Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “APPROXIMATIONS”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

Gaussian approximation potential for amorphous Si : H

Hydrogenation of amorphous silicon (a–Si : H) is critical for reducing defect densities, passivating midgap states and surfaces, and improving photoconductivity in silicon-based electro-optical devices. Modeling the atomic-scale structure of this material is critical to understanding these processes, which in turn is needed to describe c–Si/a–Si : H heterojunctions that are at the heart of modern solar cells with world-record efficiency. Density functional theory (DFT) studies achieve the required high accuracy but are limited to moderate system sizes of 100 atoms or so by their high computational cost. Simulations of amorphous materials have been hindered by this high cost because large structural models are required to capture the medium-range order that is characteristic of such materials. Empirical potential models are much faster, but their accuracy is not sufficient to correctly describe the frustrated local structure. Data-driven, machine-learned interatomic potentials have broken this impasse and have been highly successful in describing a variety of amorphous materials in their elemental phase. Here, we extend the Gaussian approximation potential (GAP) for silicon by incorporating the interaction with hydrogen, thereby significantly improving the degree of realism with which amorphous silicon can be modeled. We show that our Si : H GAP enables the simulation of hydrogenated silicon with an accuracy very close to DFT but with computational expense and run times reduced by several orders of magnitude for large structures. Here, we demonstrate the capabilities of the Si : H GAP by creating models of hydrogenated liquid and amorphous silicon and showing that their energies, forces, and stresses are in excellent agreement with DFT results, and their structure as captured by bond and angle distributions are in agreement with both DFT and experiments.

36 MATERIALS SCIENCE↗

Laplacian-level meta-generalized gradient approximation for solid and liquid metals

In this work, we derive and motivate a Laplacian-level, orbital-free meta-generalized-gradient approximation (LL-MGGA) for the exchange-correlation energy, targeting accurate ground-state properties of sp and sd metallic condensed matter, in which the density functional for the exchange-correlation energy is only weakly nonlocal due to perfect long-range screening. Our model for the orbital-free kinetic energy density restores the fourth-order gradient expansion for exchange to the r 2 SCAN meta-GGA [Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)], yielding a LL-MGGA we call OFR2. OFR2 matches the accuracy of SCAN for prediction of common lattice constants and improves the equilibrium properties of alkali metals, transition metals, and intermetallics that were degraded relative to the PBE GGA values by both SCAN and r 2 SCAN. We compare OFR2 to the r 2 SCAN -L LL-MGGA [Mejia-Rodriguez and Trickey, Phys. Rev. B 102, 121109(R) (2020)] and show that OFR2 tends to outperform r 2 SCAN -L for the equilibrium properties of solids, but r 2 SCAN -L much better describes the atomization energies of molecules than OFR2 does. For best accuracy in molecules and nonmetallic condensed matter, we continue to recommend SCAN and r 2 SCAN. Numerical performance is discussed in detail, and our paper provides an outlook to machine learning.

36 MATERIALS SCIENCE↗

Active learning approach to simulations of strongly correlated matter with the ghost Gutzwiller approximation

Quantum embedding (QE) methods such as the ghost Gutzwiller approximation (gGA) offer a powerful approach to simulating strongly correlated systems, but come with the computational bottleneck of computing the ground state of an auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an active learning (AL) framework integrated within the gGA to address this challenge. The methodology is applied to the single-band Hubbard model and results in a significant reduction in the number of instances where the EH must be solved. Through a principal component analysis (PCA), we find that the EH parameters form a low-dimensional structure that is largely independent of the geometric specifics of the systems, especially in the strongly correlated regime. Our AL strategy enables us to discover this low-dimensionality structure on the fly, while leveraging it for reducing the computational cost of gGA, laying the groundwork for more efficient simulations of complex strongly correlated materials. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Linear Approximation Line Pack Model for Integrated Electricity and Natural Gas Systems OPF

With the increasing installation of renewable energy electricity generation capacity, the penetration of natural gas fired generation is also substantailly increasing in power systems due to their fast response capability to mitigate system variability and uncertainty. The dependencies between the electricity system and the natural gas system are becoming more important to maintain the reliability of both systems. In integrated electricity and natural gas systems (IEGSs) operations, the nonlinearity of the natural gas system brings challenges to the system operators. In this paper, the IEGSs optimal power flow (OPF) model is proposed that includes the line pack of the gas system via linear approximation. The simulation results demonstrate that the proposed model can obtain optimal solutions efficiently that are comparable in accuracy as the nonlinear line pack model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Approximation of the Frequency-Amplitude Curve Using the Homotopy Analysis Method

The Frequency-Amplitude (F-A) curve on power system oscillation under a large disturbance characterizes how a natural oscillation mode transitions to nonlinear oscillations with growing amplitudes and decaying frequencies. The existing formulation of the F-A curve is derived by solving elliptical integrals on oscillation of a single-machine-infinite-bus equivalent about the targeted oscillation mode. The formula is in a form of infinite series and needs to sum a large number of terms for satisfactory accuracy. This paper introduces an explicit, approximate expression obtained from the Homotopy Analysis Method on the F-A curve. The proposed F-A curve expression is derived from an SMIB system and verified on the IEEE 3-machine 9-bus system to show how the oscillation frequency of a dominant mode varies with oscillation amplitude under large disturbances.

frequency-amplitude (F-A) curve↗

Simulations of Quantum Approximate Optimization Algorithm on HPC-QC Integrated Systems

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗

Quantum Approximate Optimization Algorithm on Different Qubit Systems

Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗

Graph Sparsification by Approximate matrix Multiplication

Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of sparsifying a weighted graph, while sharing the same vertices as the original graph but reducing the number of edges, is through spectral sparsification. We study this problem through the perspective of RandNLA. Specifically, we utilize randomized matrix multiplication to give a clean and simple analysis of how sampling according to edge weights gives a spectral approximation to graph Laplacians, without requiring spectral information. Through the CR–MM algorithm, we attain a simple and computationally efficient sparsifier whose resulting Laplacian estimate is unbiased and of minimum variance. Here, we define a new notion of additive spectral sparsifiers, which has not been considered in the literature.

