INVARIANT TORI OF THE POINCARE RETURN MAP AS SOLUTIONS OF FUNCTIONAL DIFFERENCE EQUATIONS.
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Warnock, R.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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SIMULATION OF A STORAGE RING FREE ELECTRON LASER WITH A MAPPING ALGORITHM FOR DISTRIBUTION FUNCTIONS
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Ziemann, V.↗
Integrating Very-High-Resolution UAS Data and Airborne Imaging Spectroscopy to Map the Fractional Composition of Arctic Plant Functional Types in Western Alaska: Supporting Data
Remote sensing maps of plant functional type (PFT) fractional cover (FCover), dominant PFT, and FCover uncertainty derived from NASA's Airborne Visible / Infrared Imaging Spectrometer - Next Generation (AVIRIS-NG). The AVIRIS-NG imaging spectroscopy data (380-2510 nm) was collected as a part of the collaboration between NASA's Arctic-Boreal Vulnerability Experiment (ABoVE; Miller et al., 2019) and DOE's Next Generation Ecosystem Experiment in the Arctic (NGEE-Arctic). This package includes maps of the NGEE-Arctic Council watershed on the Seward Peninsula, Alaska, created using AVIRIS-NG imagery collected on July 9th, 2019. The map data and metadata are provided as GeoTIFF (*.tif), ENVI image (*.dat), and text (*.txt, *hdr) formats. Additional map quicklooks are provided as *.pdf files and GIS *.kml files. These datasets are provided in support of Yang et al., (2023), "Integrating Very-High-Resolution UAS Data and Airborne Imaging Spectroscopy to Map the Fractional Composition of Arctic Plant Functional Types in Western Alaska".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).
54 ENVIRONMENTAL SCIENCES↗
Mapping the current–current correlation function near a quantum critical point
The current–current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson’s localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau–insulator or plateau–plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current–current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current–current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Landmark-Warped Emulators for Models with Misaligned Functional Response
Many computer models output functional data, and in some cases, these functional data have similar, but misaligned, shape characteristics. In this paper, we introduce a general approach for building emulators for computer models that output misaligned functional data when key values in the functional response (landmarks) can be easily identified. This approach has two main parts: modeling the aligned (using the landmarks) functional data, and modeling the functions that map the misaligned data to the aligned space (warping functions). As the warping functions are required to be monotonic, we give special attention to modeling monotonic functional response data. We discuss how our approach can be easily applied for a variety of typical emulators, such as Gaussian processes, Bayesian multivariate adaptive regression splines, and Bayesian additive regression trees, and how sensitivity analysis can be performed. We demonstrate our approach by building emulators for two applications: (1) a high-energy-density physics computer model used to simulate inertial confinement fusion ignition experiments, where model outputs are highly misaligned, and (2) a multiphysics continuum hydrocode used to simulate high-velocity impact experiments, where model outputs are only slightly misaligned. In case (1) traditional methods cannot be applied, while in (2) they can be applied, but the proposed method performs significantly better.
