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At least 19 records

Data-Consistent Inversion for Stochastic Input-to-Output Maps

Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Finally, numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

97 MATHEMATICS AND COMPUTING↗

Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Determining process–structure–property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process–structure and structure–property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification framework based on push-forward probability measures, which combines techniques from measure theory and Bayes’ rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

36 MATERIALS SCIENCE↗

Consistent Nuclear Data Evaluations for Criticality Safety [Slides]

This presentation covers consistent nuclear data evaluations for criticality safety. Topics include the evaluation procedure, n+ 139 La evaluation, the work in progress for the n+ 233 U evaluation (emphasis on capture), and a concluding Summary.

07 ISOTOPE AND RADIATION SOURCES↗

Plant Characteristics, Porewater, Gas Flux, and Soil Biogeochemistry at Council Road Site Mile Marker 71, Seward Peninsula, Alaska, 2023

Data collected at Council, AK (64°51’35.0”N 163°41’59.1”W) during a summer campaign in 2023. Water data consists of soil porewater collected by centrifuging soil cores and also by field collection with porewater samplers (rhizons). Gas data consists of CO2, CH4 and N2O surface soil fluxes measured with a portable FTIR analyzer. Plant and root data consists of biomass, root length, diameter and mass. Soil data consists of total C and N. Air, water and soil samples span two main locations: a thermokarst wetland and an upland tussock. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).This dataset was generated to broadly address the following research question: how will climate change (i.e., thawing permafrost, landscape change) alter the ecosystem flux (sink versus source) of important greenhouse gases such as CO2, CH4 and N2O?Description of the contents of this data package: This dataset contains 5 different individual .csv files containing plant, soil, water and gas data. No software is needed to utilize them. PFTCover: Plant functional type ground cover in 1x1 meter plots. SoilCores: Solidphase and porewater phase soil biogeochemical variablesPlantData: Above and belowground plant traits. GasFlux: Surface plant-soil gas measurementsFieldPorewater: Field collected porewater biogeochemical variables

54 ENVIRONMENTAL SCIENCES↗

Greenhouse Rhizobox Experiment with Plant Characteristics, Porewater, Gas Flux, and Soil Biogeochemistry data, Seward Peninsula, Alaska, 2024

Data collected from a greenhouse rhizobox experiment (2024) using soils and plants collected at Council, AK (64°51’35.0”N 163°41’59.1”W) during a summer campaign in 2023. Water data consists of soil porewater collected by porewater samplers (rhizons). Gas data consists of CO2 and CH4 surface soil fluxes measured with an FTIR (Fourier-transformed infrared red) analyzer. Plant and root data consists of biomass, root length. This study is a part of The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).This dataset was generated to broadly address the following research question: how will climate change (i.e., thawing permafrost, landscape change) alter the ecosystem flux (sink versus source) of important greenhouse gases such as CO2 and CH4?Description of the contents of this data package: Rhizobox2024_Data.csv: This dataset contains plant, water and gas data. No software is needed to utilize them.nga535_flmd.csv: The file contains file level metadatanga535.dd.csv: This file contains the data dictionaryMethods.pdf: This file contains the data collection methods

54 ENVIRONMENTAL SCIENCES↗

SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees

Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.

97 MATHEMATICS AND COMPUTING↗

Stability and Convergence of Solutions to Stochastic Inverse Problems Using Approximate Probability Densities

Data-consistent inversion is designed to solve a class of stochastic inverse problems where the solution is a pullback of a probability measure specified on the outputs of a quantities of interest (QoI) map. Here, this work presents stability and convergence results for the case where finite QoI data result in an approximation of the solution as a density. Given their popularity in the literature, separate results are proven for three different approaches to measuring discrepancies between probability measures: f-divergences, integral probability metrics, and L p metrics. In the context of integral probability metrics, we also introduce a pullback probability metric that is well-suited for data-consistent inversion. This fills a theoretical gap in the convergence and stability results for data-consistent inversion that have mostly focused on convergence of solutions associated with approximate maps. Numerical results are included to illustrate key theoretical results with intuitive and reproducible test problems that include a demonstration of convergence in the measure-theoretic "almost" sense.

