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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Non-pairwise additivity of the leading-order dispersion energy

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained in terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is −0.11 kJ mol{sup −1} well{sup −1}, which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Tempering stochastic density functional theory

Here, we introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of ≈4-5 for the total energy and ≈1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Symmetry breaking and self-interaction correction in the chromium atom and dimer

Density functional approximations to the exchange–correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew–Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ~4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. In conclusion, these results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

An empirical method for geometric calibration of a photon counting detector-based cone beam CT system

BACKGROUND: Geometric calibration is essential in developing a reliable computed tomography (CT) system. It involves estimating the geometry under which the angular projections are acquired. Geometric calibration of cone beam CTs employing small area detectors, such as currently available photon counting detectors (PCDs), is challenging when using traditional-based methods due to detectors’ limited areas. OBJECTIVE: This study presented an empirical method for the geometric calibration of small area PCD-based cone beam CT systems. METHODS: Unlike the traditional methods, we developed an iterative optimization procedure to determine geometric parameters using the reconstructed images of small metal ball bearings (BBs) embedded in a custom-built phantom. An objective function incorporating the sphericities and symmetries of the embedded BBs was defined to assess performance of the reconstruction algorithm with the given initial estimated set of geometric parameters. The optimal parameter values were those which minimized the objective function. The TIGRE toolbox was employed for fast tomographic reconstruction. To evaluate the proposed method, computer simulations were carried out using various numbers of spheres placed in various locations. Furthermore, efficacy of the method was experimentally assessed using a custom-made benchtop PCD-based cone beam CT. RESULTS: Computer simulations validated the accuracy and reproducibility of the proposed method. The precise estimation of the geometric parameters of the benchtop revealed high-quality imaging in CT reconstruction of a breast phantom. Within the phantom, the cylindrical holes, fibers, and speck groups were imaged in high fidelity. The CNR analysis further revealed the quantitative improvements of the reconstruction performed with the estimated parameters using the proposed method. CONCLUSION: Apart from the computational cost, we concluded that the method was easy to implement and robust.

Instruments & Instrumentation↗
DOE OSTI2015

On the statistics of biased tracers in the Effective Field Theory of Large Scale Structures

With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial non-Gaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo three-point functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of an N-body simulation where the normalization parameter of the linear power spectrum is set to σ 8 = 0.9. For the lowest mass bin, we find percent level agreement up to k ≃ 0.3 h Mpc –1 for the one-loop two-point functions, and up to k ≃ 0.15 h Mpc –1 for the tree-level three-point functions, with the k-reach decreasing with higher mass bins. In conclusion, this is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Assessing the accuracy of compound formation energies with quantum Monte Carlo

Accurately predicting the formation energy of a compound, which describes its thermodynamic stability, is a key challenge in materials physics. Here, we employ a many-body quantum Monte Carlo (QMC) with single-reference trial functions to compute the formation energy of two electronically disparate compounds, the intermetallic VPt2 and the semiconductor CuI, for which standard density functional theory (DFT) predictions using both the Perdew-Burke-Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) density functional approximations deviate markedly from available experimental values. For VPt2, we find an agreement between QMC, SCAN, and PBE0 estimates, which therefore remain in disagreement with the much less exothermic experimental value. For CuI, the QMC result agrees with neither SCAN nor PBE pointing towards DFT exchange-correlation biases, likely related to the localized Cu 3d electrons. Compared to the behavior of some density functional approximations within DFT, spin-averaged QMC exhibits a smaller but still appreciable deviation when compared to experiment. The QMC result is slightly improved by incorporating spin-orbit corrections for CuI and solid I 2 , so that experiment and theory are brought into imperfect but reasonable agreement within about 120 meV/atom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

PV Validation Hub

The Validation Hub will be a clearinghouse for the transfer of novel algorithms and software from the PV research community to industry. Potential algorithms tested in the Hub could include the estimation of various PV loss factors and the detection of various operational issues. The primary function of the Hub will be for developers to submit executable code which will run on hosted data sets. Developers will receive private reports on the accuracy and performance (e.g., run-time) of the submitted algorithms, and public high level summaries will be hosted. These summaries will indicate the organization who submitted the algorithm (e.g., links to GitHub pages, documentation websites, etc.), high-level accuracy metrics, and standardized performance metrics. These results will be stored in a publicly available database, accessible through the Hub, with the ability for users to sort and filter the results. In short, the Hub will be presented to public users as a collection of interactive leaderboards, organized around specific analysis tasks pertinent to the PV data science community. These tasks include things such as the estimation of various PV loss factors and the detection of various operational issues. We will present progress on the development of this hub, including preliminary results of comparative validation of PV data science algorithms and progress towards building the platform itself.

