Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient methods”

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 829 records · Page 46

First order nonadiabatic coupling matrix elements between excited states: Implementation and application at the TD-DFT and pp-TDA levels

The recently proposed rigorous yet abstract theory of first order nonadiabatic coupling matrix elements (fo-NACME) between electronically excited states [Z. Li and W. Liu, J. Chem. Phys. 141, 014110 (2014)] is specified in detail for two widely used models: The time-dependent density functional theory and the particle-particle Tamm-Dancoff approximation. The actual implementation employs a Lagrangian formalism with atomic-orbital based direct algorithms, which makes the computation of fo-NACME very similar to that of excited-state gradients. Although the methods have great potential in investigating internal conversions and nonadiabatic dynamics between excited states of large molecules, only prototypical systems as a first pilot application are considered here to illustrate some conceptual aspects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ab-initio study of B{sub 2}-type technetium AB (A=Tc, B=Nb and Ta) intermetallic compounds

The structural, electronic and elastic properties of AB type (A = Tc, B = Nb and Ta) technetium intermetallic compounds are studied using full potential linearized plane wave (FP-LAPW) method within generalized gradient approximation (GGA). The calculated lattice parameters agree well with the experimental results. The elastic constants obey the stability criteria for cubic system. Ductility for these compounds has been analyzed using the Pugh’s rule and Cauchy’s pressure and found that all the compounds are ductile in nature. Bonding nature is discussed in terms of Fermi surface and band structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electronic structure, elasticity, bonding features and mechanical behaviour of zinc intermetallics: A DFT study

The structural stability, electronic structure, elastic and mechanical properties of TiZn and ZrZn intermetallics have been studied using ab-initio full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation for exchange and correlation potentials. The various structural parameters, such as lattice constant (a{sub 0}), bulk modulus (B), and its pressure derivative (B’) are analysed and compared. The investigation of elastic constants affirm that both TiZn and ZrZn are elastically stable in CsCl (B{sub 2} phase) structure. The electronic structures have been analysed quantitatively from the band structure which reveals the metallic nature of these compounds. To better illustrate the nature of bonding and charge transfer, we have also studied the Fermi surfaces. The three well known criterion of ductility namely Pugh’s rule, Cauchy’s pressure and Frantsevich rule elucidate the ductile nature of these compounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A first principles study of half-metallic ferromagnetism in In{sub 1-x}Ti{sub x}P (x = 0.06) diluted magnetic semiconductor

A first principles approach has been used to calculate the electronic and magnetic properties of In{sub 1-x}Ti{sub x}P (x = 0.06) diluted magnetic semiconductor (DMS) compound. The calculations have been carried out using the highly precise all electron full potential Linear Augmented Plane Wave (FPLAPW) method within generalized gradient approximation (GGA) as exchange-correlation (XC) potentials. The estimated results show that the Ti-doping generate robust half metallic ferromagnetism with the 100% spin polarization at Fermi level (E{sub F}) in InP. Due to this peculiar property, the resultant compound behaves as true half-metallic ferromagnet which is best suited for spintronic applications. The total magnetic moments of this compound are mainly due to Ti-d states present at E{sub F} with almost negligible contribution from other atoms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High mass and halo resolution from fast low resolution simulations

Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. Here we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition resolution and develop a halo finder "relaxed-FoF", where we allow different linking lengths for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also calibrate small-scale velocities of small halos to improve the power spectrum in redshift space. For the matter statistics, we incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scales. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.

79 ASTRONOMY AND ASTROPHYSICS↗

Indigo: A Domain-Specific Language for Fast, Portable Image Reconstruction

© 2018 IEEE. Linear operators used in iterative methods like conjugate gradient have typically been implemented either as ''matrix-driven'' subroutines backed by explicit sparse or dense matrices, or as ''matrix-free'' subroutines that implement specific linear operations directly (e.g. FFTs). The matrix-driven approach is generally more portable because it can target widely-Available BLAS libraries, but it can be inefficient in terms of time and space complexity. In contrast, the matrix-free approach is more performant because it leverages structure in operations, but it requires each operator be re-implemented on each new platform. To increase performance and portability, we propose a hybrid approach that represents linear operators as expression trees. Leaf nodes in the tree are either matrix-free or matrix-driven operators, and interior nodes represent mathematical compositions (sums, products, transposes) or structural compositions (stacks, block diagonals, etc.) of the leaf operators. This representation enables expert-guided reordering and fusion transformations that can improve performance or reduce memory pressure. We implement our approach in a domain-specific language called Indigo. We assess Indigo on image reconstruction problems arising in four application areas: magnetic resonance imaging, ptychography, magnetic particle imaging, and fluorescent microscopy. We give performance results from vendor BLAS libraries, and we introduce specializations to Sparse BLAS routines that achieve near-Roofline performance on multi-core, many-core, and GPU systems.

