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DOE OSTI2020

Wide neural networks with bottlenecks are deep Gaussian processes

There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not apply to architectures that require one or more of the hidden layers to remain narrow. In this paper, we consider the wide limit of BNNs where some hidden layers, called "bottlenecks", are held at finite width. The result is a composition of GPs that we term a "bottleneck neural network Gaussian process" (bottleneck NNGP). Although intuitive, the subtlety of the proof is in showing that the wide limit of a composition of networks is in fact the composition of the limiting GPs. We also analyze theoretically a single-bottleneck NNGP, finding that the bottleneck induces dependence between the outputs of a multi-output network that persists through extreme post-bottleneck depths, and prevents the kernel of the network from losing discriminative power at extreme post-bottleneck depths.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Meshfree Multiphysics Damage Modeling of Li-ion Battery Materials

Through repeated charging and discharging cycles, the electrodes of a Li-ion battery experience significant swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries and material interfaces. Chemo-mechanical damage models are generally simulated by one of two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a coupled chemo-mechanical crack propagation model that enhances accuracy while maintaining high computational efficiency. This model features a fully coupled, iterative electrochemistry solution, which informs the meshfree damage model of impending crack formation. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

damage modeling↗

DOE OSTI2023

Neural Network Enhanced RKPM for Electrochemical-Mechanical Coupled Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant charge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. For Li-ion batteries, for example, lithium moving between electrodes during charging and discharging process causes expansion and contraction of grains, and the strongly anisotropic and nonlinearly [Li]-dependent grain material properties can cause grains to expand into and contract away from each other, leading to chemo-mechanical cracking. In the first part of this work, a RKPM based computational framework for solving the coupled solid-phase lithium conservation with Fickian diffusion and the lithium concentration dependent anisotropic mechanical problem subjected to a highly nonlinear Butler-Volmer boundary condition is introduced. The choice of RKPM completeness conditions for lithium concentration and mechanical deformation fields, and the variational consistency condition for the domain integration of the coupled problem is first determined. In the second part of this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material, by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that is necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure.

damage modeling↗

DOE OSTI2013

Fuel temperature reactivity coefficient calculation by Monte Carlo perturbation techniques

We present an efficient method to estimate the fuel temperature reactivity coefficient (FTC) by the Monte Carlo adjoint-weighted correlated sampling method. In this method, a fuel temperature change is regarded as variations of the microscopic cross sections and the temperature in the free gas model which is adopted to correct the asymptotic double differential scattering kernel. The effectiveness of the new method is examined through the continuous energy MC neutronics calculations for PWR pin cell problems. The isotope-wise and reaction-type-wise contributions to the FTCs are investigated for two free gas models - the constant scattering cross section model and the exact model. It is shown that the proposed method can efficiently predict the reactivity change due to the fuel temperature variation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

CYRANO3 the EDF fuel code performance: Global overview and recent developments on MOX fuel

CYRANO3 is the thermal mechanical industrial code developed and used by EDF to simulate the nuclear fuel rod performance in pile, and during the disposal storage period as well. This code has already been used successfully for the last ten years by the EDF engineering teams in justifying the overall reloading options covering various fuels: UO{sub 2}, UO{sub 2} + gadolinium, MOX, UO{sub 2} plus additives, and various cladding as well proposed by the nuclear fuel suppliers. Its particularity is related to a construction around a standard one-dimensional thermal and mechanical finite elements kernel with an appropriate architecture to plug in any new functionalities or models. Since the beginning it is developed as a module able integrating within a core calculation chain. Other constrain is to always guaranty a running time consistent with the calculation of a core within a reasonable time. The objective is to provide the EDF designers with a convivial and qualified code, with robust algorithms and able to quickly evolve with computer performances. Algorithms are able to account for adiabatic transients and are robust enough to avoid any undesirable overflows. The permanent challenge is indeed to provide with the more descriptive simulations not degrading to much the running time. Developments are obviously performed within the strict Quality Insurance rules. The code is then associated to a large documentation base, including model specification, realization, validation and test procedures. Maintenance is managed through a system of anomaly and improvement forms. Computers are still evolving quickly. Therefore, after an architecture adaptation, the CYRANO3 code is now integrated in the PLEIADES platform as a PWR industrial application. The platform is an exchange space allowing sharing functionalities, models and properties. In this paper, we will give a global overview of the capabilities of CYRANO3 code to simulate the thermomechanical behavior of fuel rods, and we will focus on recent developments realized on MOX fuel. In CYRANO3 code, heterogeneous models (neutronic model, micromechanical behavior law and fission gas model) are developed for MOX fuels and integrated in order to account for differential evolutions between phases under irradiation. The methodology and these models are presented in this paper. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

