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DOE OSTI2025

Simultaneous prediction of structural properties in epitaxially–grown GaN with quantum and conventional multi–output learning algorithms

Hundreds of GaN thin film crystal plasma–assisted molecular beam epitaxy synthesis experiment records spanning two decades were organized into a dataset correlating the growth experiment design parameters with discrete, binary determinations of crystallinity and surface morphology. Conventional data science techniques as well as both quantum and classical multi–output supervised machine learning algorithms were implemented to investigate the relationships between the operating parameter data and the structural figures of merit. Correlation coefficients, decision tree nodes, p–values, and SHAP values all support substrate temperature and gallium effusion cell conditions as being statistically significant for simultaneously influencing GaN crystallinity and surface morphology. Here, a conventional deep neural network learned best from the data, followed by a quantum–classical hybrid gradient boosting algorithm. When combined with calculations of uncertainty intervals based on VennAbers predictors, machine learning predictions of both structural properties show good agreement with results reported in published experimental literature.

36 MATERIALS SCIENCE↗

DOE OSTI2025

ArborX 2.0

ArborX library tackles a problem of efficiently finding geometric objects that are close in space. Variations of this problem, such as finding the nearest neighbors of a point, or finding all objects within a certain distance, are inherent components of applications in many fields. The data may be large so that solving the problem efficiently may require significant computational resources, such as multiple processors or accelerators such as general purpose GPUs. ArborX' main advantage in its ability to solve large problems efficiently utilizing a combination of distributed and on-node parallelism. ArborX can be run efficiently on a wide variety of hardware, including GPUs from different vendors, which distinguishes it from other available libraries which typically choose only few of these. The other advantage is that it supports both types of user problems: spatial problems (useful for intersections and finding objects within certain distance), and nearest neighbor problems. ArborX also supports flexible interface in its interaction with a user. Particularly, it allows a user to call user's own function on a positive match, a functionality not rarely available in other libraries. ArborX implements construction and traversal algorithms using efficient tree structures, such as bounding volume hierarchy (BVH). At its core, ArborX uses linear BVH for its low construction cost and sufficient quality. ArborX implements both spatial and nearest-neighbor traversal algorithms. ArborX also provides several clustering algorithms (minimum spanning tree, DBSCAN, HDBSCAN*), interpolation using minimum least squares and ray tracing. ArborX is written using C++, and is parallelized using the message passing interface (MPI) for the distributed communication, and the Kokkos library for on-node parallelism. This approach allows ArborX to be run on a wide variety of hardware, from common laptops and desktops to supercomputers while using the same codebase.

Prokopenko, Andrey [Oak Ridge National Laboratory ↗

DOE OSTI2023

Tools for analysis of optimization models

The software is code for analyzing, debugging, and solving optimization models. The code implements several algorithms and provides convenient APIs to apply these algorithms to optimization models. The algorithms are primarily based on graph theory. They compute well-known partitions of graphs, and use these partitions to provide the user information about their optimization model, including diagnosing certain types of structural modeling errors. Some algorithms may be used as a subroutine to solve an optimization problem, and may call an optimization solver to facilitate this. Well-known linear algebra routines are called to provide further diagnostics. The software contains no data and no models other than toy models used for testing.

Parker, Robert↗

DOE OSTI2020

Adaptive Machine Learning for Bragg Coherent Diffraction Imaging (BCDI) of 3D Electron Density Maps with Application to La 2-x Ba x CuO 4 (LBCO) High Temperature Superconductor Studies [PowerPoint]

Understanding mesoscale heterogeneity is important for evaluating fatigue and failure of structural materials and for manufacturing processes. Data-driven tools can facilitate in guiding effort investment (measurements and computations) at various stages of the materials development. Our 3D reconstruction approach is to find a set of coefficients which define a bounding surface of the electron density. Data for training the 3D CNN was generated by sampling coefficients from uniform distributions. Test vs. prediction values are shown for the 28 even-valued coefficients for 1000 test structures, with the best and worst performers highlighted. The adaptive part of this work utilized a model independent extremum seeking (ES). The predictions of the CNN were used as the starting point for the ES algorithm. The convergence of the ES algorithm for 3 different structures is illustrated, and the robustness of the adaptive ML approach was demonstrated on experimentally measured 3D crystal from high energy diffraction microscopy. Reconstruction of a non-uniform density volume with different levels of Poisson noise is also shown. Preliminary attempts at reconstructing measured La 2-x Ba x CuO 4 diffraction patterns have so far failed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Optimizing group structures using hierarchical division

