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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

O(N) Quantum Molecular Dynamics (QMD) Algorithms, Code Requirements, Release Notes, and Library Deployment

The Exascale Computing Project (ECP) Co-design Center for Particle Applications (CoPA) is addressing the challenges for particle applications to run on upcoming exascale computing architectures. This includes short- and long-range molecular dynamics (MD), particle-in-cell (PIC), and quantum molecular dynamics (QMD). This document addresses $\mathcal{O}(N)$ QMD. The goal of this CoPA team is to develop $\mathcal{O}(N)$ linear scaling methods for QMD optimized for new and next generation architectures. This will provide the capability to simulate larger systems and run for longer timeframes than is possible today. Focus is initially on the density matrix construction. This requires efficient matrix formats and linear algebra operations for distributed architectures. A significant reduction in the wallclock time for an MD timestep is necessary to achieve practical large scale QMD. Equally challenging is to develop scalable distributed implementations. This requires the exploration of efficient data formats (dense, sparse, etc.), data decomposition and distribution across compute nodes using block- and graph-based methods. Traditional programming models such as MPI/OpenMP, hybrid MPI/OpenMP/Accelerator, as well as asynchronous task-based models will be explored to achieve maximum parallelism. Parallelism at the level of a matrix operation, solver, and/or application needs to be explored to gain the most benefit on new and emerging architectures. This report serves as a “living document” of the additions and enhancements throughout the ECP CoPA project for $\mathcal{O}(N)$ QMD. The following sections address the applications we are working with, the quantum chemistry libraries (BML and PROGRESS), and our co-design exploration through the use of a proxy application.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint d design optimization requires coupling an adjoint enabled computational fluid dynamics (CFD) solver with an adjoint enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Boundary Layer Transition↗
DOE OSTI2014

SU-E-T-462: Fixed-Jaw Optimization for Critical Structure Sparing in IMRT Treatment Planning: Beam Modeling Cautions for Non-Routine Use

Purpose: Multiple publications exist concerning fixed-jaw utilization to avoid linac carriage shifts and reduce intensity modulated radiotherapy (IMRT) treatment times. The purpose of this work is to demonstrate delivery QA discrepancies and illustrate the need for improved treatment planning system (TPS) commissioning for non-routine use. Methods: A 6cm diameter spherical target was delineated on a virtual phantom containing the Iba Matrixx linear array within the Varian Eclipse TPS. Optimization was performed for target coverage for the following 3 scenarios: a single open, zero degree field where the X and Y jaws completely cover the target; the same field using an asymmetric, fixed-jaw technique where the upper Y jaw does not cover the superior 2cm of the target; and both of the aforementioned directed at the target at 315 and 45 degree gantry angles, respectively. This final orientation was also irradiated on a linac for delivery analysis. A sarcoma patient case was also analyzed where the fixed jaw technique was utilized for kidney sparing. Results: The open beam results were as predicted but the fixed-jaw results demonstrate a pronounced fluence increase along the asymmetric, upper jaw. Analysis of the delivery of the combined beam plan Resultin 83% of pixels evaluated passing gamma criteria of 3%, 3mm DTA. Analysis for the sarcoma patient, in the plane of the shielded kidney, indicated 93% passing although the maximum dose discrepancies in this region were approximately 23%. Conclusion: Optimization within the target is routinely performed using MLC leaf-end characteristics. The fixed-jaw technique forces optimization of target coverage to utilize the penumbra profiles of the associated beamdefining jaw. If the profiles were collected using a common 0.125cc ionization chamber, the resolution may be insufficient resulting in a planvs.-delivery mismatch. It is recommended that high-resolution beam characteristics be considered when non-routine planning methods are utilized.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗
NASA NTRS1991

Estimation of optimal Kalman filter gain from non-optimal filter residuals

This paper presents a novel method of estimating the optimal steady state Kalman filter gain of a linear discrete time-invariant system from a non-optimal Kalman filter residual sequence. The relation between the optimal residual sequence and a signal derived from the non-optimal residual sequence is described by a Moving Average (MA) model whose coefficients are expressed in terms of the state space parameters and the optimal steady state Kalman filter gain. In order to identify the MA model, a whitening filter of the derived signal, which corresponds to an AutoRegressive (AR) model of the signal, is first identified using the least-squares method. Then the inverse filter of the whitening filter, which corresponds to the MA model, is calculated. From the coefficients of the identified MA model, the optimal steady state Kalman filter gain can be obtained. Numerical example is provided to illustrate the feasibility of this approach.