Driscoll, Michael↗

Adaptive Quantum Generative Training using an Unbounded Loss Function

We propose a generative quantum learning algorithm using the Adaptive Derivative-Assembled Problem Tailored ansatz (ADAPT) framework in which the loss function to be minimized is the maximal quantum Rényi divergence of order two, an unbounded function that mitigates barren plateaus which inhibit training variational circuits. We benchmark this method against other state-of-the-art adaptive algorithms by learning random two-local thermal states. We perform numerical experiments of up to 12 qubits comparing our method learning algorithms that use linear objective functions and show that Rényi-ADAPT is capable of constructing shallow quantum circuits competitive with existing methods, while the gradients remain favorable resulting from the maximal Rényi divergence loss function.

quantum algorithms, quantum machine learning, quan↗

SU-C-18A-05: Registration Accuracy of MR-Based Images to On-Board Megavoltage Cone-Beam CT for Brain Patient Setup

Purpose: To quantify the difference in isocenter shifts when co-registering MR and MR-based pseudo CTs (pCT) with on-board megavoltage conebeam CT (CBCT) images. Methods: Fast Spoiled Gradient Echo MRs were used to generate pCTs (research version of Advantage Sim MD™, GE Healthcare) for ten patients who had prior brain radiotherapy. The planning CT (rCT) for each was co-registered with the MR, and the plan isocenter and two other reference points were transferred to the MR and pCT. CBCT images (with the machine isocenter) from a single treatment day were coregistered with the 3 test images (MR, pCT and rCT), by two observers and by an automated registration algorithm. The reference points were used to calculate patient shifts and rotations from the registrations. The shifts calculated from the test image registrations were compared to each other and to the shifts performed by the therapists who treated the patients on that day. Results: The average difference in absolute value between the isocenter shifts from the MR-, pCT- and rCT-CBCT registrations, and the therapist shifts, were 2.02, 3.01 and 0.89 mm (craniocaudal), 1.14, 1.34 and 0.46 mm (lateral), and 1.37, 3.43 and 1.43 mm (vertical), respectively. The MR- and pCT-CBCT registrations differed by 1.99, and 2.53 mm (craniocaudal), 1.36, and 1.37 mm (lateral), and 0.74 and 2.34 mm (vertical), respectively, from the average rCT-CBCT shifts. On average, differences of 2.39 (craniocaudal), 1.28 (lateral) and 2.84 mm (vertical) were seen between the MR and pCT shifts. Rotations relative to the CBCT coordinate system were on average <2° for the MR and rCT, and <6° for the pCT. Conclusion: In this study, FSPGR MR-CBCT registrations were more precise compared to the pCT-CBCT registrations. For improved accuracy, MR sequences that are optimal for bony anatomy visualization are necessary. GE healthcare has provided a research version of Advantage Sim MD to UCSF. No financial support was provided.

60 APPLIED LIFE SCIENCES↗

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

Source-to-Source Automatic Differentiation of OpenMP Parallel Loops

This article presents our work toward correct and efficient automatic differentiation of OpenMP parallel worksharing loops in forward and reverse mode. Automatic differentiation is a method to obtain gradients of numerical programs, which are crucial in optimization, uncertainty quantification, and machine learning. The computational cost to compute gradients is a common bottleneck in practice. For applications that are parallelized for multicore CPUs or GPUs using OpenMP, one also wishes to compute the gradients in parallel. Here, we propose a framework to reason about the correctness of the generated derivative code, from which we justify our OpenMP extension to the differentiation model. We implement this model in the automatic differentiation tool Tapenade and present test cases that are differentiated following our extended differentiation procedure. Performance of the generated derivative programs in forward and reverse mode is better than sequential, although our reverse mode often scales worse than the input programs.