algorithm↗
DOE OSTI2024

NEON AOP Survey of Upper East River CO Watersheds: Waveform LiDAR Binary Data

The waveform Light Detection and Ranging (LiDAR) data in this package were generated through a National Ecological Observatory Network Airborne Observation Platform (NEON AOP) acquisition over watersheds of interest surrounding Crested Butte, Colorado. The remote sensing imagery acquired by the NEON AOP supports an interdisciplinary project on hydrology, biogeochemistry, and ecosystem functioning in a snow-dominated headwater environment. These waveform LiDAR data enable spatially continuous estimation of vegetation structure parameters to facilitate analyses of the major environmental drivers of structural and compositional variability. The package contains 97 compressed file archives in 7-zip (.7z) format, each corresponding to one acquisition flightpath. Within each .7z archive is a set of constituent files describing properties of the LiDAR waveforms, such as return intensity, geolocation, outgoing pulse and other behavior of the sensor and signals. Once downloaded, the files must first be unzipped using the widely distributed command-line software utility 7z, using the command '7z x \[filename\].7z \[target_directory\]'. All files within the .7z archives can be opened in IDL, MatLab, or the open-source R statistical computing environment. Further details about the data package are in the attached user guide (neon_aop_crbu_waveformlidar_userguide.pdf). This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

2018 NEON and 2025 CHESS Campaigns↗
DOE OSTI2022

Building surrogate models of nuclear density functional theory with Gaussian processes and autoencoders

From the lightest Hydrogen isotopes up to the recently synthesized Oganesson (Z = 118), it is estimated that as many as about 8,000 atomic nuclei could exist in nature. Most of these nuclei are too short-lived to be occurring on Earth, but they play an essential role in astrophysical events such as supernova explosions or neutron star mergers that are presumed to be at the origin of most heavy elements in the Universe. Understanding the structure, reactions, and decays of nuclei across the entire chart of nuclides is an enormous challenge because of the experimental difficulties in measuring properties of interest in such fleeting objects and the theoretical and computational issues of simulating strongly-interacting quantum many-body systems. Nuclear density functional theory (DFT) is a fully microscopic theoretical framework which has the potential of providing such a quantitatively accurate description of nuclear properties for every nucleus in the chart of nuclides. Thanks to high-performance computing facilities, it has already been successfully applied to predict nuclear masses, global patterns of radioactive decay like β or γ decay, and several aspects of the nuclear fission process such as, e.g., spontaneous fission half-lives. Yet, predictive simulations of nuclear spectroscopy—the low-lying excited states and transitions between them—or of nuclear fission, or the quantification of theoretical uncertainties and their propagation to basic or applied nuclear science applications, would require several orders of magnitude more calculations than currently possible. However, most of this computational effort would be spent into generating a suitable basis of DFT wavefunctions. Such a task could potentially be considerably accelerated by borrowing tools from the field of machine learning and artificial intelligence. In this paper, we review different approaches to applying supervised and unsupervised learning techniques to nuclear DFT.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

State-of-the-art ab initio potential energy curve for the krypton atom pair and thermophysical properties of dilute krypton gas

A new reference krypton-krypton interatomic potential energy curve was developed by means of quantum-chemical ab initio calculations for 36 interatomic separations. Highly accurate values for the interaction energies at the complete basis set limit were obtained using the coupled-cluster method with single, double, and perturbative triple excitations as well as t-aug-cc-pV5Z and t-aug-cc-pV6Z basis sets including mid-bond functions, with the 6Z basis set being newly constructed for this study. Higher orders of coupled-cluster terms were considered in a successive scheme up to full quadruple excitations. Core-core and core-valence correlation effects were included. Furthermore, relativistic effects were studied not only at a scalar relativistic level using second-order direct perturbation theory, but also utilizing full four-component and Gaunt-effect computations. An analytical pair potential function was fitted to the interaction energies, which is characterized by a depth of 200.88 K with an estimated standard uncertainty of 0.51 K. Thermophysical properties of low-density krypton were calculated for temperatures up to 5000 K. Second and third virial coefficients were obtained from statistical thermodynamics. Viscosity and thermal conductivity as well as the self-diffusion coefficient were computed using the kinetic theory of gases. The theoretical results are compared with experimental data and with results for other pair potential functions from the literature, especially with those calculated from the recently developed ab initio potential of Waldrop et al. [J. Chem. Phys. 142, 204307 (2015)]. Highly accurate experimental viscosity data indicate that both the present ab initio pair potential and the one of Waldrop et al. can be regarded as reference potentials, even though the quantum-chemical methods and basis sets differ. However, the uncertainties of the present potential and of the derived properties are estimated to be considerably lower.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Perfect separation of intraband and interband excitations in PdCoO 2