Characterization of spent filters from the water polishing system of IEA-R1 Reactor - 15451

The aim of this paper is to report studies performed to determine the activity of gamma emitters present in polypropylene cartridge filters from the polishing system of the IEA-R1 Reactor cooling-water primary circuit. The activities were calculated using the dose rates measured with hand-held detectors, after the ratios of the emission rates of photons were evaluated by gamma spectrometry, and the Point Kernel method, which correlates the activity of a source with the dose rates at various distances. The method described can be used to determine routinely the radioactive inventory of these filters, avoiding the necessity of destructive radiochemical analysis, or the necessity of calibrating the geometry of measurement. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2016

An Investigation of MCNP6.1 Beryllium Oxide S(α,β) Cross Sections

In MCNP6.1, materials are constructed by identifying the constituent isotopes (or elements in a few cases) individually. This list selects the corresponding microscopic cross sections calculated from the free-gas model to create the material macroscopic cross sections. The free-gas model and the corresponding material macroscopic cross sections assume that the interactions of atoms do not affect the nuclear cross sections. With certain compounds, the free-gas model cross sections are not sufficient because molecular effects or crystalline structure effects do affect the neutron scattering cross sections at low energies. These effects are included in the MCNP6.1 thermal scattering kernels, or S(α,β) thermal neutron scattering data. To treat a particular isotope (or isotopes) as a molecular compound in the thermal regime, one or more of the available S(α,β) data sets is selected (with the MT card). As MCNP6.1 transports particles, the free-gas model cross sections are used down to the energy where S(α,β) data are available. At that point, the S(α,β) cross sections automatically overrides the free-gas cross sections. Most of the S(α,β) files have a maximum energy of 10 eV. In MCNP6.1, a binary compound may have one or two S(α,β) libraries. Beryllium oxide (BeO) is one of the materials that has two S(α,β) libraries one for the beryllium S(α,β) cross sections (be-o) and one for the oxygen S(α,β) cross sections (o-be). From its moderating properties, it is apparent that the S(α,β) library for the beryllium must be included to accurately model beryllium oxide. The necessity of the S(α,β) library for oxygen is less clear because oxygen is a relatively poor moderator. This paper investigates the effect of using only the be-o S(α,β) library or using both be-o and o-be S(α,β) libraries. The objective is to provide guidance on the use of the beryllium oxide S(α,β) libraries in criticality safety analyses. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Western North Pacific Tropical Cyclone Model Tracks in Present and Future Climates

Western North Pacific tropical cyclone (TC) model tracks are analyzed in two large multimodel ensembles, spanning a large variety of models and multiple future climate scenarios. Two methodologies are used to synthesize the properties of TC tracks in this large data set: cluster analysis and mass moment ellipses. First, the models' TC tracks are compared to observed TC tracks' characteristics, and a subset of the models is chosen for analysis, based on the tracks' similarity to observations and sample size. Potential changes in track types in a warming climate are identified by comparing the kernel smoothed probability distributions of various track variables in historical and future scenarios using a Kolmogorov-Smirnov significance test. Two track changes are identified. The first is a statistically significant increase in the north-south expansion, which can also be viewed as a poleward shift, as TC tracks are prevented from expanding equatorward due to the weak Coriolis force near the equator. The second change is an eastward shift in the storm tracks that occur near the central Pacific in one of the multimodel ensembles, indicating a possible increase in the occurrence of storms near Hawaii in a warming climate. The dependence of the results on which model and future scenario are considered emphasizes the necessity of including multiple models and scenarios when considering future changes in TC characteristics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Physics Discovery in Nanoplasmonic Systems via Autonomous Experiments in Scanning Transmission Electron Microscopy