97 MATHEMATICS AND COMPUTING↗

NeuroFEM

SAND2025-00525O NeuroFEM is a software tool that demonstrates a neuromorphic algorithm for solving finite element problems. It sets up a 2D finite element problem for the Poisson equation on a disk, constructs synaptic matrices, and simulates neural dynamics to solve the resulting sparse linear system. The software illustrates how the algorithm converges to the solution and plots the results, showcasing a neuromorphic counterpart to traditional methods like Conjugate Gradient or GMRES. This tool is designed to highlight the potential of neuromorphic algorithms for solving sparse linear systems, which are prevalent in various computational applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

Effects of Jacobian Matrix Regularization on the Detectability of Adversarial Samples

The well-known vulnerability of Deep Neural Networks to adversarial samples has led to a rapid cycle of increasingly sophisticated attack algorithms and proposed defenses. While most contemporary defenses have been shown to be vulnerable to carefully configured attacks, methods based on gradient regularization and out-of-distribution detection have attracted much interest recently by demonstrating higher resilience to a broad range of attack algorithms. However, no study has yet investigated the effect of combining these techniques. In this paper, we consider the effect of Jacobian matrix regularization on the detectability of adversarial samples on the CIFAR-10 image benchmark dataset. We find that regularization has a significant effect on detectability, and in some cases can make an undetectable attack on a baseline model detectable. In addition, we give evidence that regularization may mitigate the known weaknesses of detectors to high-confidence adversarial samples. The defenses we consider here are highly generalizable, and we believe they will be useful for further investigations to transfer machine learning robustness to other data domains.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Samoa Updater: An Application of the Levenberg-Marquardt Method to Update DELFIC Predictions Using Field Measurements

The US Department of Energy (DOE) Forensics Operations (DFO) is a member of the Ground Collections Task Force (GCTF), which is responsible for sample collection of radiological debris for attribution should a nuclear detonation ever occur in the United States. The DFO runs the Defense Land Fallout Interpretive Code (DELFIC) Fallout Planning Tool to predict the deposition of fallout from a nuclear detonation. This prediction is refined using the DELFIC Updater tool, which takes ground measurements and adjusts DELFIC inputs to minimize the difference between prediction and observation, yielding improved predictions of fallout in locations both measured and not yet measured. Samoa, a framework for uncertainty analysis and optimization, is used to improve DELFIC predictive fallout modeling. This new capability using Samoa, dubbed “Samoa Updater,” is compared with the current DELFIC Updater, a brute-force sampling approach. Samoa Updater uses the Levenberg– Marquardt (LM) method, a gradient-based nonlinear least squares approach that uses the functional shape of the input space to increase optimization speed. In simulated test cases Samoa Updater yields faster and more accurate solutions than the current Updater.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

What Makes You Hold on to That Old Car? Joint Insights From Machine Learning and Multinomial Logit on Vehicle-Level Transaction Decisions

What makes you hold on to that old car? While the vast majority of household vehicles are still powered by conventional internal combustion engines, the progress of adopting emerging vehicle technologies will critically depend on how soon the existing vehicles are transacted out of the household fleet. Leveraging a nationally representative longitudinal data set, the Panel Study of Income Dynamics, this study examines how household decisions to dispose of or replace a given vehicle are: 1) influenced by the vehicle’s attributes, 2) mediated by households’ concurrent socio-demographic and economic attributes, and 3) triggered by key life cycle events. Coupled with a newly developed machine learning interpretation tool, TreeExplainer, we demonstrate an innovative use of machine learning models to augment traditional logit modeling to both generate behavioral insights and improve model performance. We find the two gradient-boosting-based methods, CatBoost and LightGBM, are the best performing machine learning models for this problem. The multinomial logistic model can achieve similar performance levels after its model specification is informed by TreeExplainer. Both machine learning and multinomial logit models suggest that while older vehicles are more likely to be disposed of or replaced than newer ones, such probability decreases as the vehicles serve the family longer. Pickup trucks and sport utility vehicles are less likely to be disposed of or replaced than cars, and leased vehicles are more likely to be transacted than owned vehicles. We find that married families, families with higher education levels, homeowners, and older families tend to keep their vehicles longer. Life events such as childbirth, residential relocation, and change of household composition and income are found to increase vehicle disposal and/or replacement. We provide additional insights on the timing of vehicle replacement or disposal, in particular, the presence of children and childbirth events are more strongly associated with vehicle replacement among younger parents.