97 MATHEMATICS AND COMPUTING↗
Validation and uncertainty quantification of detector response functions for a $1"×2"$ NaI collimated detector intended for inverse radioisotope source mapping applications
Detector response functions (DRFs) are often used for inverse analysis. We compute the DRF of a sodium iodide (NaI) nuclear material holdup field detector using the code named g03 developed by the Center for Engineering Applications of Radioisotopes (CEAR) at NC State University. Three measurement campaigns were performed in order to validate the DRF’s constructed by g03: on-axis detection of calibration sources, off-axis measurements of a highly enriched uranium (HEU) disk, and on-axis measurements of the HEU disk with steel plates inserted between the source and the detector to provide attenuation. Furthermore, this work quantifies the uncertainty of the Monte Carlo simulations used in and with g03, as well as the uncertainties associated with each semi-empirical model employed in the full DRF representation. Overall, for the calibration source measurements, the response computed by the DRF for the prediction of the full-energy peak region of responses was good, i.e. within two standard deviations of the experimental response. In contrast, the DRF tended to overestimate the Compton continuum by about 45–65% due to inadequate tuning of the electron range multiplier fit variable that empirically represents physics associated with electron transport that is not modeled explicitly in g03. For the HEU disk measurements, computed DRF responses tended to significantly underestimate (more than 20%) the secondary full-energy peaks (any peak of lower energy than the highest-energy peak computed) due to scattering in the detector collimator and aluminum can, which is not included in the g03 model. We ran a sufficiently large number of histories to ensure for all of the Monte Carlo simulations that the statistical uncertainties were lower than their experimental counterpart’s Poisson uncertainties. The uncertainties associated with least-squares fits to the experimental data tended to have parameter relative standard deviations lower than the peak channel relative standard deviation in most cases and good reduced chi-square values. The highest sources of uncertainty were identified as the energy calibration polynomial factor (due to limited source availability and NaI resolution) and the Ba-133 peak fit (only a very weak source was available), which were 20% and 10%, respectively.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
A coupled neutronic/thermal-hydraulic scheme between COBAYA3 and SUBCHANFLOW within the NURESIM simulation platform
Multi-scale, multi-physics problems reveal significant challenges while dealing with coupled neutronic/thermal-hydraulic solutions. Current generation of codes applied to Light Water Reactors (LWR) are based on 3D neutronic nodal methods coupled with one or two phase flow thermal-hydraulic system or sub-channel codes. In addition, spatial meshing and temporal schemes are crucial for the proper description of the non-symmetrical core behavior in case of transient and accidents e.g. reactivity insertion accidents. This paper describes the coupling approach between the 3D neutron diffusion code COBAYA3 and the sub-channel code SUBCHANFLOW within SALOME. The coupling is done inside the SALOME open source platform that is characterized by a powerful pre- and post-processing capabilities and a novel functionality for mapping of the neutronic and thermal hydraulic domains. The peculiar functionalities of SALOME and the steps required for the code integration and coupling are presented. The validation of the coupled codes is done based on two benchmarks the PWR MOX/UO{sub 2} RIA and the TMI-1 MSLB benchmark. A discussion of the prediction capability of COBAYA3/SUBCHANFLOW compared to other coupled solutions will be provided too. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Advanced multi-modal mass spectrometry imaging reveals functional differences of placental villous compartments at microscale resolution
The placenta is a complex and heterogeneous organ that links the mother and fetus, playing a crucial role in nourishing and protecting the fetus throughout pregnancy. Integrative spatial multi-omics approaches can provide a systems-level understanding of molecular changes underlying the mechanisms leading to the histological variations of the placenta during healthy pregnancy and pregnancy complications. Herein, we advance our metabolome-informed proteome imaging (MIPI) workflow to include lipidomic imaging, while also expanding the molecular coverage of metabolomic imaging by incorporating on-tissue chemical derivatization (OTCD). The improved MIPI workflow advances biomedical investigations by leveraging state-of-the-art molecular imaging technologies. Lipidome imaging identifies molecular differences between two morphologically distinct compartments of a placental villous functional unit, syncytiotrophoblast (STB) and villous core. Next, our advanced metabolome imaging maps villous functional units with enriched metabolomic activities related to steroid and lipid metabolism, outlining distinct molecular distributions across morphologically different villous compartments. Complementary proteome imaging on these villous functional units reveals a plethora of fatty acid- and steroid-related enzymes uniquely distributed in STB and villous core compartments. Integration across our advanced MIPI imaging modalities enables the reconstruction of active biological pathways of molecular synthesis and maternal-fetal signaling across morphologically distinct placental villous compartments with micrometer-scale resolution.
60 APPLIED LIFE SCIENCES↗
Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach
We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Extending Conformal Prediction to Hidden Markov Models with Exact Validity via de Finetti’s Theorem for Markov Chains
Conformal prediction is a widely used method to quantify uncertainty in settings where the data is independent and identically distributed (IID), or more generally, exchangeable. Conformal prediction takes in a pre-trained classifier and a calibration dataset as inputs, and returns a function which maps feature vectors to subsets of classes. The output of the returned function for a new feature vector is guaranteed to contain the true class with a pre-specified confidence. Despite its success and usefulness in IID settings, extending conformal prediction to non-exchangeable (e.g., Markovian) data in a manner that provably preserves all desirable theoretical properties has largely remained an open problem. As a solution, we extend conformal prediction to the setting of a Hidden Markov Model (HMM) with unknown parameters. The key idea behind the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti’s Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are then viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework and is general enough to be useful in many sequential prediction problems.