Creating group structures with few groups that give low errors is a difficult problem in reactor analysis. In recent years, automated optimization techniques have been applied to this task. We continue this trend by applying the hierarchical division algorithm to generate optimized group structures that minimize a cost function. At each stage, the algorithm adds a single group boundary to an existing group structure, dividing one group into two to increase the resolution of the group structure. The location of the added boundary is the one that gives the lowest error over all possible new boundary locations. Our implementation requires a beginning group structure, a set of candidate new boundary locations, and a set of reference reaction rates. As a proof of concept, we used WIMS-69 as the initial group structure, XMAS-172 as the ending group structures, and a 344-group reference group structure. Testing on two simple, homogenized reactor problems, we found that hierarchical division was able to reduce the error by a factor of around 5 with an increase of only 15% in the number of groups. Because hierarchical division can get stuck in local minima, it often reaches a plateau in its error reduction capability as many groups are added. Nevertheless, we find hierarchical division has strong potential to make good group structures into great group structures at a modest increase in computational cost. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. Furthermore, the learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low energy structures of Pd n (n = 1-21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pdn clusters of any structure. Low energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters and large cluster isomers share similarities in both shape and energy, and elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Ice Load Project Final Technical Report

As interest and investment in offshore wind projects increase worldwide, some turbines will be installed in locations where ice of significant thickness forms on the water surface. This ice moves under the driving forces of wind, current, and thermal effects and may result in substantial forces on bottom-fixed support structures. The North and Baltic Seas in Europe have begun to see significant wind energy development and the Great Lakes of the United States and Canada may host wind energy development in the near future. Design of the support structures for these projects is best performed through the use of an integrated tool that can calculate the cumulative effects of forces due to turbine operations, wind, waves, and floating ice. The dynamic nature of ice forces requires that these forces be included in the design simulations, rather than added as static forces to simulation results. The International Electrotechnical Commission (IEC) standard[2] for offshore wind turbine design and the International Organization for Standardization (ISO) standard[3] for offshore structures provide requirements and algorithms for the calculation of forces induced by surface ice; however, currently none of the major wind turbine dynamic simulation codes provides the ability to model ice loads. The scope of work of the project described in this report includes the development of a suite of subroutines, collectively named IceFloe, that meet the requirements of the IEC and ISO standards and couples with four of the major wind turbine dynamic simulation codes. The mechanisms by which ice forces impinge on offshore structures generally include the forces required for crushing of the ice against vertical-sided structures and the forces required to fracture the ice as it rides up on conical-sided structures. Within these two broad categories, the dynamic character of the forces with respect to time is also dependent on other factors such as the velocity and thickness of the moving ice and the response of the structure. In some cases, the dynamic effects are random and in other cases they are deterministic, such as the effect of structural resonance and coupling of the ice forces with the defection of the support structure. The initial versions of the IceFloe routines incorporate modules that address these varied force and dynamic phenomena with seven alternative algorithms that can be specified by the user. The IceFloe routines have been linked and tested with four major wind turbine aeroelastic simulation codes: FAST, a tool developed under the management of the National Renewable Energy Laboratory (NREL) and available free of charge from its web site; Bladed[4], a widely-used commercial package available from DNV GL; ADAMS[5], a general purpose multi-body simulation code used in the wind industry and available from MSC Software; and HAWC2[6], a code developed by and available for purchase from Danmarks Tekniske Universitet (DTU). Interface routines have been developed and tested with full wind turbine simulations for each of these codes and the source code and example inputs and outputs are available from the NREL website.

