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Results for “reduced basis method”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Application of the reduced basis method to nonlinear transient thermal analysis

An effort to apply the reduced basis method to nonlinear transient thermal analysis is described. The method combines the classical Rayleigh-Ritz and modal superposition techniques with contemporary finite element methods to retain modeling versatility as the degrees of freedom in a problem are reduced. The essence of the method is to use a few thermal modes from eigenvalue analyses as basis vectors to represent the temperature response for a given thermal problem similar to the use of vibration modes to represent displacements in a dynamic response problem. Approximate temperature distributions were obtained using the reduced basis method for a small section of the Shuttle Orbiter lower wing undergoing reentry heating. Good agreement was obtained between the reduced basis method solutions and full system solutions with reductions in the degrees of freedom of up to a factor of four. The good agreement indicates the reduced basis method has the potential for significant reduction in computing effort for thermal analysis; however, considerable work remains to determine techniques for selecting the type and number of basis vectors needed for approximate solutions to more complex transient thermal problems.

Shore, C. P.↗
DOE OSTI2022

Training and projecting: A reduced basis method emulator for many-body physics

Here, we present the reduced basis method as a tool for developing emulators for equations with tun able parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few values of the model parameters and then projects the equations over a well-chosen low-dimensional subspace. We connect some of the results in the eigenvector continuation literature to the formalism of reduced basis methods and show how these methods can be applied to a broad set of problems. As we illustrate, the possible success of the formalism on such problems can be diagnosed beforehand by a principal component analysis. We apply the reduced basis method to the one-dimensional Gross-Pitaevskii equation with a harmonic trap ping potential and to nuclear density functional theory for 48 Ca, achieving speed-ups of more than x150 and x250, respectively, when compared to traditional solvers. The outstanding performance of the approach, together with its straightforward implementation, show promise for its application to the emulation of computationally demanding calculations, including uncertainty quantification.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Applications of reduced-basis methods to the nuclear single-particle spectrum

Reduced-basis methods provide a powerful framework for building efficient and accurate emulators. Although widely applied in many fields to simplify complex models, reduced-basis methods have only been recently introduced into nuclear physics. In this Letter we build an emulator to study the single-particle structure of atomic nuclei. By scaling a suitable mean-field Hamiltonian, a “universal” reduced basis is constructed capable of accurately and efficiently reproduce the entire single-particle spectrum of a variety of nuclei. Indeed, the reduced-basis model reproduces both ground- and excited-state energies as well as the associated wave functions with remarkable accuracy. Here our results bode well for more demanding applications that use Bayesian optimization to calibrate nuclear energy density functionals.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

Comparison of advanced reduced-basis methods for transient structural analysis

Two advanced reduced-basis methods for linear, transient structural analysis, the force-derivative method and the Lanczos method, are compared to two widely-used modal methods, the mode-displacement method and the mode-acceleration method. Comparisons are made for two linear example problems: a proportionally-damped cantilevered beam subject to a discrete tip load which varies linearly with time, and a discretely-damped multispan beam subject to a uniformly distributed load which varies as a quintic function of time. Results from the methods are compared in terms of the number of basis vectors required to obtain a desired level of accuracy and the associated computational times. The results are problem dependent, and it is shown that for the cantilevered beam problem, the mode-acceleration and force-derivative methods are the most efficient in terms of the number of basis vectors and computational time. The force-derivative method is shown to be the most effective method for solving the multispan beam problem with closely-spaced frequencies. In general, the force-derivative method is shown to produce an accurate solution using very few basis vectors and to require less computational time as compared to the other methods studied.

Mcgowan, David M.↗
NASA NTRS1993

Development and comparison of advanced reduced-basis methods for the transient structural analysis of unconstrained structures

The development of two advanced reduced-basis methods, the force derivative method and the Lanczos method, and two widely used modal methods, the mode displacement method and the mode acceleration method, for transient structural analysis of unconstrained structures is presented. Two example structural problems are studied: an undamped, unconstrained beam subject to a uniformly distributed load which varies as a sinusoidal function of time and an undamped high-speed civil transport aircraft subject to a normal wing tip load which varies as a sinusoidal function of time. These example problems are used to verify the methods and to compare the relative effectiveness of each of the four reduced-basis methods for performing transient structural analyses on unconstrained structures. The methods are verified with a solution obtained by integrating directly the full system of equations of motion, and they are compared using the number of basis vectors required to obtain a desired level of accuracy and the associated computational times as comparison criteria.