The temperature dependence of the optical properties of the delafossite PdCoO 2 has been measured in the a-b planes over a wide frequency range. The optical conductivity due to the free-carrier (intraband) response falls well below the interband transitions, allowing the plasma frequency to be determined from the f-sum rule. Drude-Lorentz fits to the complex optical conductivity yield estimates for the free-carrier plasma frequency and scattering rate. Here, the in-plane plasma frequency has also been calculated using density functional theory. The experimentally determined and calculated values for the plasma frequencies are all in good agreement; however, at low temperature the optically determined scattering rate is much larger than the estimate for the transport scattering rate, indicating a strong frequency-dependent renormalization of the optical scattering rate. In addition to the expected in-plane infrared-active modes, two very strong features are observed that are attributed to the coupling of the in-plane carriers to the out-of-plane longitudinal optic modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Estimates for disk and ejecta masses produced in compact binary mergers

There is irresistible observational evidence that binary systems of compact objects with at least one neutron star are progenitors of short gamma-ray bursts, as well as a production site for r -process elements, at least when some matter is ejected by the merger and an accretion disk is formed. Here, the recent observations of gravitational waves in conjunction with electromagnetic counterparts fuel the need for models predicting the outcome of a given merger and the properties of the associated matter outflows as a function of the initial parameters of the binary. In this manuscript, we provide updated fitting formulas that estimate the disk mass for double neutron star binaries and ejecta masses for black hole–neutron star and double neutron star binaries, fitted to the results of numerical simulations. Our proposed fitting formulas improve on existing models by aiming for analytical simplicity, by covering a larger region of parameter space, and by accounting for regions of parameter space not covered by numerical simulations but with physically manifest merger outcomes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Development of cell-based assay for predictively evaluating the FcγR-mediated human immune cell activation by therapeutic monoclonal antibodies

Therapeutic monoclonal antibodies (mAbs) have important roles in treatments for various cancers and inflammatory diseases. Their highly target specificities provide controlled safety profiles. However, therapeutic mAbs commonly pose a risk of the induction of the release of cytokines, which may result in adverse events including infusion reaction and cytokine release syndrome. Several mechanisms are involved in the cytokine releases induced by therapeutic mAbs, and the activation of immune effector cells via Fcγ receptors (FcγRs) is one of the putative mechanisms for most IgG-subclass mAbs. The relationship between cytokine releases and mAbs' Fc functions is not fully understood. Here we developed a simple reporter cell-based assay for estimating the FcγR-mediated activation of human immune effector cells by mAbs. Our use of the cell-based assay to compare Fc-engineered mAbs with different FcγR-activation profiles revealed that the releases of inflammatory cytokines and chemokines from human peripheral blood mononuclear cells (hPBMCs) induced by the mAbs were elevated by treatment with Fc-engineered mAbs with higher FcγR-activation properties. Our results also suggested the involvement of monocytic effector cells in the activation of hPBMCs as sources of released cytokines and chemokines, which may lead to the immune cell-mediated adverse events. Our new reporter cell assay is a promising tool for evaluating and predicting the activation of human immune cells by novel Fc-engineered mAbs. - Highlights: • A simple reporter assay for estimating the FcγR activation by mAbs is developed. • mAbs with higher FcγR-activation properties strongly activate hPBMC. • Monocytic effector cells are involved in the activation of hPBMCs by mAbs. • The reporter assay is useful for predicting the FcγR-mediated responses of hPBMCs.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Redefining fine roots improves understanding of belowground contributions to terrestrial biosphere processes

Fine roots acquire essential soil resources and mediate biogeochemical cycling in terrestrial ecosystems. Estimates of carbon and nutrient allocation to build and maintain these structures remain uncertain due to challenges in consistent measurement and interpretation of fine-root systems. We define fine roots as all roots less than or equal to 2 mm in diameter, yet it is now recognized that this approach fails to capture the diversity of form and function observed among fine-root orders. We demonstrate how order-based and functional classification frameworks improve our understanding of dynamic root processes in ecosystems dominated by perennial plants. In these frameworks, fine roots are separated into either individual root orders or functionally defined into a shorter-lived absorptive pool and a longer-lived transport fine root pool. Furthermore, using these frameworks, we estimate that fine-root production and turnover represent 22% of terrestrial net primary production globally a ca. 30% reduction from previous estimates assuming a single fine-root pool. In the future we hope to develop tools to rapidly differentiate functional fine-root classes, explicit incorporation of mycorrhizal fungi in fine-root studies, and wider adoption of a two-pool approach to model fine roots provide opportunities to better understand belowground processes in the terrestrial biosphere.

