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At least 145 records · Page 8

Spin–Orbit Matrix Elements for a Combined Spin-Flip and IP/EA approach

We introduce a practical approach for computing the Breit–Pauli spin–orbit matrix elements of multiconfigurational systems with both spin and spatial degeneracies based on our recently developed RAS-nSF-IP/EA method (Houck, S. E.; et al. J. Chem. Theory Comput. 2019, 15, 2278). The spin–orbit matrix elements over all the multiplet components are computed using a single one-particle reduced density matrix as a result of the Wigner–Eckart theorem. A mean field spin–orbit approximation was used to account for the two-electron contributions. Basis set dependence as well as the effect of including additional excitations is presented. The effect of correlating the core and semicore orbitals is also examined. Surprisingly accurate results are obtained for spin–orbit coupling constants, despite the fact that the efficient wave function approximations we research neglect the bulk of dynamical correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Augmenting machine learning of Grad–Shafranov equilibrium reconstruction with Green's functions

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using principal component analysis of plasma toroidal current densities (J t ) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for the poloidal flux (ψ) and diagnostics generated from the toroidal current (J t ). Similar to the idea of a physics-informed neural network (NN), this physically enforces consistency between ψ, J t , and the synthetic diagnostics. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. The results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J t with median R 2 = 0.9993 and R 2 = 0.978, respectively. A comprehensive NN using a network architecture search is also employed to predict the coefficients of the basis functions. The NN demonstrates significantly better performance compared to the least squares method with median R 2 = 0.9997 and 0.9916 for J t and ψ, respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems

Here, we introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of $20 \sim 50 \times $ in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F 2 demonstrates favorable agreements with standard quantum-chemical calculations Bytautas et al (2007 J. Chem. Phys. 127 164317).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mean Flow from Phase Averages in the 2D Boussinesq Equations

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods.

Wingate, Beth A.↗

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree–Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. Here, the accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, R cut . R cut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small R cut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

LibERI—A portable and performant multi-GPU accelerated library for electron repulsion integrals via OpenMP offloading and standard language parallelism

A portable and performant graphics processing unit (GPU)-accelerated library for electron repulsion integral (ERI) evaluation, named LibERI, has been developed and implemented via directive-based (e.g., OpenMP and OpenACC) and standard language parallelism (e.g., Fortran DO CONCURRENT). Offloaded ERIs consist of integrals over low and high contraction s, p, and d functions using the rotated-axis and Rys quadrature methods. GPU codes are factorized based on previous developments with two layers of integral screening and quartet presorting. In this work, the density screening is moved to the GPU to enhance the computational efficacy for large molecular systems. Here, the L-shells in the Pople basis set are also separated into pure S and P shells to increase the ERI homogeneity and reduce atomic operations and the memory footprint. LibERI is compatible with any quantum chemistry drivers supporting the MolSSI Driver Interface. Benchmark calculations of LibERI interfaced with the GAMESS software package were carried out on various GPU architectures and molecular systems. The results show that the LibERI performance is comparable to other state-of-the-art GPU-accelerated codes (e.g., TeraChem and GMSHPC) and, in some cases, outperforms conventionally developed ERI CUDA kernels (e.g., QUICK) while fully maintaining portability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Abstract for CRADA between National Energy Technology Laboratory and Western Michigan University

NETL will team up with Western Michigan University (WMU) on designing, developing, and testing the integration of enzyme/Deep Eutectic Solvent (DES) treatment with kraft pulping with a focus on optimizing kraft pulp conditions and testing pulp strength, and optical, and barrier properties. NETL will perform pulping experiments by combining Kraft pulping with DES to allow lower temperature, and reduced chemical use thus improved yield. The main purpose of this study is to investigate different heating methods during chlorine dioxide bleaching of kraft pulps. This study also compares the methods with one another with respect to pulp properties and fiber morphologies. In addition, the energy consumption and quality of bleached pulps under different bleaching conditions are going to be analyzed to provide a solid basis for scale up microwave bleaching process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A parallel p ‐adaptive discontinuous Galerkin method for the Euler equations with dynamic load‐balancing on tetrahedral grids

Abstract A novel p ‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p ‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p ‐adaptation.