17 WIND ENERGY↗

DOE OSTI2016

An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (≈20pJ/word on-die to ≈10,000 pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use many-core processors on each compute nodes that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignment constraints and avoids gather/scat;ter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of ×2 to ×2.5 speed-up in double precision for particle shape factor of orders 1–3. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles). Program summary Program Title: vec_deposition Program Files doi:http://dx.doi.org/10.17632/nh77fv9k8c.1 Licensing provisions: BSD 3-Clause Programming language: Fortran 90 External routines/libraries: OpenMP > 4.0 Nature of problem: Exascale architectures will have many-core processors per node with long vector data registers capable of performing one single instruction on multiple data during one clock cycle. Data register lengths are expected to double every four years and this pushes for new portable solutions for efficiently vectorizing Particle-In-Cell codes on these future many-core architectures. One of the main hotspot routines of the PIC algorithm is the current/charge deposition for which there is no efficient and portable vector algorithm. Solution method: Here we provide an efficient and portable vector algorithm of current/charge deposition routines that uses a new data structure, which significantly reduces gather/scatter operations. Vectorization is controlled using OpenMP 4.0 compiler directives for vectorization which ensures portability across different architectures. Restrictions: Here we do not provide the full PIC algorithm with an executable but only vector routines for current/charge deposition. These scalar/vector routines can be used as library routines in your 3D Particle-In-Cell code. However, to get the best performances out of vector routines you have to satisfy the two following requirements: (1) Your code should implement particle tiling (as explained in the manuscript) to allow for maximized cache reuse and reduce memory accesses that can hinder vector performances. The routines can be used directly on each particle tile. (2) You should compile your code with a Fortran 90 compiler (e.g Intel, gnu or cray) and provide proper alignment flags and compiler alignment directives (more details in README file).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. Finally, we envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Variational quantum eigensolver with reduced circuit complexity

Abstract The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Quantum-classical hybrid algorithm using an error-mitigating N -representability condition to compute the Mott metal-insulator transition

Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence, connectivity, and gate errors required for their experimental realization. Here we propose a class of quantumclassical hybrid algorithms that computes the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $N$-representability conditions, constraints for representing an $N$-electron wave function, which mitigate noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H 3 into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of “chemical accuracy,” even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Streamline integration as a method for two-dimensional elliptic grid generation

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A Geometric Measure Theory Approach to Identify Complex Structural Features on Soft Matter Surfaces

The structural features that protrude above or below a soft matter interface are well-known to be related to interfacially mediated chemical reactivity and transport processes. It is a challenge to develop a robust algorithm for identifying these organized surface structures, as the morphology can be highly varied and they may exist on top of an interface containing significant interfacial roughness. A new algorithm that employs concepts from geometric measure theory, algebraic topology, and optimization is developed to identify candidate structures at a soft matter surface, and then, using a probabilistic approach, to rank their likelihood of being a complex structural feature. The algorithm is tested for a surfactant laden water/oil interface, where it is robust to identifying protrusions responsible for water transport against a set identified by visual inspection. To our knowledge, this is the first example of applying geometric measure theory to analyze the properties of a chemical/materials science system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Design of emitter structures based on resonant perfect absorption for thermophotovoltaic applications

We report a class of thermophotovoltaic emitter structures built upon planar films that support resonant modes, known as perfectly-absorbing modes, that facilitate an exceptional optical response for selective emission. These planar structures have several key advantages over previously-proposed designs for TPV applications: they are simple to fabricate, are stable across a range of temperatures and conditions, and are capable of achieving some of the highest spectral efficiencies reported of any class of emitter structure. Utilization of these emitters leads to exceptionally high device efficiencies under low operating temperature conditions, which should open new opportunities for waste heat management. We present a theoretical framework for understanding this performance, and show that this framework can be leveraged as a search algorithm for promising candidate structures. In addition to providing an efficient theoretical methodology for identifying high-performance emitter structures, our methodology provides new insight into underlying design principles and should pave way for future design of structures that are simple to fabricate, temperature stable, and possess exceptional optical properties. (C) 2015 Optical Society of America

Foley, Jonathan J.↗

DOE OSTI2021

Thermodynamically consistent algorithms for models of incompressible multiphase polymer solutions with a variable mobility

Here we present a general strategy for developing structure and property preserving numerical algorithms for thermodynamically consistent models of incompressible multiphase polymer solutions with a variable mobility. We first present a formalism to derive thermodynamically consistent, incompressible, multiphase polymer models. Then, we develop the general strategy, known as the supplementary variable method, to devise thermodynamically consistent numerical approximations to the models. We illustrate the numerical strategy using newly developed models of incompressible diblock copolymer solutions coupled with an electric and a magnetic field, respectively. Mesh refinement is conducted to verify convergence rates of the developed schemes. Some numerical examples are given to exhibit underlying dynamics absent from and driven by the external fields, respectively, highlighting differences between models with the variable and constant mobilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Exact and fast calculation of the X-ray pair distribution function

A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

36 MATERIALS SCIENCE↗