Mcgowan, David M.↗
DOE OSTI2023

Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the calibration is enabled by the emulation of the high-fidelity model through the implementation of a reduced basis method (RBM)—a set of dimensionality reduction techniques that can speed up demanding calculations involving partial differential equations by several orders of magnitude. The RBM emulator we build—using only 100 evaluations of the high-fidelity model—is able to accurately reproduce the model calculations in tens of milliseconds on a personal computer, an increase in speed of nearly a factor of 3,300 when compared to the original solver. Besides the analysis of the posterior distribution of parameters, we present model calculations for masses and radii with properly estimated uncertainties. We also analyze the model correlation between the slope of the symmetry energy L and the neutron skin of 48 Ca and 208 Pb. The straightforward implementation and outstanding performance of the RBM makes it an ideal tool for assisting the nuclear theory community in providing reliable estimates with properly quantified uncertainties of physical observables. Such uncertainty quantification tools will become essential given the expected abundance of data from the recently inaugurated and future experimental and observational facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Reduced-basis method for few-body bound-state emulation

Recent advances in both theoretical and computational methods have enabled large-scale, precision calculations of the properties of atomic nuclei. With the growing complexity of modern nuclear theory, however, also comes the need for novel methods to perform systematic studies and quantify the uncertainties of models when confronted with experimental data. Here, this study presents an application of such an approach, the reduced basis method, to substantially lower computational costs by constructing a significantly smaller Hamiltonian subspace informed by previous solutions. Our method shows comparable efficiency and accuracy to other dimensionality reduction techniques on an artificial three-body bound system while providing a richer representation of physical information in its projection and training subspace. This methodological advancement can be applied in other contexts and has the potential to greatly improve our ability to systematically explore theoretical models and thus enhance our understanding of the fundamental properties of nuclear systems.

cluster models↗
NASA NTRS1982

Development of a reduced basis technique for transient thermal analysis

A technique to reduce the degrees of freedom in static and dynamic problems, the reduced basis method, is described. The method combines the classical Rayleigh-Ritz approximation with contemporary finite element methods to retain modeling versatility as the degrees of freedom are reduced. Applications to a nonlinear dynamic response problem are discussed efforts to apply the method to nonlinear transient thermal response problems are summarized. The selection of basis vectors for reducing the system of equations is addressed.

Shore, C. P.↗
NASA NTRS1974

Approximate techniques of structural reanalysis

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Noor, A. K.↗
DOE OSTI2025

Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description

Here, this work applies a reduced basis method to study the continuum physics of a finite quantum system—either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [Zhang, Phys. Rev. Lett. 135, 242501 (2025)], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.

ab initio calculations↗
DOE OSTI2024

Universal reduced basis for the calibration of covariant energy density functionals

The reduced basis method is used to construct a “universal” basis of Dirac orbitals that may be applicable throughout the nuclear chart to calibrate covariant energy density functionals. Relative to the successful development of a reduced basis emulator for the nonrelativistic Schrödinger equation, the Dirac equation adds an extra layer of complexity due to the existence of negative energy states, which complicates building an efficient reduced basis. However, once this problem is mitigated, the resulting reduced basis is able to accurately and efficiently reproduce the high-fidelity model at a fraction of the computational cost. We are confident that the resulting reduced basis will serve as a foundational element in developing rapid and accurate emulators. In turn, these emulators will play a critical role in the Bayesian optimization of covariant energy density functionals.

Bayesian methods↗
DOE OSTI2024

Colloquium: Eigenvector continuation and projection-based emulators

Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this Colloquium, the development, theory, and applications of eigenvector continuation and projection-based emulators are presented. In conclusion, the basic concepts are introduced, the underlying theory and convergence properties are discussed, and recent applications for quantum systems and future prospects are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