97 MATHEMATICS AND COMPUTING↗

A Technique for Estimating Liquid Droplet Diameter and Liquid Water Content in Stratocumulus Clouds Using Radar and Lidar Measurements

This paper describes a technique for estimating the liquid water content (LWC) and a characteristic particle diameter in stratocumulus clouds using radar and lidar observations. The uncertainty in LWC estimate from radar and lidar measurements is significantly reduced once the characteristic particle diameter is known. The technique is independent of the drop size distribution. It is applicable for a broad range of W-band reflectivity Z between -30 and 0 dBZ and all values of lidar backscatter β observations. No partitioning of cloud or drizzle is required on the basis of an arbitrary threshold of Z as in prior studies. A method for estimating droplet diameter and LWC was derived from the electromagnetic simulations of radar and lidar observations. In situ stratocumulus cloud and drizzle probe spectra were input to the electromagnetic simulation. The retrieved droplet diameter and LWC were validated using in situ measurements from the southeastern Pacific Ocean. The retrieval method was applied to radar and lidar measurements from the northeastern Pacific. Uncertainty in the retrieved droplet diameter and LWC that are due to the measurement errors in radar and lidar backscatter measurements are 7% and 14%, respectively. The retrieved LWC was validated using the concurrent G-band radiometer estimates of the liquid water path.

54 ENVIRONMENTAL SCIENCES↗

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II↗

Reinforcement Learning Control for Enhancing Marine Hydrokinetic Turbine Energy Generation

This paper proposes a reinforcement learning-based method to maximize power generation for a direct-drive marine hydrokinetic turbine. A high levelized cost of energy (LCOE) is preventative in the widespread adoption of many marine energy conversion technologies. A straightforward way to reduce LCOE is to increase conversion efficiency and ensure maximum energy generation. The proposed method utilizes a damping control methodology, varying applied generator torque via a linear relationship between the applied damping coefficient and rotor speed. A state-action-reward-state-action (SARSA) algorithm has been used to learn the optimal control action for a given flow velocity. The proposed SARSA methodology uses Gaussian radial basis functions to create a three-dimensional surface to estimate the relationship between damping coefficient, incoming flow velocity, and coefficient of power (C p ). Here, the SARSA algorithm was compared against a baseline optimal tip speed ratio controller over a year-long flow velocity case profile while considering the effects of biofouling on the turbine system, where the proposed RL method generated 0.92% more energy than the baseline.

Damp↗

Neuromorphic scaling advantages for energy-efficient random walk computations

Computing stands to be radically improved by neuromorphic computing (NMC) approaches inspired by the brain's incredible efficiency and capabilities. Most NMC research, which aims to replicate the brain's computational structure and architecture in man-made hardware, has focused on artificial intelligence; however, less explored is whether this brain-inspired hardware can provide value beyond cognitive tasks. We demonstrate that high-degree parallelism and configurability of spiking neuromorphic architectures makes them well-suited to implement random walks via discrete time Markov chains. Such random walks are useful in Monte Carlo methods, which represent a fundamental computational tool for solving a wide range of numerical computing tasks. Additionally, we show how the mathematical basis for a probabilistic solution involving a class of stochastic differential equations can leverage those simulations to provide solutions for a range of broadly applicable computational tasks. Despite being in an early development stage, we find that NMC platforms, at a sufficient scale, can drastically reduce the energy demands of high-performance computing platforms.

59 BASIC BIOLOGICAL SCIENCES↗

NSTX-U National Research Program: White Paper in Response to Call from FESAC Sub-Committee