Chen, Chung-Wen↗
NASA NTRS1993

Optimization by decomposition in structural and multidisciplinary applications

An algorithm for a general, multilevel structural optimization by substructuring is derived, based on the linear decomposition concept that is rooted in the Bellman's Optimality Criterion enhanced with the optimum sensitivity derivatives used as a means to account for coupling among the subproblems, each of which is limited to optimization of a substructure. The algorithm applies also to those multidisciplinary problems whose subproblems form a hierarchy similar to that of substructures. In systems where the subproblems communicate with each other at the same level, the decomposition becomes non-hierarchic and the system may be optimized as a whole based on the derivatives of the system behavior with respect to the design variables computed by a method that bypasses finite differencing on the system analysis. When a multidisciplinary system includes a structure as its part, a hybrid, hierarchic/non-hierarchic decomposition applies. Numerical examples and references to computational experience accumulated to date illustrate the discussion.

Sobieszczanski-Sobieski, Jaroslaw↗
DOE OSTI2017

Towards optimal extraction of cosmological information from nonlinear data

One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density, and 2-LPT dynamics in the optimization steps used to reconstruct the initial density modes. We demonstrate that the method gives an unbiased estimator of the initial power spectrum, providing among other a near optimal reconstruction of linear baryonic acoustic oscillations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

A rotor optimization using regression analysis

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Giansante, N.↗
DOE OSTI2016

Clinically Applicable Monte Carlo–based Biological Dose Optimization for the Treatment of Head and Neck Cancers With Spot-Scanning Proton Therapy

Purpose: Our aim is to demonstrate the feasibility of fast Monte Carlo (MC)–based inverse biological planning for the treatment of head and neck tumors in spot-scanning proton therapy. Methods and Materials: Recently, a fast and accurate graphics processor unit (GPU)–based MC simulation of proton transport was developed and used as the dose-calculation engine in a GPU-accelerated intensity modulated proton therapy (IMPT) optimizer. Besides dose, the MC can simultaneously score the dose-averaged linear energy transfer (LET{sub d}), which makes biological dose (BD) optimization possible. To convert from LET{sub d} to BD, a simple linear relation was assumed. By use of this novel optimizer, inverse biological planning was applied to 4 patients, including 2 small and 1 large thyroid tumor targets, as well as 1 glioma case. To create these plans, constraints were placed to maintain the physical dose (PD) within 1.25 times the prescription while maximizing target BD. For comparison, conventional intensity modulated radiation therapy (IMRT) and IMPT plans were also created using Eclipse (Varian Medical Systems) in each case. The same critical-structure PD constraints were used for the IMRT, IMPT, and biologically optimized plans. The BD distributions for the IMPT plans were obtained through MC recalculations. Results: Compared with standard IMPT, the biologically optimal plans for patients with small tumor targets displayed a BD escalation that was around twice the PD increase. Dose sparing to critical structures was improved compared with both IMRT and IMPT. No significant BD increase could be achieved for the large thyroid tumor case and when the presence of critical structures mitigated the contribution of additional fields. The calculation of the biologically optimized plans can be completed in a clinically viable time (<30 minutes) on a small 24-GPU system. Conclusions: By exploiting GPU acceleration, MC-based, biologically optimized plans were created for small–tumor target patients. This optimizer will be used in an upcoming feasibility trial on LET{sub d} painting for radioresistant tumors.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.

58 GEOSCIENCES↗
DOE OSTI2023

Phase-based design of CO 2 capture, transport, and storage infrastructure via SimCCS 3.0

The design of optimal infrastructure is essential for the deployment of commercial and large-scale carbon capture and storage (CCS) technology. During the design process, it is important to consider CO 2 capture and storage locations and CO 2 transportation pipelines to minimize the total project cost. SimCCS, first introduced in 2009, is an integrated open-source tool to optimize CCS infrastructure. The core CCS infrastructure design problem in SimCCS is structured as a mixed-integer linear programming problem by selecting the optimal pipeline routes, searching CO 2 source capture and storage locations, and determining the corresponding CO 2 amounts to meet desired capture targets. Multiple important and practical features have been developed to the latest version of SimCCS, SimCCS 3.0 . One of these features is phase-based modeling which enables users to dynamically design the CCS infrastructure. We demonstrate the phased-based modeling capability using two CCS infrastructure optimization case studies. The results from these case studies reveal that the phase-based modeling capability in SimCCS is particularly useful to optimize the dynamic deployment of CCS projects.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A set of test problems for nonlinear optimization

The software is a set of test problems for nonlinear optimization algorithms, including subroutines such as linear algebra routines and automatic differentiation algorithms. The test problems come from chemical engineering open literature, and describe optimization tasks related to the design and operation of processes such as carbon capture, Hydrogen production, heat exchange, and distillation.

