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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Assessing equation of state-independent relations for neutron stars with nonparametric models

Relations between neutron star properties that do not depend on the nuclear equation of state offer insights on neutron star physics and have practical applications in data analysis. Such relations are obtained by fitting to a range of phenomenological or nuclear physics equation of state models, each of which may have varying degrees of accuracy. In this study we revisit commonly used relations and reassess them with a very flexible set of phenomenological nonparametric equation of state models that are based on Gaussian processes. Our models correspond to two sets: equations of state which mimic hadronic models, and equations of state with rapidly changing behavior that resemble phase transitions. Here we quantify the accuracy of relations under both sets and discuss their applicability with respect to expected upcoming statistical uncertainties of astrophysical observations. We further propose a goodness-of-fit metric which provides an estimate for the systematic error introduced by using the relation to model a certain equation-of-state set. Overall, the nonparametric distribution is more poorly fit with existing relations, with the I–Love–Q relations retaining the highest degree of universality. Fits degrade for relations involving the tidal deformability, such as the binary-Love and compactness-Love relations, and when introducing phase transition phenomenology. For most relations, systematic errors are comparable to current statistical uncertainties under the nonparametric equation of state distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

Here, we investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A system identification approach for non-intrusive reduced order modeling of radiation-induced photocurrents

In this study, development of compact photocurrent models is currently dominated by analytical techniques that rely on physical assumptions to render the governing equations solvable in a closed form. Violation of these assumptions can reduce the accuracy of the models and/or limit their scope. In this paper we show that system identification of nonlinear state-space systems can serve as an alternative numerical basis for non-intrusive reduced order modeling of photocurrent effects. To that end we develop a compact gray box photocurrent model (GBPM) by using a state-space representation with a low-dimensional latent state equation that mimics a mathematical model for the response of an idealized class of devices to ionizing radiation. In so doing we obtain a model that learns the dynamics of a quantity of interest directly from its measurements without requiring snapshots of the internal device state or its discretized model, and can be inferred from very small data sets. To demonstrate the approach we train the GBPM using a small experimental data set for a Z5236 Zener diode and a small synthetic data set obtained by simulating a synthetic pn-junction device. We then compare the GBPMs with black box models trained on the same data and show that performance of the latter is limited by the size of the data set, while the former are able to achieve excellent performance in both the reproductive and the predictive regimes.

97 MATHEMATICS AND COMPUTING↗