Both scientific and technical innovation is needed for the realization of an attractive engineering solution for a timely and cost-effective Pilot Plant, the design and construction of which is the overarching recommendation of the FESAC Long Range Plan, and the 2021 NASEM Pilot Plant reports, which underpin the Bold Decadal Vision. The two most significant plasma physics gaps to close for a Compact Pilot Plant (CPP) are core confinement improvement and heat flux mitigation, neither of which have been closed in an integrated fashion for any planned fusion power production device. High core confinement and stability are essential for producing majority self-driven plasmas in CPPs with reduced size and auxiliary heating power requirements, with an improvement in confinement being the major driver for cost reduction of a CPP. The National Spherical Tokamak Experiment - Upgrade (NSTX-U) is a unique low aspect ratio research facility that will address the fundamental challenge of developing the science and technology basis for a CPP design that integrates high core and edge confinement with the ability to mitigate very high incident heat fluxes. NSTX-U capabilities will enable the high performance, already achieved on NSTX, to extend into physics regimes much closer to those anticipated in Spherical Tokamak (ST)-based CPPs. These confinement and stability properties will be assessed by a full complement of diagnostics and analysis tools, which will also aid in the development of the underlying theory and predictive models needed for further optimization. Both conventional and transformative heat flux mitigation methods, such as liquid lithium plasma-facing components, will be developed and tested in-situ in NSTX-U at incident heat fluxes of ~100 MW/m 2 , and will inform plans and reduce risk for a subsequent major upgrade to the device to fully heated, high-Z wall and full liquid lithium divertor capability, a technology that potentially could then be implemented on any magnetic confinement device at any aspect ratio. NSTX-U research is fully complementary to programs performed on other STs, nationally and internationally. Furthermore, NSTX-U research has a direct connection to the private sector by informing design choices for future power production facilities being developed by these companies. The NSTX-U program will operate as a national User Facility, with collaborating researchers, engineers, and graduate students from 19 outside institutions, and open to participation and experiments led by researchers from both public and private entities. The research program will advance workforce development through training of young scientists, engineers, and technicians, and it will also serve for further diagnostic innovation, especially for high heat flux and high-Z wall environments, and implementation of advanced artificial intelligence (AI) for plasma and heat flux control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of off-diagonal elements in the Wannier Hamiltonian on DFT + DMFT for low-symmetry materials: Study of Li 2 MnO 3

Here, we study the effect of the off-diagonal elements of the Wannier Hamiltonian on the electronic structure of the low-symmetry material Li 2 MnO 3 ( C2/m ), using dynamical mean field theory calculations with a continuous-time quantum Monte Carlo impurity solver. The presence of significant off-diagonal elements leads to a pronounced suppression of the energy gap. The off-diagonal elements are largest when the Wannier projection is used based on the global coordinate, and they remain substantial even with the projection using the local coordinate close to the direction of Mn-O bonds. We show that the energy gap is enhanced by the diagonalization of the Mn d block in the full p-d Hamiltonian with the application of a unitary rotation matrix. Additionally, the inclusion of small double counting energy is crucial for achieving the experimental gap by reducing p-d hybridization. Furthermore, we establish the efficiency of a low-energy (d-only basis) model for studying the electronic structure of Li 2 MnO 3 , as the Wannier basis represents a hybridized state of Mn d and O p orbitals. These findings suggest an appropriate approach for investigating low-symmetry materials using the density functional theory plus dynamical mean field theory (DFT + DMFT) method. We also find that the antiferromagnetic ground state $\Gamma$ 2u is stable with U ≤ 2 eV within density functional theory+$U$ calculations, which is much smaller than the widely used U = 5 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Calculated Reduction Potentials of Electrolyte Species in Lithium–Sulfur Batteries

In this work, reduction potentials of electrolyte molecules in the lithium–sulfur (Li/S) battery and their variations in several solvent environments are studied using the density functional theory method with Dunning’s triple-ζ correlation consistent basis set. Reliable reduction potential values are key for electrolyte additive design needed for suppressing polysulfide dissolution shuttle mechanism, resulting in poor cycle performance and severe self-discharge of the Li/S battery. Although isolated electrolyte molecules have reduction potentials outside the operating voltage range of the Li/S battery, complexation with other electrolyte species enables the electrolyte molecules to be reduced within the operating voltage range. Among the electrolyte species considered in this study, bis(fluorosulfonyl)imide (FSI – ) and fluoroethylene carbonate (FEC) yield reduction potentials within the expected range, suggesting the development of fluorine-containing additives as a promising line of research.

25 ENERGY STORAGE↗

Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.

97 MATHEMATICS AND COMPUTING↗