Nettasinghe, Don Buddhika Wijayantha↗
The multiscale coarse-graining method. XI. Accurate interactions based on the centers of charge of coarse-grained sites
It is essential to be able to systematically construct coarse-grained (CG) models that can efficiently and accurately reproduce key properties of higher-resolution models such as all-atom. To fulfill this goal, a mapping operator is needed to transform the higher-resolution configuration to a CG configuration. Certain mapping operators, however, may lose information related to the underlying electrostatic properties. In this paper, a new mapping operator based on the centers of charge of CG sites is proposed to address this issue. Four example systems are chosen to demonstrate this concept. Within the multiscale coarse-graining framework, CG models that use this mapping operator are found to better reproduce the structural correlations of atomistic models. The present work also demonstrates the flexibility of the mapping operator and the robustness of the force matching method. For instance, important functional groups can be isolated and emphasized in the CG model.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Phase retrieval using Gaussian basis functions
A wavefront map of arbitrary aperture can be represented by a sum of Gaussian basis functions. Its performance is compared here to other representation methods such as orthonormal polynomials and Fourier modes. Gaussian basis functions can be applied to phase retrieval of high-frequency wavefront maps. Experiments show good agreement with direct measurements by a wavefront sensor. Finally, optimum measurement conditions are discussed based on the statistics of wavefront properties.
47 OTHER INSTRUMENTATION↗
Neural networks to learn protein sequence–function relationships from deep mutational scanning data
Understanding the relationship between protein sequence and function is necessary to design new and useful proteins with applications in bioenergy, medicine, and agriculture. The mapping from sequence to function is tremendously complex because it involves thousands of molecular interactions that are coupled over multiple lengths and timescales. We show that neural networks can learn the sequence–function mapping from large protein datasets. Neural networks are appealing for this task because they can learn complicated relationships from data, make few assumptions about the nature of the sequence–function relationship, and can learn general rules that apply across the length of the protein sequence. We demonstrate that learned models can be applied to design new proteins with properties that exceed natural sequences.
59 BASIC BIOLOGICAL SCIENCES↗
Learning to Predict Physical Properties Using Sums of Separable Functions
We present an algorithm for learning the function that maps a material structure to its value on some property, given the value of this function on several structures. We pose this problem as one of learning (regressing) a function of many variables from scattered data. Each structure is first converted to a weighted set of points by a process that removes irrelevant translations and rotations but otherwise retains full information about the structure. Then, incorporating a weighted average for each structure, we construct the multivariate regression function as a sum of separable functions, following the paradigm of separated representations. The algorithm can treat all finite and periodic structures within a common framework, and in particular does not require all structures to lie on a common lattice. We show how the algorithm simplifies when the structures do lie on a common lattice, and we present numerical results for that case.
36 MATERIALS SCIENCE↗
Regular zeros of quadratic maps and their application
Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. Bibliography: 13 titles.
97 MATHEMATICS AND COMPUTING↗
Exact solitary solution of Schamel equation in plasmas with negative ions
A theoretical investigation is carried out for understanding the properties of the solitary solution in plasmas with negative ions. Schamel equation for a plasma consisting of electron, positive ions and negative ions has been derived by using the reductive perturbation method. The effects of negative ions and the density on the properties of the solitary solution is discussed. We make use of the extended mapping method and auxiliary equation to obtain the solution of Schamel equation. This solution includes the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. Furthermore, we show that the incorporate negative ion effects in the nonlinear propagation of ion acoustic waves that are controlled by trapped electrons and the results of the solitary solution in plasmas with negative ions model are discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data
Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.
42 ENGINEERING↗
Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels
We report artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