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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 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world’s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger “outer-loop” time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum Reinforcement Learning for Volt-VAR Control in Power Distribution Systems

Volt-VAR control (VVC) is crucial in active distribution networks for optimizing voltage profiles and minimizing network losses. While traditional deep reinforcement learning (DRL) algorithms exhibit promise for VVC, they often require extensive computational resources to handle such a high-dimensional problem. As a potential solution, quantum reinforcement learning (QRL) algorithms integrate the computational capabilities of quantum computing into the DRL framework. However, existing QRL algorithms struggle with complex VVC problems due to the limitations of current quantum hardware. To bridge this gap, this paper proposes an innovative QRL algorithm featuring an end-to-end architecture that integrates a classical autoencoder, variational quantum circuits (VQCs), and classical post-processing layers. This design efficiently compresses high-dimensional grid states, enabling VQCs to leverage quantum advantages while producing multiple control device outputs tailored for VVC tasks. Numerical studies on three representative distribution systems verify the effectiveness and scalability of the proposed QRL algorithm, and demonstrate its enhanced performance over classical approaches with only approximately 1% of the parameters. Additionally, the robustness of our developed algorithm is validated through noisy quantum environments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

PSelInv—A Distributed Memory Parallel Algorithm for Selected Inversion: The Symmetric Case

We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call PSelInv. The PSelInv method computes selected elements of a general sparse matrix Athat can be decomposed as A= LU, where L is lower triangular and U is upper triangular. The implementation described in this article focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization SuperLU-DIST. Yet, the underlying data structure and design of PSelInv allows it to be easily combined with other factorization routines, such as PARDISO. We discuss general parallelization strategies such as data and task distribution schemes. Specifically, we describe how to exploit the concurrency exposed by the elimination tree associated with the LU factorization of A. We demonstrate the efficiency and accuracy of PSelInv by presenting several numerical experiments. In particular, we show that PSelInv can run efficiently on more than 4,000 cores for a modestly sized matrix. We also show how PSelInv can be used to accelerate large-scale electronic structure calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Fixman compensating potential for general branched molecules

The technique of constraining high frequency modes of molecular motion is an effective way to increase simulation time scale and improve conformational sampling in molecular dynamics simulations. However, it has been shown that constraints on higher frequency modes such as bond lengths and bond angles stiffen the molecular model, thereby introducing systematic biases in the statistical behavior of the simulations. Fixman proposed a compensating potential to remove such biases in the thermodynamic and kinetic properties calculated from dynamics simulations. Previous implementations of the Fixman potential have been limited to only short serial chain systems. In this paper, we present a spatial operator algebra based algorithm to calculate the Fixman potential and its gradient within constrained dynamics simulations for branched topology molecules of any size. Our numerical studies on molecules of increasing complexity validate our algorithm by demonstrating recovery of the dihedral angle probability distribution function for systems that range in complexity from serial chains to protein molecules. We observe that the Fixman compensating potential recovers the free energy surface of a serial chain polymer, thus annulling the biases caused by constraining the bond lengths and bond angles. The inclusion of Fixman potential entails only a modest increase in the computational cost in these simulations. We believe that this work represents the first instance where the Fixman potential has been used for general branched systems, and establishes the viability for its use in constrained dynamics simulations of proteins and other macromolecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Numerical Oscillation Prevention for PV Inverter Controllers in Quasi-Steady-State Simulators

Droop-based PV inverter control methods are popular for preventing overvoltage in low voltage networks with high installations of PV solar. Quasi-steady-state simulators (QSTS) can be used to reduce the computational burden of conducting long-term techno-economic analyses of such PV inverter controllers. If dynamic models for droop-based controllers are directly implemented in QSTS, numerical oscillation occurs and the controllers fail to converge to their steady-state operation. In this paper, a power network sensitivity-based algorithm is proposed for preventing numerical oscillation while implementing active and reactive droop-based PV inverter controllers in quasisteady state simulation tool (e.g. in GridLAB-D). Convergence of the sensitivity-based algorithm is verified using a typical radial distribution feeder. It is found that all three controllers reached converged state in less than 15 iterations.

GridLAB-D, PV inverter control, quasi-steady-state↗
DOE OSTI2017

Distributed Optimal Dispatch of Distributed Energy Resources Over Lossy Communication Networks

In this paper, we consider the economic dispatch problem (EDP), where a cost function that is assumed to be strictly convex is assigned to each of distributed energy resources (DERs), over packet dropping networks. The goal of a standard EDP is to minimize the total generation cost while meeting total demand and satisfying individual generator output limit. We propose a distributed algorithm for solving the EDP over networks. The proposed algorithm is resilient against packet drops over communication links. Under the assumption that the underlying communication network is strongly connected with a positive probability and the packet drops are independent and identically distributed (i.i.d.), we show that the proposed algorithm is able to solve the EDP. Numerical simulation results are used to validate and illustrate the main results of the paper.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

