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Results for “algorithmic differentiation”

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.

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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Measurement of the inclusive jet cross-section in proton-proton collisions at $ \sqrt{s}=7 $ TeV using 4.5 fb -1 of data with the ATLAS detector

The inclusive jet cross-section is measured in proton-proton collisions at a centre-of-mass energy of 7 TeV using a data set corresponding to an integrated luminosity of 4.5 fb -1 collected with the ATLAS detector at the Large Hadron Collider in 2011. Jets are identified using the anti-k t algorithm with radius parameter values of 0.4 and 0.6. The double-differential cross-sections are presented as a function of the jet transverse momentum and the jet rapidity, covering jet transverse momenta from 100 GeV to 2 TeV. Next-to-leading-order QCD calculations corrected for non-perturbative effects and electroweak effects, as well as Monte Carlo simulations with next-to-leading-order matrix elements interfaced to parton showering, are compared to the measured cross-sections. A quantitative comparison of the measured cross-sections to the QCD calculations using several sets of parton distribution functions is performed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Measurement of inclusive charged-particle jet production in pp and p-Pb collisions at $ \sqrt{s_{\textrm{NN}}} $ = 5.02 TeV

Measurements of inclusive charged-particle jet production in pp and p-Pb collisions at center-of-mass energy per nucleon-nucleon collision $\sqrt{^sNN}$ = 5.02 TeV and the corresponding nuclear modification factor $R^{ch jet}_{pPb}$ are presented, using data collected with the ALICE detector at the LHC. Jets are reconstructed in the central rapidity region |η jet | < 0.5 from charged particles using the anti-k T algorithm with resolution parameters R = 0.2, 0.3, and 0.4. The p T -differential inclusive production cross section of charged-particle jets, as well as the corresponding cross section ratios, are reported for pp and p-Pb collisions in the transverse momentum range 10 < $p^{ch}_{T,jet}$ < 140 GeV/c and 10 < $p^{ch}_{T,jet}$ < 160 GeV/c, respectively, together with the nuclear modification factor $R^{ch jet}_{pPb}$ in the range 10 < $p^{ch}_{T,jet}$ < 140 GeV/c. The analysis extends the p T range of the previously-reported charged-particle jet measurements by the ALICE Collaboration. The nuclear modification factor is found to be consistent with one and independent of the jet resolution parameter with the improved precision of this study, indicating that the possible influence of cold nuclear matter effects on the production cross section of charged-particle jets in p-Pb collisions at $\sqrt{^sNN}$ = 5.02 TeV is smaller than the current precision. The obtained results are in agreement with other minimum bias jet measurements available for RHIC and LHC energies, and are well reproduced by the NLO perturbative QCD Powheg calculations with parton shower provided by PYTHIA8 as well as by JETSCAPE simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Determining the memory kernel from a fixed point measurement data for a parabolic equation with memory effect

We consider an inverse problem for a parabolic equation with memory effect. This inverse problem aims to identify the memory kernel function from a fixed point measurement data. Based on the fixed point arguments, we derive the global in time existence and uniqueness of our inverse problem. Moreover, we present a numerical algorithm to reconstruct the memory kernel function. Numerical simulations show the effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A two-grid penalty method for American options

In this paper we consider the pricing of American options, governed by a partial differential complementarity problem. The differential problem is first approximated by a semi-linear PDE using two distinct penalty approaches which are well known in computational finance. We then initiate the two-grid algorithm by solving the nonlinear problem on a coarse grid and further the linearized in the interpolated coarse-grid solution problem on a fine grid. By means of the maximum principle the algorithm is shown to be of fourth order convergence rate in space. Numerical experiments verify the presented two-grid approach where we draw some interesting conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A line search algorithm for wind field adjustment with incomplete data and RBF approximation

The problem of concern in this work is the construction of free divergence fields given scattered horizontal components. As customary, the problem is formulated as a PDE constrained least squares problem. The novelty of our approach is to construct the so-called adjusted field, as the unique solution along an appropriately chosen descent direction. The latter is obtained by the adjoint equation technique. It is shown that the classical adjusted field of Sasaki’s is a particular case. On choosing descent directions, the underlying mass consistent model leads to the solution of an elliptic problem which is solved by means of a radial basis functions method. Finally, some numerical results for wind field adjustment are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps

In this article, we propose new Monte Carlo techniques for moving a diffusive particle in a discontinuous media. In this framework, we characterize the stochastic process that governs the positions of the particle. The key tool is the reduction of the process to a Skew Brownian motion (SBM). In a zone where the coefficients are locally constant on each side of the discontinuity, the new position of the particle after a constant time step is sampled from the exact distribution of the SBM process at the considered time. To do so, we propose two different but equivalent algorithms: a two-steps simulation with a stop at the discontinuity and a one-step direct simulation of the SBM dynamic. Some benchmark tests illustrate their effectiveness.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

The Degree of Rate Control: A Powerful Tool for Catalysis Research

The “degree of rate control” (DRC) is a mathematical approach for analysing multi-step reaction mechanisms that has proven very useful in catalysis research. It identifies the “ratecontrolling transition states and intermediates” (i.e., those whose DRCs are large in magnitude). Even in mechanisms with over 30 intermediates and transition states, these are generally just a few distinct chemical species whose energies, if they could be independently changed, would achieve a faster net reaction rate to the product of interest. For example, when there is a single “rate-determining step”, the DRC for its transition state (TS) is 1, which means (by definition) that if this TS’s energy could be decreased by kBT (where kB is Boltzmann’s constant and T is temperature), the net rate would increase by a factor of e. Since the (relative) energies of these key adsorbed intermediates and transition states can be adjusted by modifying the catalyst or solvent, or even a reactant’s molecular structure, the DRC values provide important ideas for catalyst improvement. The species with large DRCs are also the ones whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. A tutorial on DRC analysis, the calculation of DRCs, and examples of the applications of DRCs in catalysis research is presented here. Applications of DRC analysis include: clarifying reaction kinetics, improving the accuracy of computational models, improving reaction conditions, improving choice of oxidant in selective oxidation, incorporation in algorithms which calculate net reaction rates of multistep mechanisms without solving the differential equations involved, and high-throughput computational screening of catalyst materials. Since DRC values can be determined experimentally, we conclude a full microkinetic model is not required to take advantage of DRC analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Physics-informed machine learning

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Pade spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems

Pade spectrum decomposition is an optimal sum-over-poles expansion scheme of Fermi function and Bose function [J. Hu, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 133, 101106 (2010)]. In this work, we report two additional members to this family, from which the best among all sum-over-poles methods could be chosen for different cases of application. Methods are developed for determining these three Pade spectrum decomposition expansions at machine precision via simple algorithms. We exemplify the applications of present development with optimal construction of hierarchical equations-of-motion formulations for nonperturbative quantum dissipation and quantum transport dynamics. Numerical demonstrations are given for two systems. One is the transient transport current to an interacting quantum-dots system, together with the involved high-order co-tunneling dynamics. Another is the non-Markovian dynamics of a spin-boson system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Fast cooling for a system of stochastic oscillators

We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired steady state corresponding to reduced thermal noise. Among the feedback controls achieving the desired asymptotic transfer, we find that the most efficient one from an energy point of view is characterized by time-reversibility. We also extend the theory of Schrödinger bridges to this model, thereby steering the system in finite time and with minimum effort to a target steady-state distribution. The system can then be maintained in this state through the optimal steady-state feedback control. The solution, in the finite-horizon case, involves a space-time harmonic function φ, and −logφ plays the role of an artificial, time-varying potential in which the desired evolution occurs. This framework appears extremely general and flexible and can be viewed as a considerable generalization of existing active control strategies such as macromolecular cooling. In the case of a quadratic potential, the results assume a form particularly attractive from the algorithmic viewpoint as the optimal control can be computed via deterministic matricial differential equations. An example involving inertial particles illustrates both transient and steady state optimal feedback control.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A non-intrusive parallel-in-time approach for simultaneous optimization with unsteady PDEs

This paper presents a non-intrusive framework for integrating existing unsteady partial differential equation (PDE) solvers into a parallel-in-time simultaneous optimization algorithm. The time-parallelization is provided by the non-intrusive software library XBraid [Parallel multigrid in time, software available at http://llnl.gov/casc/xbraid], which applies an iterative multigrid reduction technique to the time domain of existing time-marching schemes for solving unsteady PDEs. Its general user-interface has been extended in [S. Günther, N.R. Gauger, and J.B. Schroder, A non-intrusive parallel-in-time adjoint solver with the XBraid library, Comput. Vis. Sci. 19 (2018), pp. 85–95. Available at arXiv, math.OC/1705.00663] for computing adjoint sensitivities such that gradients of output quantities with respect to design changes can be computed parallel-in-time alongside with the primal PDE solution. In this paper, the primal and adjoint XBraid iterations are embedded into a simultaneous optimization framework, namely the One-shot method. In this method, design updates towards optimality are employed after each state and adjoint update such that optimality and feasibility of the design and the PDE solution are reached simultaneously. Finally, the time-parallel optimization method is validated on an advection-dominated flow control problem which shows significant speedup over a classical time-serial optimization algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Shor's quantum algorithm using electrons in semiconductor nanostructures