97 MATHEMATICS AND COMPUTING↗

PredCom: A Predictive Approach to Collecting Approximated Communication Traces

Communication traces collected from MPI applications are an important source of information for performance optimization as they can help analysts determine communication patterns and identify inefficiencies. However, their collection, especially at scale, is time consuming, since it usually requires running the complete target application on a large number of nodes. In this work, we present PredCom, a tool-chain to generate a predictive communication proxy based on information gathered from a few small scale runs, which allows us to extract approximate communication traces with an accuracy high enough for most analysis goals. For this, we combine LLVM passes on the original source code (to capture static program structure) with parameter prediction (to capture dynamic and scaling behavior). This approach drastically reduces the time needed for collecting the communication traces, even for traces on large numbers of MPI processes. Here, we demonstrate that PredCom generates communication traces of various applications up to 1612x faster with an accuracy loss of 0.11 on average compared to the original large-scale traces, and we show that the generated traces can be used to optimize process placement.

97 MATHEMATICS AND COMPUTING↗

Approximating Trajectory Constraints With Machine Learning – Microgrid Islanding With Frequency Constraints

Here, we introduce deep earning aided constraint encoding to tackle the frequency-constraint microgrid scheduling problem. The nonlinear function between system operating condition and frequency nadir is approximated by using a neural network, which admits an exact mixed-integer formulation (MIP). This formulation is then integrated with the scheduling problem to encode the frequency constraint. With the stronger representation power of the neural network, the resulting commands can ensure adequate frequency response in a realistic setting in addition to islanding success. The proposed method is validated on a modified 33-node system. Successful islanding with a secure response is simulated under the scheduled commands using a detailed three-phase model in Simulink. The advantages of our model are particularly remarkable when the inertia emulation functions from wind turbine generators are considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Posterior Covariance Matrix Approximations

Here, the Davis equation of state (EOS) is commonly used to model thermodynamic relationships for high explosive (HE) reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive Variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.

97 MATHEMATICS AND COMPUTING↗

A fivefold UO$_2^{2+}$ node is a path to dodecagonal quasicrystal approximants in coordination polymers [plus supplemental information]

Aperiodic formations continue to focus interest in areas ranging from advanced scientific theories to practical everyday applications. Starting from diverse and tightly bonded intermetallic compounds, this world showed an important breakthrough toward the so-called soft systems of meso/macroscale: liquid crystals, thin films, polymers, proteins, etc. This work opens a route for making bulk quasicrystals (QC) in an unprecedented but very common area, with molecular ligands. Since these systems are, to a large extent, transparent, they extend the possible areas of QC application to previously unreachable corners, e.g., photonics. We combined efficient bridging ligands with uranyl pentagonal bonding centers and, unexpectedly, brought the unique attributes of f-element coordination chemistry to an interdisciplinary area of aperiodic formations. Taking advantage of the planar coordination of uranyl ions, we were able to direct the structure expansion solely in two directions with a characteristic snub square tiling, a predicted but previously unobtainable dodecagonal approximant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

97 MATHEMATICS AND COMPUTING↗

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗

Punzi-loss: a non-differentiable metric approximation for sensitivity optimisation in the search for new particles

We present the novel implementation of a non-differentiable metric approximation and a corresponding loss-scheduling aimed at the search for new particles of unknown mass in high energy physics experiments. We call the loss-scheduling, based on the minimisation of a figure-of-merit related function typical of particle physics, a Punzi-loss function, and the neural network that utilises this loss function a Punzi-net. We show that the Punzi-net outperforms standard multivariate analysis techniques and generalises well to mass hypotheses for which it was not trained. This is achieved by training a single classifier that provides a coherent and optimal classification of all signal hypotheses over the whole search space. Our result constitutes a complementary approach to fully differentiable analyses in particle physics. We implemented this work using PyTorch and provide users full access to a public repository containing all the codes and a training example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Auger spectroscopy beyond the ultra-short core-hole relaxation time approximation

Abstract We present a time-dependent computational approach to study Auger electron spectroscopy (AES) beyond the ultra-short core-hole relaxation time approximation and, as a test case, we apply it to the paradigmatic example of a one-dimensional Mott insulator represented by a half-filled Hubbard chain. The Auger spectrum is usually calculated by assuming that, after the creation of a core-hole, the system thermalizes almost instantaneously. This leads to a relatively simple analytical expression that uses the ground-state with a core-hole as a reference state and ignores all the transient dynamics related to the screening of the core-hole. In this picture, the response of the system can be associated to the pair spectral function. On the other hand, in our numerical calculations, the core hole is created by a light pulse, allowing one to study the transient dynamics of the system in terms of the pulse duration and in the non-perturbative regime. Time-dependent density matrix renormalization group calculations reveal that the relaxation process involves the creation of a polarization cloud of doublon excitations that have an effect similar to photo-doping. As a consequence, there is a leak of spectral weight to higher energies into what otherwise would be the Mott gap. For longer pulses, these excited states, mostly comprised of doublons, can dominate the spectrum. By changing the duration of the light-pulse, the entire screening process can be resolved in time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