97 MATHEMATICS AND COMPUTING↗

Consistent Nuclear Data Evaluations for Criticality Safety

Evaluations of nuclear data are based on statistical analysis of available experimental data and their uncertainties plus model calculations and their uncertainties. As the models are currently rather limited, the evaluations are heavily biassed toward experimental data, with the caveat that a thorough analysis is also required to understand possible discrepancies between data sets. Hence, as new experimental data become available, they are incorporated into the evaluation procedure. Recent measurements of the 233 U capture to fission cross section ratio at the Los Alamos Neutron Science Center have prompted a re-evaluation of the capture cross section in the resonance and fast regions up to 250 keV. We will discuss the challenges of including the new fast neutron experimental data in an evaluation that is consistent with the resonance region. We will also discuss our consistent evaluation procedure based on the Hauser-Feshbach statistical model for nuclear reactions and its application to the evaluations of 239 Pu and 139 La neutron-induced reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Current data are consistent with flat spatial hypersurfaces in the Λ CDM cosmological model but favor more lensing than the model predicts

Here, we study the performance of three pairs of tilted, and a pair of untilited, ΛCDM cosmological models, with three of these four pairs allowing for non-flat spatial hypersurfaces, against cosmic microwave background (CMB) temperature and polarization power spectrum data (P18), measurements of the Planck 2018 lensing potential power spectrum (lensing), and a large compilation of non-CMB data (non-CMB). For the eight models, we measure cosmological parameters and study whether or not pairs of the data sets (as well as subsets of them) are mutually consistent in these models. Half of these models allow the lensing consistency parameter A L , which re-scales the gravitational potential power spectrum, to be an additional free parameter to be determined from data, while the other three have A L = 1 which is the theoretically expected value. The pair of untilted non-flat ΛCDM models are incompatible with P18 data. The tilted spatially-flat models assume the usual primordial spatial inhomogeneity power spectrum that is a power law in wave number. The tilted non-flat models assume either the primordial power spectrum used in the Planck group anal yses [Planck P(q)], that has recently been numerically shown to be a good approximation to what is quantum-mechanically generated from a particular choice of closed inflation model initial conditions, or a recently computed power spectrum [new P(q)] that quantum-mechanically follows from a different set of non-flat inflation model initial conditions. In the tilted non-flat models with A L = 1 we find differences between P18 data and non-CMB data cosmological parameter constraints, which are large enough to rule out the Planck P(q) model at 3σ but not the new P(q) model. No significant differences are found when cosmological parameter constraints obtained with two different data sets are compared within the standard tilted flat ΛCDM model. While both P18 data and non-CMB data separately favor a closed geometry, with spatial curvature density parameter Ω k < 0, when P18+non-CMB data are jointly analyzed the evidence in favor of non-flat hypersurfaces subsides. Differences between P18 data and non-CMB data cosmological constraints subside when A L is allowed to vary. From the most restrictive P18+lensing+non-CMB data combination we get almost model-independent constraints on the cosmological parameters and find that the A L > 1 option is preferred over the Ω k < 0 one, with the A L parameter, for all models, being larger than unity by ~ 2.5σ. According to the deviance information criterion, in the P18+lensing+non-CMB analysis, the varying A L option is on the verge of being strongly favored over the A L = 1 one, which could indicate a problem for the standard tilted flat ΛCDM model. These data are consistent with flat spatial hypersurfaces but more and better data could improve the constraints on Ω k and might alter this conclusion. Error bars on some cosmological parameters are significantly reduced when non-CMB data are used jointly with P18+lensing data. For example, in the tilted flat ΛCDM model for P18+lensing+non-CMB data the Hubble constant H 0 = 68.09 ± 0.38 km s -1 Mpc -1 , which is consistent with that from a median statistics analysis of a large compilation of H 0 measurements as well as with a number of local measurements of the cosmological expansion rate. This H 0 error bar is 31% smaller than that from P18+lensing data alone.

79 ASTRONOMY AND ASTROPHYSICS↗

Crustal Strain Rates in the Western United States and Their Relationship with Earthquake Rates

Abstract We present a suite of strain rate models for the western United States based on geologic and geodetic data. The geologic data consist of Quaternary fault-slip rates and the geodetic data consists of a new compilation of Global Positioning System (GPS) velocities derived from continuous, semicontinuous, and campaign measurements. We remove postseismic deformation from the GPS time series in order for our geodetic strain rate model to best capture the interseismic strain accumulation rate. We present models based on either geologic or geodetic data, but also create a hybrid model. Although there are some differences between the models, the large-scale features are the same, with the noticeable exception for the Pacific Northwest where interseismic strain is naturally more distributed than the long-term strain release. We also present a map of earthquake rate densities based on mainshocks, and the result has similar spatial features similar to the strain rate models (at least in the southwestern United States). We perform a general correlation analysis between strain rate and seismicity rate (south of Cascadia) and find a change in linearity between seismicity and strain rates from slow to faster deforming areas with seismicity rates relatively lower for the latter. The extent of that change depends a bit on assumptions made on the declustering and completeness of the catalog, but the finding of a change in slope is robust across the different strain rate models. Linearity for all areas is only expected when Gutenberg–Richter parameters and parameters involved in the conversion from strain to moment rate are uniform across the study area. We discuss these qualifications, but find no single satisfactory explanation for our observation. Moreover, when considering a rather short time and space, theoretical considerations of sampling from a power-law distribution actually predict there to be a power law instead of a linear relationship, generally consistent with our observation.

Geochemistry & Geophysics↗