Abstract Physics‐driven discovery in an autonomous experiment has emerged as a dream application of machine learning in physical sciences. Here, this work develops and experimentally implements a deep kernel learning (DKL) workflow combining the correlative prediction of the target functional response and its uncertainty from the structure, and physics‐based selection of acquisition function, which autonomously guides the navigation of the image space. Compared to classical Bayesian optimization (BO) methods, this approach allows to capture the complex spatial features present in the images of realistic materials, and dynamically learn structure–property relationships. In combination with the flexible scalarizer function that allows to ascribe the degree of physical interest to predicted spectra, this enables physical discovery in automated experiment. Here, this approach is illustrated for nanoplasmonic studies of nanoparticles and experimentally implemented in a truly autonomous fashion for bulk‐ and edge plasmon discovery in MnPS 3 , a lesser‐known beam‐sensitive layered 2D material. This approach is universal, can be directly used as‐is with any specimen, and is expected to be applicable to any probe‐based microscopic techniques including other STEM modalities, scanning probe microscopies, chemical, and optical imaging.

42 ENGINEERING↗

DOE OSTI2018

Realization of an Al≡Al Triple Bond in the Gas-Phase Na 3 Al 2 - Cluster via Double Electronic Transmutation

We report the discovery of homodinuclear multiple bonds composed of Group 13 elements represents one of the most challenging frontiers in modern chemistry. A classical triple bond such as N≡N and HC≡CH contains one σ bond and two π bonds constructed from the p orbitals perpendicular to the σ bond. However, the traditional textbook triple bond between two Al atoms has remained elusive. Here we report an Al≡Al triple bond in the designer Na 3 Al 2 - cluster predicted in silico, which was subsequently generated by pulsed arc discharge followed by mass spectrometry and photoelectron spectroscopy characterizations. Being effectively Al 2- due to the electron donation from Na, the Al atoms in Na 3 Al 2 - undergo a double electronic transmutation into Group 15 elements, thus the Al 2- ≡Al 2- kernel mimics the P≡P and N≡N molecules. Lastly, we anticipate this work will stimulate more endeavors in discovering materials using Al 2- ≡Al 2- as a building block in the gas phase and in the solid state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Boron-Made N 2 : Realization of a B$\equiv$B Triple Bond in the B 2 Al 3 – Cluster

Until now, all B≡B triple bonds have been achieved by adopting two ligands in the L→B≡B←L manner. Herein, we report an alternative route of designing the B≡B bonds based on the assumption that by acquiring two extra electrons, an element with the atomic number Z can have properties similar to those of the element with the atomic number Z + 2. Specifically, we show that due to the electron donation from Al to B, the negatively charged B≡B kernel in the B 2 Al 3 – cluster mimics a triple N≡N bond. Comprehensive computational searches reveal that the global minimum structure of B 2 Al 3 – exhibits a direct B–B distance of 1.553 Å, and its calculated electron vertical detachment energies are in excellent agreement with the corresponding values of the experimental photoelectron spectrum. Chemical bonding analysis revealed one σ and two π bonds between the two B atoms, thus confirming a classical textbook B≡B triple bond, similar to that of N 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Performance analysis of distributed symmetric sparse matrix vector multiplication algorithm for multi-core architectures

In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important features of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Investigating power capping toward energy-efficient scientific applications: Investigating Power Capping toward Energy-Efficient Scientific Applications

The emergence of power efficiency as a primary constraint in processor and system design poses new challenges concerning power and energy awareness for numerical libraries and scientific applications. Power consumption also plays a major role in the design of data centers, which may house petascale or exascale-level computing systems. At these extreme scales, understanding and improving the energy efficiency of numerical libraries and their related applications becomes a crucial part of the successful implementation and operation of the computing system. In this paper, we study and investigate the practice of controlling a compute system's power usage, and we explore how different power caps affect the performance of numerical algorithms with different computational intensities. Further, we determine the impact, in terms of performance and energy usage, that these caps have on a system running scientific applications. This analysis will enable us to characterize the types of algorithms that benefit most from these power management schemes. Our experiments are performed using a set of representative kernels and several popular scientific benchmarks. Lastly, we quantify a number of power and performance measurements and draw observations and conclusions that can be viewed as a roadmap to achieving energy efficiency in the design and execution of scientific algorithms.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Providing performance portable numerics for Intel GPUs

