change is impacting the diversity of tree species and essential ecosystem functions and services of forests. It is therefore critical to understand and predict how the diversity of tree species is spatially distributed within and among forest biomes. Satellite remote sensing platforms have been used for decades to map forest structure and function but are limited in their capacity to monitor change by their relatively coarse spatial resolution and the complexity of scales at which different dimensions of biodiversity are observed in the field. Recently, airborne remote sensing platforms making use of passive high spectral resolution (i.e., hyperspectral) and active lidar data have been operationalized, providing an opportunity to disentangle how biodiversity patterns vary across space and time from field observations to larger scales. Most studies to date have focused on single sites and/or one sensor type; here we ask how multiple sensor types from the National Ecological Observatory Network’s Airborne Observation Platform (NEON AOP) perform across multiple sites in a single biome at the NEON field plot scale (i.e., 40 m × 40 m). Location Eastern USA. Time period 2017–2018. Taxa studied Trees. Methods With a fusion of hyperspectral and lidar data from the NEON AOP, we assess the ability of high resolution remotely sensed metrics to measure biodiversity variation across eastern US temperate forests. We examine how taxonomic, functional, and phylogenetic measures of alpha diversity vary spatially and assess to what degree remotely sensed metrics correlate with in situ biodiversity metrics. Results Models using estimates of forest function, canopy structure, and topographic diversity performed better than models containing each category alone. Our results show that canopy structural diversity, and not just spectral reflectance, is critical to predicting biodiversity. Main conclusions We found that an approach that jointly leverages spectral properties related to leaf and canopy functional traits and forest health, lidar derived estimates of forest structure, fine‐resolution topographic diversity, and careful consideration of biogeographical differences within and among biomes is needed to accurately map biodiversity variation from above.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The effect of quasar redshift errors on Lyman-α forest correlation functions

ABSTRACT Using synthetic Lyman-α forests from the Dark Energy Spectroscopic Instrument (DESI) survey, we present a study of the impact of errors in the estimation of quasar redshift on the Lyman-α correlation functions. Estimates of quasar redshift have large uncertainties of a few hundred km s−1 due to the broadness of the emission lines and the intrinsic shifts from other emission lines. We inject Gaussian random redshift errors into the mock quasar catalogues, and measure the auto-correlation and the Lyman-α-quasar cross-correlation functions. We find a smearing of the BAO feature in the radial direction, but changes in the peak position are negligible. However, we see a significant unphysical correlation for small separations transverse to the line of sight which increases with the amplitude of the redshift errors. We interpret this contamination as a result of the broadening of emission lines in the measured mean continuum, caused by quasar redshift errors, combined with the unrealistically strong clustering of the simulated quasars on small scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Hydrological niche segregation defines forest structure and drought tolerance strategies in a seasonal Amazon forest

The relationship between rooting depth and above-ground hydraulic traits can potentially define drought resistance strategies that are important in determining species distribution and coexistence in seasonal tropical forests, and understanding this is important for predicting the effects of future climate change in these ecosystems. We assessed the rooting depth of 12 dominant tree species (representing c. 42% of the forest basal area) in a seasonal Amazon forest using the stable isotope ratios (δ 18 O and δ 2 H) of water collected from tree xylem and soils from a range of depths. We took advantage of a major ENSO-related drought in 2015/2016 that caused substantial evaporative isotope enrichment in the soil and revealed water use strategies of each species under extreme conditions. We measured the minimum dry season leaf water potential both in a normal year (2014; Ψ non-ENSO ) and in an extreme drought year (2015; Ψ ENSO ). Furthermore, we measured xylem hydraulic traits that indicate water potential thresholds trees tolerate without risking hydraulic failure (P 50 and P 88 ). We demonstrate that coexisting trees are largely segregated along a single hydrological niche axis defined by root depth differences, access to light and tolerance of low water potential. These differences in rooting depth were strongly related to tree size; diameter at breast height (DBH) explained 72% of the variation in the δ 18 Oxylem. Additionally, δ 18 O xylem explained 49% of the variation in P50 and 70% of P88, with shallow-rooted species more tolerant of low water potentials, while δ 18 O of xylem water explained 47% and 77% of the variation of minimum Ψ non-ENSO and Ψ ENSO . We propose a new formulation to estimate an effective functional rooting depth, i.e. the likely soil depth from which roots can sustain water uptake for physiological functions, using DBH as predictor of root depth at this site. Based on these estimates, we conclude that rooting depth varies systematically across the most abundant families, genera and species at the Tapajós forest, and that understorey species in particular are limited to shallow rooting depths. Our results support the theory of hydrological niche segregation and its underlying trade-off related to drought resistance, which also affect the dominance structure of trees in this seasonal eastern Amazon forest. Synthesis. Our results support the theory of hydrological niche segregation and demonstrate its underlying trade-off related to drought resistance (access to deep water vs. tolerance of very low water potentials). We found that the single hydrological axis defining water use traits was strongly related to tree size, and infer that periodic extreme droughts influence community composition and the dominance structure of trees in this seasonal eastern Amazon forest.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Public charging infrastructure for plug-in electric vehicles: What is it worth?

