Publications

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Hydrogen lithography has been used to template phosphine-based surface chemistry to fabricate atomic-scale devices, a process we abbreviate as atomic precision advanced manufacturing (APAM). Here, we use mid-infrared variable angle spectroscopic ellipsometry (IR-VASE) to characterize single-nanometer thickness phosphorus dopant layers (δ-layers) in silicon made using APAM compatible processes. A large Drude response is directly attributable to the δ-layer and can be used for nondestructive monitoring of the condition of the APAM layer when integrating additional processing steps. The carrier density and mobility extracted from our room temperature IR-VASE measurements are consistent with cryogenic magneto-transport measurements, showing that APAM δ-layers function at room temperature. Finally, the permittivity extracted from these measurements shows that the doping in the APAM δ-layers is so large that their low-frequency in-plane response is reminiscent of a silicide. However, there is no indication of a plasma resonance, likely due to reduced dimensionality and/or low scattering lifetime.

Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including graph mining, recommender systems and natural language processing. Due to the compute-intensive nature of applications that must perform repeated NMF, several parallel implementations have been developed. However, existing parallel NMF algorithms have not addressed data locality optimizations, which are critical for high performance since data movement costs greatly exceed the cost of arithmetic/logic operations on current computer systems. In this paper, we present a novel optimization method for parallel NMF algorithm based on the HALS (Hierarchical Alternating Least Squares) scheme that incorporates algorithmic transformations to enhance data locality. Efficient realizations of the algorithm on multi-core CPUs and GPUs are developed, demonstrating a new Accelerated Locality-Optimized NMF (ALO-NMF) that obtains up to 2.29x lower data movement cost and up to 4.45x speedup over existing state-of-the-art parallel NMF algorithms.

We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the posterior variance of the MFGP, our framework naturally enables uncertainty quantification, providing estimates of confidence in the predictions. We used density functional theory as high-fidelity prediction, while a ML interatomic potential is used as low-fidelity prediction. Practical materials’ design efficiency is demonstrated by reproducing the ternary composition dependence of a quantity of interest (bulk modulus) across the full aluminum–niobium–titanium ternary random alloy composition space. The MFGP is then coupled to a Bayesian optimization procedure, and the computational efficiency of this approach is demonstrated by performing an on-the-fly search for the global optimum of bulk modulus in the ternary composition space. The framework presented in this manuscript is the first application of MFGP to atomistic materials simulations fusing predictions between density functional theory and classical interatomic potential calculations.

Sparse triangular solver is an important kernel in many computational applications. However, a fast, parallel, sparse triangular solver on a manycore architecture such as GPU has been an open issue in the field for several years. In this paper, we develop a sparse triangular solver that takes advantage of the supernodal structures of the triangular matrices that come from the direct factorization of a sparse matrix. We implemented our solver using Kokkos and Kokkos Kernels such that our solver is portable to different manycore architectures. This has the additional benefit of allowing our triangular solver to use the team-level kernels and take advantage of the hierarchical parallelism available on the GPU. We compare the effects of different scheduling schemes on the performance and also investigate an algorithmic variant called the partitioned inverse. Our performance results on an NVIDIA V100 or P100 GPU demonstrate that our implementation can be 12.4 × or 19.5 × faster than the vendor optimized implementation in NVIDIA's CuSPARSE library.

Efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line search can, therefore, not be performed, the use of limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) and conjugate gradient algorithms in conjunction with orthogonal spin optimization (OSO) approach is shown to greatly outperform the previously used velocity projection and dissipative Landau-Lifschitz dynamics optimization methods. The implementation makes use of energy weighted springs for the distribution of the discretization points along the path and this is found to improve performance significantly. The various methods are applied to several test problems using a Heisenberg-type Hamiltonian, extended in some cases to include Dzyaloshinskii-Moriya and exchange interactions beyond nearest neighbours. Minimum energy paths are found for magnetization reversals in a nano-island, collapse of skyrmions in two-dimensional layers and annihilation of a chiral bobber near the surface of a three-dimensional magnet. The LBFGS-OSO method is found to outperform the dynamics based approaches by up to a factor of 8 in some cases.

Hyperdynamics (HD) is a method for accelerating the timescale of standard molecular dynamics (MD). It can be used for simulations of systems with an energy potential landscape that is a collection of basins, separated by barriers, where transitions between basins are infrequent. HD enables the system to escape from a basin more quickly while enabling a statistically accurate renormalization of the simulation time, thus effectively boosting the timescale of the simulation. In the work of Kim et al. [J. Chem. Phys. 139, 144110 (2013)], a local version of HD was formulated, which exploits the intrinsic locality characteristic typical of most systems to mitigate the poor scaling properties of standard HD as the system size is increased. Here, we discuss how both HD and local HD can be formulated to run efficiently in parallel. We have implemented these ideas in the LAMMPS MD code, which means HD can be used with any interatomic potential LAMMPS supports. Together, these parallel methods allow simulations of any size to achieve the time acceleration offered by HD (which can be orders of magnitude), at a cost of 2-4× that of standard MD. As examples, we performed two simulations of a million-atom system to model the diffusion and clustering of Pt adatoms on a large patch of the Pt(100) surface for 80 μs and 160 μs.

The Corrected Rigid Spheres (CRIS) equation of state (EOS) model [Kerley, J. Chem. Phys. 73, 469 (1980); 73, 478 (1980); 73, 487 (1980)], developed from fluid perturbation theory using a hard sphere reference system, has been successfully used to calculate the EOS of many materials, including gases and metals. The radial distribution function (RDF) plays a pivotal role in choosing the sphere diameter, through a variational principle, as well as the thermodynamic response. Despite its success, the CRIS model has some shortcomings in that it predicts too large a temperature for liquid-vapor critical points, can break down at large compression, and is computationally expensive. We first demonstrate that an improved analytic representation of the hard sphere RDF does not alleviate these issues. Relaxing the strict adherence of the RDF to hard spheres allows an accurate fit to the isotherms and vapor dome of the Lennard-Jones fluid using an arbitrary reference system. The second order correction is eliminated, limiting the breakdown at large compression and significantly reducing the computation cost. The transferability of the new model to real systems is demonstrated on argon, with an improved vapor dome compared to the original CRIS model.

This paper presents model formulations for generators that have the ability to use multiple fuels and to switch between them if necessary. These models are used to generate different scenarios of fuel switching penetration from a test power system. With these scenarios, for a severe disruption in the fuel supply to multiple generators, the paper analyzes the effect that fuel switching has on the resilience of the power system. Load not served is used as the proxy metric to evaluate power system resilience. The paper shows that the presence of generators with fuel switching capabilities considerably reduces the amount and duration of the load shed by the system facing the fuel disruption.

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This paper continues our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. We consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. We conclude with numerical studies illustrating the optimization-based formulations and comparing them with AFC.

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