58 GEOSCIENCES↗
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Sequence-defined Pareto frontier of a copolymer structure

The correlations between the sequence of monomers in a macromolecule and its three-dimensional (3D) structure is a grand challenge in polymer science. The properties and functions of macromolecules depend on their 3D shape that has appeared to be dictated by their monomer sequence. However, the progress towards understanding the sequence–structure-property correlations and their utilization in materials engineering are slow because it is almost impossible to characterize an astronomically large number of possible sequences of a copolymer using traditional experimental and simulation methods. To address this problem, here, we combine evolutionary computing and coarse-grained molecular dynamics (CGMD) simulation and study the sequence-structure correlations of a model AB-type copolymer in a solution and assess the impact of sequence on the packing density in its bulk phase. The CGMD-based evolutionary algorithm (EA) screens the sequence space of a single chain copolymer efficiently and identifies a wide range of single-molecule structures including extremal radii of gyration. The data are utilized to estimate the Pareto front of the structure-space of a binary copolymer as a function of its composition. The monomer packings in single-molecule solution phase and multimolecular bulk phase are found to be identical. Finally, this work highlights the opportunities of sequence-specific control of macromolecular structure for designing target materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Infiltration Data Package for the E-Area Low-Level Waste Facility Performance Assessment

The infiltration data package contains the input parameters, the cap design and material properties assumptions, and the modeling results for the Hydrologic Evaluation of Landfill Performance (HELP) infiltration model simulations performed in support of the E-Area Low-Level Waste Facility Performance Assessment (PA). The infiltration estimates establish the upper boundary condition for the PORFLOW vadose-zone model and GoldSim model simulations for the following E-Area disposal unit types: Slit and Engineered Trenches, Low-Activity Waste Vault (LAWV), Intermediate-Level Vault (ILV), Componentin- Grout (CIG) special waste form trench segments, and the Naval Reactor Component Disposal Areas (NRCDAs). The infiltration data package builds upon relevant, foundational PA technical reports and memoranda from the past 15 years and is supported by three important components: the HELP model input parameter datasheets, HELP model input and output filenames and directory structure, and infiltration rates as a function of time for each scenario for each disposal unit type. For Slit and Engineered Trenches, a single best-estimate Bahia-grass case of two-percent slope and 585- foot slope length represents an upper bound on intact closure-cap infiltration rates over a 10,000-year period. Building upon the single, bounding, and intact case, two different approaches were considered for incorporating the effect of localized cap subsidence on infiltration rates in the PORFLOW flow and transport model simulations. In the first approach, a Monte Carlo probabilistic model was developed to calculate infiltration rates for 0.54%, 2%, 3.6%, and 4.9% subsidence scenariosa reflecting historical and future non-crushable content for the Slit and Engineered Trenches. The resulting blended (spatially and slope-length averaged) infiltration rates become an inflow upper boundary condition for the PORFLOW vadose zone model simulations. In the second and preferred approach, a Monte Carlo rectangle packing algorithm (Danielson, 2019) and a simplified equation for the total mass flux of water draining into a subsided compartment (Equation 1) will be employed to implement a weighted blending of radionuclide fluxes to the water table using the results of deterministic PORFLOW vadose zone simulations representative of specific subsidence cases. Finally, HELP-model results from sensitivity studies of the intact infiltration case were fit to a log-logistic function to generate infiltration profiles over a 10,000-year period for most-optimistic, more-optimistic, best-estimate, more-pessimistic, and most-pessimistic cases, for both the intact and four subsidence scenarios. For the LAWV and IL vaults, infiltration rate profiles for a 10,000-year period were developed for both an on-vault (above the concrete/metal vault roof) and an off-vault (10-foot soil zone adjacent to vault walls) scenario. The purpose of the off-vault simulations was to confirm that subsurface runoff from the concrete vault roof will adequately drain through the lowermost backfill layers adjacent to the vault walls. The LAWV and ILV infiltration profiles assume collapse of the concrete roof at relative Years 2,905 and 7,100, respectively. The identical Bahia-grass case with two-percent slope and 585-foot slope length assumed for the Slit and Engineered Trenches will represent an upper bound on intact infiltration rates for the NRCDAs and CIG special waste form as well. While the NRCDA casks are assumed to remain structurally intact (i.e., non-assumed to collapse 300 years after the end of operations. Because both rows of the existing CIG trench segments in ST23 (formerly CIG01) extend across the planned cap crest, the subsided CIG trench segments are treated conservatively in the HELP model as a 100%-subsidence case with zero subsurface run-on. The CIG special waste form trench segment infiltration profile, therefore, consists of an intact-cap period from relative Year 100 to Year 300, followed by a 100%-subsidence period from relative Year 300 to Year 10,100.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