A lack of charging infrastructure is an important barrier to the growth of the plug-in electric vehicle (PEV) market. Public charging infrastructure has tangible and intangible value, such as reducing range anxiety or building confidence in the future of the PEV market. Quantifying the value of public charging infrastructure can inform analysis of investment decisions and can help predict the impact of charging infrastructure on future PEV sales. Estimates of willingness to pay (WTP) based on stated preference surveys are limited by consumers' lack of familiarity with PEVs. As an alternative, we focus on quantifying the tangible value of public PEV chargers in terms of their ability to displace gasoline use for PHEVs and to enable additional electric (e-) vehicle miles for BEVs, thereby mitigating the limitations of shorter range and longer recharging time. Simulation studies provide data that can be used to quantify e-miles enabled by public chargers and the value of additional e-miles can be inferred from econometric estimates of WTP for increased vehicle range. Functions are synthesized that estimate the WTP for public charging infrastructure by plug-in hybrid and battery electric vehicles, conditional on vehicle range, annual vehicle travel, pre-existing charging infrastructure, energy prices, vehicle efficiency, and household income. A case study based on California's public charging network in 2017 indicates that, to the purchaser of a new BEV with a 100-mile range and home recharging, existing public fast chargers are worth about $1500 for intraregional travel, and fast chargers along intercity routes are valued at over $6500.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Uncertainty Quantification for Point Spread Functions in X-Ray Radiography

X-ray radiographers have tools for estimating the point spread function (PSF) which determines the extent of the blur in images. Knowledge of uncertainties in their estimations can be extremely valuable, and existing methods do not provide this information. We have developed a new technique using a Bayesian framework that will provide useful uncertainties to the estimated PSF.

point spread function↗

DOE OSTI2024

A Cellular Automaton Simulation for Predicting Phase Evolution in Solid-State Reactions

New computational tools for solid-state synthesis recipe design are needed in order to accelerate the experimental realization of novel functional materials proposed by high-throughput materials discovery workflows. This work contributes a cellular automaton simulation framework for predicting the time-dependent evolution of intermediate and product phases during solid-state reactions as a function of precursor choice and amount, reaction atmosphere, and heating profile. The simulation captures the effects of reactant particle spatial distribution, particle melting, and reaction atmosphere. Reaction rates based on rudimentary kinetics are estimated using density functional theory data from the Materials Project and machine learning estimators for the melting point and the vibrational entropy component of the Gibbs free energy. The resulting simulation framework allows for the prediction of the likely outcome of a reaction recipe before any experiments are performed. We analyze five experimental solid-state recipes for BaTiO 3 , CaZrN 2 , and YMnO 3 found in the literature to illustrate the performance of the model in capturing reaction selectivity and reaction pathways as a function of temperature and precursor choice. This simulation framework offers an easier way to optimize existing recipes, aid in the identification of intermediates, and design effective recipes for yet unrealized inorganic solids in silico .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a nonparametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications.

42 ENGINEERING↗

DOE OSTI2019

GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a nonparametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