An investigation of exploitation versus exploration in GBEA optimization of PORS 15 and 16 Problems

It was hypothesized that the variations in time to solution are driven by the competing mechanisms of exploration and exploitation.This thesis explores this hypothesis by examining two contrasting problems that embody the hypothesized tradeoff between exploration and exploitation. Plus one recall store (PORS) is an optimization problem based on the idea of a simple calculator with four buttons: plus, one, store, and recall. Integer addition and store are classified as operations, and one and memory recall are classified as terminals. The goal is to arrange a fixed number of keystrokes in a way that maximizes the numerical result. PORS 15 (15 keystrokes) represents the subset of difficult PORS problems and PORS 16 (16 keystrokes) represents the subset of PORS problems that are easiest to optimize. The goal of this work is to examine the tradeoff between exploitation and exploration in graph based evolutionary algorithm (GBEA) optimization. To do this, computational experiments are used to examine how solutions evolve in PORS 15 and 16 problems when solved using GBEAs. The experiment is comprised of three components; the graphs and the population, the evolutionary algorithm rule set, and the example problems. The complete, hypercube, and cycle graphs were used for this experiment. A fixed population size was used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Developing highly scalable fluid solvers for enabling multiphysics simulation.

We performed an investigation into explicit algorithms for the simulation of incompressible flows using methods with a finite, but small amount of compressibility added. Such methods include the artificial compressibility method and the lattice-Boltzmann method. The impetus for investigating such techniques stems from the increasing use of parallel computation at all levels (processors, clusters, and graphics processing units). Explicit algorithms have the potential to leverage these resources. In our investigation, a new form of artificial compressibility was derived. This method, referred to as the Entropically Damped Artificial Compressibility (EDAC) method, demonstrated superior results to traditional artificial compressibility methods by damping the numerical acoustic waves associated with these methods. Performance nearing that of the lattice- Boltzmann technique was observed, without the requirement of recasting the problem in terms of particle distribution functions; continuum variables may be used. Several example problems were investigated using a finite-di erence and finite-element discretizations of the EDAC equations. Example problems included lid-driven cavity flow, a convecting Taylor-Green vortex, a doubly periodic shear layer, freely decaying turbulence, and flow over a square cylinder. Additionally, a scalability study was performed using in excess of one million processing cores. Explicit methods were found to have desirable scaling properties; however, some robustness and general applicability issues remained.

Clausen, Jonathan R↗
DOE OSTI2023

Computationally Efficient Control Co-Design Optimization Framework with Mixed-Fidelity Fluid and Structure Analysis: OpenTurbineCoDe (OTCD) - ARPA-E ATLANTIS Phase I Project (Final Technical Report)

The goal of the Department of Energy (DOE) Advanced Research Projects Agency-Energy (ARPA-E) Aerodynamic Turbines Lighter and Afloat with Nautical Technologies and Integrated Servo-control (ATLANTIS) Program is to develop new technologies for floating offshore wind turbines, or wind farms, using the discipline of control co-design (CCD.) In this context, our goal is to develop a computationally efficient optimization framework for design of floating offshore wind turbines. Our specific aim is to utilize high-fidelity structural, aerodynamic, aero-structural tools, and to derive control-oriented reduced- or low-order models directly from the high-fidelity tools. We proposed a mixed-fidelity modeling approach which means that we are also using low- and mid-fidelity tools when necessary. This research is conducted by a multidisciplinary team consisting of Rutgers University, University of Michigan, Brigham Young University, and the National Renewable Energy Laboratory (NREL). The computational framework, called OpenTurbineCoDe, is designed to integrate, where possible, traditional structural, aerodynamic, aeroelastic models (e.g., OpenFAST) and advanced control algorithms with higher fidelity simulation tools including Reynolds-averaged Navier–Stokes (RANS) solvers, and three-dimensional structural finite element solvers. All the high-fidelity tools used in this research provide numerically exact gradients to facilitate both efficient optimization and local linearization for control implementation.

17 WIND ENERGY↗
DOE OSTI2018

Modeling the diffusion of heat energy within composites of homogeneous materials using the uncertainty principle

The goal of this paper is to develop a highly accurate and efficient numerical method for the solution of a time-dependent partial differential equation with a piecewise constant coefficient, on a finite interval with periodic boundary conditions. The resulting algorithm can be used, for example, to model the diffusion of heat energy in one space dimension, in the case where the spatial domain represents a medium consisting of two homogeneous materials. The resulting model has, to our knowledge, not yet been solved in closed form through analytical methods, and is difficult to solve using existing numerical methods, thus suggesting an alternative approach. The approach presented in this paper is to represent the solution as a linear combination of wave functions that change frequencies at the interfaces between different materials. It is demonstrated through numerical experiments that using the Uncertainty Principle to construct a basis of such functions, in conjunction with a spectral method, a mathematical model for heat diffusion through different materials can be solved much more efficiently than with conventional time-stepping methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Numerical Optimization Algorithms and Software for Systems Biology