33 ADVANCED PROPULSION SYSTEMS↗

Approximate analysis of thermal convection in a crystal-growth cell for Spacelab 3

The transient and steady thermal convection in microgravity is described. The approach is applicable to many three dimensional flows in containers of various shapes with various thermal gradients imposed. The method employs known analytical solutions to two dimensional thermal flows in simpler geometries, and does not require recourse to numerical calculations by computer.

Dressler, R. F.↗

Determination of the isotopic composition of atmospheric methane and its application in the Antarctic

A procedure for establishing the C-13/C-12 ratio and the C-14 abundance in the atmospheric methane is discussed. The method involves air sample collection, measurement of the methane mixing ratio by gas chromotography followed by quantitative conversion of the methane in the air samples to CO2 and H2O, and analysis of the resulting CO2 for the C-13/C-12 ratio by stable isotope ratio mass spectrometry and measurement of C-14 content by accelerator mass spectrometry. The carbon isotropic composition of methane in air collected at Baring Head, New Zealand, and in air collected on aircraft flights between New Zealand and Antarctica is determined by the method, and no gradient in the composition between Baring Head and the South Pole station is found. As the technique is refined, and more data is gathered, small seasonal and long-term variations in C-13 are expected to be resolved.

Lowe, David C.↗

Model-based parameter estimation using cardiovascular response to orthostatic stress

This paper presents a cardiovascular model that is capable of simulating the short-term (< or approximately equal to 3 min) transient hemodynamic response to gravitational stress and a gradient-based optimization method that allows for the automated estimation of model parameters from simulated or experimental data. We perform a sensitivity analysis of the transient heart rate response to determine which parameters of the model impact the heart rate dynamics significantly. We subsequently include only those parameters in the estimation routine that impact the transient heart rate dynamics substantially. We apply the estimation algorithm to both simulated and real data and showed that restriction to the 20 most important parameters does not impair our ability to match the data.

Non-NASA Center↗

Simulation of a Periodic Jet in a Crossflow with a RANS Solver Using an Unstructured Grid

A second-order unstructured-grid code, developed and used primarily for steady aerodynamic simulations, is applied to the synthetic jet in a cross flow. The code, FUN3D, is a vertex-centered finite-volume method originally developed by Anderson[1, 2], and is currently supported by members of the Fast Adaptive Aerospace Tools team at NASA Langley. Used primarily for design[3] and analysis[4] of steady aerodynamic configurations, FUN3D incorporates a discrete adjoint capability, and supports parallel computations using MPI. A detailed description of the FUN3D code can be found in the references given above. The code is under continuous development and contains a variety of flux splitting algorithms for the inviscid terms, two methods for computing gradients, several turbulence models, and several solution methodologies; all in varying states of development. Only the most robust and reliable components, based on experiences with steady aerodynamic simulations, were employed in this work. As applied in this work, FUN3D solves the Reynolds averaged Navier-Stokes equations using the one equation turbulence model of Spalart and Allmaras[5]. The spatial discretization is formed on unstructured meshes using a vertex-centered approach. The inviscid terms are evaluated by a flux-difference splitting formulation using least-squares reconstruction and Roe-type approximate Riemann fluxes. Green-Gauss gradient evaluations are used for viscous and turbulence modeling terms. The discrete spatial operator is combined with a backward time operator which is then solved iteratively using point or line Gauss-Seidel and local time stepping in a pseudo time. For steady flows, the physical time step is set to infinity and the pseudo time step is ramped up with the iteration count. A second-order backward in time operator is used for time accurate flows with 20 to 50 steps in the pseudo time applied at each physical time step. For this effort, FUN3D was modified to support spatially varying boundary and initial conditions, and unsteady boundary conditions. Also, a specialized in/out flow boundary condition was implemented to model the action of the diaphragm. This boundary condition is described below in more detail. The grids were generated using the internally developed codes GridEX[6] for meshing the surfaces and inviscid regions of the domain, and for CAD access; and MesherX[7] for meshing the viscous regions. Grid spacing in on the surfaces and in the inviscid regions are indirectly controlled by specifying sources. The viscous layers are generated using an advancing layer technique. MeshersX allows the user to control the spatial variation of the first step off the surface, growth rates, and the termination criterion by providing small problem dependent subroutines.

Atkins, H. L.↗