Parker, Robert↗
NASA NTRS1986

On the design of classifiers for crop inventories

Crop proportion estimators that use classifications of satellite data to correct, in an additive way, a given estimate acquired from ground observations are discussed. A linear version of these estimators is optimal, in terms of minimum variance, when the regression of the ground observations onto the satellite observations in linear. When this regression is not linear, but the reverse regression (satellite observations onto ground observations) is linear, the estimator is suboptimal but still has certain appealing variance properties. In this paper expressions are derived for those regressions which relate the intercepts and slopes to conditional classification probabilities. These expressions are then used to discuss the question of classifier designs that can lead to low-variance crop proportion estimates. Variance expressions for these estimates in terms of classifier omission and commission errors are also derived.

Heydorn, R. P.↗
NASA NTRSDate not supplied

Optimization of a Solver for Computational Materials and Structures Problems on NVIDIA Volta and AMD Instinct GPUs

The Scalable Implementation of Finite Elements by NASA (ScIFEN) is a software package developed to solve complex computational materials and structures problems using the finite element method (FEM). In this paper, we describe optimization techniques to speed up the linear solver computation that occurs within the ScIFEN application. We consider GPUs from two different vendors, NVIDIA and AMD as our target platforms for optimization and highlight differences in performance and optimization techniques. The NVIDIA GPU Volta V100 is used in the Summit system deployed at Oak Ridge National Laboratory, and the new exascale system, Frontier, will be using AMD Radeon Instinct GPU. We evaluated the performance of various optimization techniques on test matrices, ranging in size from100K to 4M, that are representative of ScIFEN applications. The linear solver computation is memory-bound on both GPUs. Our experiments show that on the NVIDIA GPU we obtained up to79%of the theoretical peak bandwidth, while the AMD GPU achieved 59%. Overall, the NVIDIA V100 GPU outperforms the AMD MI 25 GPU1. We observed an overall speedup of up to37X on an NVIDIA V100 compared to an Intel Skylake 12-coremachine. The solver for a 4M degree of freedom system took under 2.5 seconds.

Mohammad Zubair↗
NASA NTRS1992

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett↗
NASA NTRS2002

Use of High Fidelity Methods in Multidisciplinary Optimization-A Preliminary Survey

Multidisciplinary optimization is a key element of design process. To date multidiscipline optimization methods that use low fidelity methods are well advanced. Optimization methods based on simple linear aerodynamic equations and plate structural equations have been applied to complex aerospace configurations. However, use of high fidelity methods such as the Euler/ Navier-Stokes for fluids and 3-D (three dimensional) finite elements for structures has begun recently. As an activity of Multidiscipline Design Optimization Technical Committee (MDO TC) of AIAA (American Institute of Aeronautics and Astronautics), an effort was initiated to assess the status of the use of high fidelity methods in multidisciplinary optimization. Contributions were solicited through the members MDO TC committee. This paper provides a summary of that survey.

Guruswamy, Guru P.↗
NASA NTRS1990

Accumulated approximation: A new method for structural optimization by iterative improvement

A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.

Rasmussen, John↗
DOE OSTI2026

Validation of the GFS model for gyrokinetic stability of NSTX pedestal data

This study presents a large database validation of the gyro fluid system (GFS) model for linear gyrokinetic stability for high-mode (H-mode) edge transport barrier conditions in the national spherical torus experiment (NSTX) tokamak. The database of linear stability calculations with the CGYRO gyrokinetic code was produced using plasma profile measurements from NSTX discharges to identify kinetic ballooning modes (KBM), trapped electron modes (TEM), and micro-tearing modes (MTM) that limit the pressure profile gradient in the H-mode barrier. A novel Bayesian optimization approach determines optimal resolution parameters for GFS specifically for spherical tokamak pedestal conditions. Our results demonstrate that GFS, with optimized resolution, can achieve accurate linear stability analysis in NSTX pedestal conditions for reduced resolution compared to CGYRO. GFS can accurately find the KBM, TEM, and MTM instability branches. Parametric analysis reveals that GFS accuracy in this extreme pedestal parameter range is degraded for low magnetic shear and near the separatrix conditions. These findings establish GFS as a fast linear eigenmode solver for spherical tokamak pedestal gyrokinetic stability and demonstrate a systematic methodology for determining the optimum resolution settings.

Yang, Minglei [Oak Ridge National Laboratory (ORNL↗