The basic aims of this work are: to develop reliable algorithms for solving optimization problems involving large stoichiometric matrices; to investigate cyclic dependency between metabolic and macromolecular biosynthetic networks; and to quantify the significance of thermodynamic constraints on prokaryotic metabolism.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Higher-order time integration of Coulomb collisions in a plasma using Langevin equations

The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler–Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(Δt) vs. O(Δt{sup 1/2})] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “area-integral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler–Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy

We fully develop the Monte Carlo many-body Green’s function (MC-GF) method with the following enhancements: (1) The truncation order of the perturbation expansion of the Dyson self-energy is raised from the second order (MC-GF2) to the third order (MC-GF3) with the aid of a computerized procedure to enumerate and transform all 84 third-order Goldstone diagrams into Monte Carlo integrable expressions and then into central processing unit (CPU)/graphical processing unit (GPU)-parallel computer codes. (2) An efficient algorithm is proposed that computes all off-diagonal and diagonal elements of the MC-GF2 and MC-GF3 self-energy matrices by common subexpression elimination. (3) The frequency-independent approximation is lifted by introducing a method that computes frequency derivatives of the MC-GF2 and MC-GF3 self-energies up to any arbitrarily high order at nearly no additional computational cost. (4) The imaginary-time integration in the Laplace-transformed expressions of the self-energy is carried out stochastically (instead of using a quadrature in the previous implementations), resulting in a 50- to 200-fold speedup. (5) The efficiency of the redundant-walker convergence acceleration scheme is analyzed numerically, and the guidelines are established to select an optimal number of walkers for maximal efficiency. When such an optimal number is used, the cost per sample is constant of molecular size on either many CPUs or many GPUs. (6) The computational cost to obtain a binding energy within a given statistical uncertainty is observed to increase as (tentatively) O(n 4 ) and O(n 5 ) of molecular size (n is the number of electrons) with and without the diagonal approximation, respectively, as opposed to O(n 5 ) and O(n 6 ) of the corresponding deterministic algorithms. With this method applied to the electron binding energies of C 60 , we show that the third-order corrections to the self-energies are much greater in electron binding energies than in ground-state energies. As a result, they display a sign of oscillatory convergence toward experimental results, not necessarily improving the agreement with increasing perturbation order, justifying MC-GF3 and motivating even higher-order methods.

Algorithms↗
DOE OSTI2023

Computational diagnostics for flame acceleration and transition to detonation in a hydrogen/air mixture

A new computational diagnostic method for pressure-induced compressibility is proposed by projecting its local contribution to the chemical explosive mode (CEM) in the chemical explosive mode analysis (CEMA) framework. The new method is validated for the study of detonation development during the deflagration-to-detonation transition (DDT) process. The flame characteristics are identified through the quantification of individual CEM contributions of chemical reaction, diffusion, and pressure-induced compressibility. Numerical simulations are performed to investigate the DDT processes in a stoichiometric hydrogen-air mixture. A Godunov algorithm, fifth-order in space, and third-order in time are used to solve the fully compressible Navier-Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model (CDM) described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The new diagnostic method is first applied to onedimensional (1D) canonical flame configurations followed by two-dimensional (2D) simulations of DDT in an obstructed channel where different detonation initiation scenarios are examined using the new CEMA projection formulation. Detailed examinations of the idealized configuration of detonation initiation through shock focusing mechanism at a flame front are also studied using the new formulation. A comparison of the currently proposed CEMA projection and the original formulation by the authors suggests that including the pressure-induced compressibility is essential for the use of CEMA in DDT process. The results also show that the new formulation of CEMA projection can successively capture the detonation initiation through either a gradient mechanism or a direct initiation mechanism, and therefore can be used as an effective local analytical tool for the computational diagnostics of detonation initiation in a DDT process. It was found that detonation development is characterized by a strong contribution of chemistry role to the CEM which is pivotal to the initiation of detonation. The role of compressibility is found enhanced at the edge of the detonation front where diffusion was found to have minimal effects on detonation development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

ARKODE: A Flexible IVP Solver Infrastructure for One-step Methods

We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge–Kutta methods, ARKODE supports one-step methods designed to treat additive splittings of the IVP, including implicit-explicit (ImEx) additive Runge–Kutta methods and multirate infinitesimal (MRI) methods. We present the role of ARKODE within the SUNDIALS suite of time integration and nonlinear solver libraries, the core ARKODE infrastructure for utilities common to large classes of one-step methods, as well as its use of “time stepper” modules enabling easy incorporation of novel algorithms into the library. Numerical results show example problems of increasing complexity, highlighting the algorithmic flexibility afforded through this infrastructure, and include a larger multiphysics application leveraging multiple algorithmic features from ARKODE and SUNDIALS.

97 MATHEMATICS AND COMPUTING↗