Summary With discrete Intel GPUs entering the high‐performance computing landscape, there is an urgent need for production‐ready software stacks for these platforms. In this article, we report how we enable the Ginkgo math library to execute on Intel GPUs by developing a kernel backed based on the DPC++ programming environment. We discuss conceptual differences between the CUDA and DPC++ programming models and describe workflows for simplified code conversion. We evaluate the performance of basic and advanced sparse linear algebra routines available in Ginkgo's DPC++ backend in the hardware‐specific performance bounds and compare against routines providing the same functionality that ship with Intel's oneMKL vendor library.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

HIPLZ: Enabling performance portability for exascale systems

While heterogeneous computing has emerged as a dominant trend in current and future High-Performance Computing (HPC) systems, it is also widely recognized that this shift has led to increased software complexity due to a proliferation of programming systems for different heterogeneous processors. One such example is the Heterogeneous-Compute Interface for Portability from AMD (HIP ), which is composed of a C Runtime API and C++ Kernel Language. Many HPC applications will likely use HIP on future exascale systems (e.g., Frontier and El Capitan), but HIP currently only targets AMD and NVIDIA processors. This limitation creates challenges for users who would also like to run their applications on exascale systems based on other architectures (e.g., Aurora, which is based on Intel hardware) that are currently not targeted by HIP . In this paper, we introduce the design and implementation of HIPLZ , a compiler and runtime system that uses the Intel Level Zero API to support HIP on Intel GPU architectures. We discuss the design of HIPLZ , derived from HIPCL (an implementation of HIP on top of OpenCL ), and portability issues that occur from using the Level Zero runtime as a backend. We evaluate our implementation by running several performance benchmarks and mini-apps written in HIP on Intel architectures using HIPLZ . Our results show that this approach provides competitive performance relative to Intel's OpenCL implementations on Intel Gen9 and UHD Graphics 770 GPUs, while providing good coverage of features needed by HPC applications. Overall, this approach is a promising demonstration of enabling performance portability for exascale systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗

DOE OSTI2016

Reduced-order modeling for nonlocal diffusion problems

In several settings, diffusive behavior is observed to not follow the rate of spread predicted by parabolic partial differential equations (PDEs) such as the heat equation. Such behaviors, often referred to as anomalous diffusion, can be modeled using nonlocal equations for which points at a finite distance apart can interact. An example of such models is provided by fractional derivative equations. Because of the nonlocal interactions, discretized nonlocal systems have less sparsity, often significantly less, compared with corresponding discretized PDE systems. As such, the need for reduced-order surrogates that can be used to cheaply determine approximate solutions is much more acute for nonlocal models compared with that for PDEs. In this paper, we consider the construction, application, and testing of proper orthogonal decomposition (POD) reduced models for an integral equation model for nonlocal diffusion. For certain modeling parameters, the model we consider allows for discontinuous solutions and includes fractional Laplacian kernels as a special case. Preliminary computational results illustrate the potential of using POD to obtain accurate approximations of solutions of nonlocal diffusion equations at much lower costs compared with, for example, standard finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Double-buffered, heterogeneous CPU + GPU integral digestion algorithm for single-excitation calculations involving a large number of excited states

The most widely used quantum-chemical models for excited states are single-excitation theories, a category that includes configuration interaction with single substitutions, time-dependent density functional theory, and also a recently developed ab initio exciton model. When a large number of excited states are desired, these calculations incur a significant bottleneck in the “digestion” step in which two-electron integrals are contracted with density or density-like matrices. We present an implementation that moves this step onto graphical processing units (GPUs), and introduce a double-buffer scheme that minimizes latency by computing integrals on the central processing units (CPUs) concurrently with their digestion on the GPUs. An automatic code generation scheme simplifies the implementation of high-performance GPU kernels. For the exciton model, which requires separate excited-state calculations on each electronically coupled chromophore, the heterogeneous implementation described here results in speedups of 2–6× versus a CPU-only implementation. For traditional time-dependent density functional theory calculations, we obtain speedups of up to 5× when a large number of excited states is computed.

97 MATHEMATICS AND COMPUTING↗