Search NASA⌕ Search

SEARCH · Search NASA

Results for “nonlinear modeling”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Erratum: “Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD” [Phys. Plasmas 24, 052508 (2017)]

The linear layer response time is evaluated inappropriately in Ref. 1. This affects analytic predictions for linear and quasilinear magnetic field penetration due to a resonant, externally applied field according to Eqs. (14) and (19) of Ref. 1, respectively. The linear layer response time for the visco-resistive regime is given according to Ref. 2 as $τ_{VR}$ =2.104$τ_{shA}$S$^{2/3}_{sh}$P$^{1/6}_{m}$, where $τ_{shA}$ ≡ $τ_A$/$k_ya$ is the local shear Alfvén time at the rational surface (called the local hydromagnetic time $τ_H$ in Ref. 2) and S sh =$Sk_ya$ is the local Lundquist number. However, Ref. 1 inadvertently omits the factor of $k_y$a in $τ_{shA}$, evaluating $τ_{VR}$ using the Alfvén time τA based on the sheared magnetic field strength at the computation boundary. The proper evaluation of $τ_{VR}$ results in a linear layer response time that is ($k_ya$) 1/3 =π -1/3 ≃0.68 shorter than that in Ref. 1. The value of the time $τ'_{VR}$ used to predict quasilinear equilibria according to Eq. (19) is shorter by the same factor. Using the correct value of $τ_{VR}$ has a direct effect on analytic predictions for the magnitude and phase of the linear penetrated field, consistent with Eq. (14) in Ref. 1. Figure 1 replaces Fig. 5 of Ref. 1, exhibiting even better agreement between NIMROD computations and analytic predictions. The highest percent difference in penetrated field magnitude is 11% and in phase is 8%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