Shor's factoring algorithm illustrates the potential power of quantum computation. Here, we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network by exploiting the potential of fully coherent electron transport assisted by the surface acoustic waves. Specifically, a nonstandard approach is used to implement, in a simple form, the quantum circuits of the modular exponentiation execution for the simplest instance of Shor's algorithm, that is, the factorization of N=15. The numerical procedure is based on a time-dependent solution of the multiparticle Schroedinger equation. The near-ideal algorithm performance and the large estimated fidelity indicate the efficiency of the protocol implemented, which also is almost insensitive to small destabilizing effects during quantum computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-F-P-56: On a New Approach to Reconstruct the Patient Dose From Phantom Measurements

Purpose: The development of complex radiation treatment schemes emphasizes the need for advanced QA analysis methods to ensure patient safety. One such tool is the Delta4 DVH Anatomy software, where the patient dose is reconstructed from phantom measurements. Deviations in the measured dose are transferred to the patient anatomy and their clinical impact is evaluated in situ. Results from the original algorithm revealed weaknesses that may introduce artefacts in the reconstructed dose. These can lead to false negatives or obscure the effects of minor dose deviations from delivery failures. Here, we will present results from a new patient dose reconstruction algorithm. Methods: The main steps of the new algorithm are: (1) the dose delivered to a phantom is measured in a number of detector positions. (2) The measured dose is compared to an internally calculated dose distribution evaluated in said positions. The so-obtained dose difference is (3) used to calculate an energy fluence difference. This entity is (4) used as input to a patient dose correction calculation routine. Finally, the patient dose is reconstructed by adding said patient dose correction to the planned patient dose. The internal dose calculation in step (2) and (4) is based on the Pencil Beam algorithm. Results: The new patient dose reconstruction algorithm have been tested on a number of patients and the standard metrics dose deviation (DDev), distance-to-agreement (DTA) and Gamma index are improved when compared to the original algorithm. In a certain case the Gamma index (3%/3mm) increases from 72.9% to 96.6%. Conclusion: The patient dose reconstruction algorithm is improved. This leads to a reduction in non-physical artefacts in the reconstructed patient dose. As a consequence, the possibility to detect deviations in the dose that is delivered to the patient is improved. An increase in Gamma index for the PTV can be seen. The corresponding author is an employee of ScandiDos.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

MueLu Multigrid Preconditioning Package

MueLu is intended for the research and development of multigrid algorithms used in the solution of sparse linear systems arising from systems of partial differential equations. The software provides multigrid source code, test programs, and short example programs to demonstrate the various interfaces for creating, accessing, and applying the solvers. MueLu currently provides an implementation of smoothed aggregation algebraic multigrid method and interfaces to many commonly used smoothers. However, the software is intended to be extensible, and new methods can be incorporated easily. MueLu also allows for advanced usage, such as combining multiple methods and segregated solves. The library supports point and block access to matrix data. All algorithms and methods in MueLu have been or will be published in the open scientific literature.

Tuminaro, Raymond↗
DOE OSTI2016

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

PATtyFams: Protein families for the microbial genomes in the PATRIC database

The ability to build accurate protein families is a fundamental operation in bioinformatics that influences comparative analyses, genome annotation, and metabolic modeling. For several years we have been maintaining protein families for all microbial genomes in the PATRIC database (Pathosystems Resource Integration Center, patricbrc.org) in order to drive many of the comparative analysis tools that are available through the PATRIC website. However, due to the burgeoning number of genomes, traditional approaches for generating protein families are becoming prohibitive. In this report, we describe a new approach for generating protein families, which we call PATtyFams. This method uses the k-mer-based function assignments available through RAST (Rapid Annotation using Subsystem Technology) to rapidly guide family formation, and then differentiates the function-based groups into families using a Markov Cluster algorithm (MCL). In conclusion, this new approach for generating protein families is rapid, scalable and has properties that are consistent with alignment-based methods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX , is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

54 ENVIRONMENTAL SCIENCES↗