Results for “parametric model dependence”

DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

Mixture Models for Dependent Observations

Parametric mixture models appropriate for data presented in homogeneous blocks of varying sizes from several unidentified source populations are considered. For most applications, the data elements within each block are dependent. Models are proposed for multivariate normal data incorporating two types of dependence, exchangeability of elements within blocks, and a Markov structure for blocks. The consequences of assuming exchangeability, when in fact the Markov structure holds, are explored. Computational problems for each model are considered, and results of a simple test of the exchangeability hypothesis for LANDSAT data are presented.

Peters, C.↗

DOE OSTI2024

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗

NASA NTRS1990

Collisionless drift-tearing modes in the magnetopause

The linear stability properties of collisionless drift-tearing modes are analyzed in a modified Harris equilibrium model of the magnetopause. Particular attention is paid to the relevance of the parametric behavior of growth rates to the 'magnetic percolation' theory of flux transfer event formation (Galeev et al., 1986). Numerical methods are used to solve the drift-tearing eigenmode equations and the results are compared with those previously obtained by analytical methods. The analytical results are found to correctly model important parametric dependencies but to typically overestimate the rate of growth. The eigenmode equations are numerically difficult, and an integration scheme utilizing Ricatti transforms is developed to affect their solution.

Gladd, N. T.↗

NASA NTRS2018

Preliminary Error Characterization and Parametric Error Model for the Automatic Dependent Surveillance - Contract Extended Projected Profile Message

A critical component of Trajectory-Based Operations (TBO) is the ability for a consistent and accurate 4-dimensional trajectory (4DT) to be shared and synchronized between airborne and ground systems as well as amongst various ground automation systems. The Aeronautical Telecommunication Network—Baseline 2 (ATN-B2) standard defines the Extended Projected Profile (EPP) trajectory that can be sent via Automatic Dependent Surveillance-Contract (ADS-C) from an aircraft to ground automation. The EPP trajectory message contains a representation of the reference trajectory from an aircraft’s Flight Management System (FMS). In this work, a set of scenarios were run in a high-fidelity aircraft and FMS simulation to perform an initial characterization of EPP trajectory errors under a given set of conditions. The parameters investigated were the route length, route type, wind magnitude error, wind direction error, and with and without a required time-of-arrival (RTA) constraint. In addition, linear regression was used to identify a set of EPP error models for the cross-track, vertical, and time errors.

Guerreiro, Nelson M.↗

DOE OSTI2023

Region and cloud regime dependence of parametric sensitivity in E3SM atmosphere model

Abstract The Department of Energy (DOE)’s Energy Exascale Earth System Model (E3SM), including its atmosphere model (EAM), has many relatively new features. In a previous study we conducted a systematic parametric sensitivity analysis for EAM based on short, perturbed parameter ensemble (PPE) simulations, mainly focusing on global mean climate features and metrics. While parameter values in global climate models are generally invariant in space and time, model response to parameters perturbation may vary by regions and climate regimes, which motivates the need to better understand the EAM model behaviors and physics at regional scale and process level. In this study, using the same set of PPE simulations and a similar sensitivity analysis framework, we identify parameters that cause largest sensitivities over different regions and compare model responses in fast atmospheric processes to the parameters across different cloud regimes for several important cloud-related fidelity metrics. We find that cloud forcing has opposite response to some parameters over mid-latitude vs. tropical land. We also analyze how the parametric sensitivity varies as stratocumulus transitions to shallow convection and to deep convection over ocean. Low cloud forcing and shortwave cloud forcing in the subtropical eastern Pacific are most sensitive to the parameters controlling the width of the probability density function (PDF) of the subgrid vertical velocity ( w’ ) ( gamma ) and the damping of the w’ skewness ( c8 ) near the coast but become more sensitive to the parameter affecting the damping of the w’ variance ( c1 ) further offshore. Detailed interpretation of the spatial dependence of parametric sensitivity is provided. We also investigate how the parametric sensitivity evolves with prediction duration. This study improves our process-level understanding of cloud physics and parameterization and provides insights for developing more advanced regime-aware parameterization schemes in global climate model.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Enhanced shear stabilization of turbulence in NSTX

In studying a particular non-stationary NSTX L-mode plasma, we observed unexpectedly high levels of flux—first with quasilinear (TGLF) modeling and subsequently with nonlinear gyrokinetic simulations. Upon more detailed analysis, a novel confinement regime was discovered in which a modest increase in E x B shear (beyond baseline experimental estimates) rapidly reduced turbulent transport to levels consistent with power balance. This modest increase is plausible given the errors inherent to the estimation of shearing rates, and the added complexity of the non-stationary (time-dependent) power balance. Remarkably, an additional small increase in shear yields the familiar ion-neoclassical transport level with what appears to be the onset of high-k electron transport only. Although analyses using the TGLF-SAT2 model successfully capture numerous parametric dependencies of this plasma, TGLF does not reproduce the rapid E x B stabilization seen in CGYRO. We believe the results presented should help to better characterize the nonlinear physics of spherical tokamak confinement regimes, provide useful ST datasets for reduced model development, and motivate more accurate experimental diagnosis of E x B shearing rates.

Atomic and molecular collisions↗

DOE OSTI2025

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Nguyen, Ngoc Cuong [Center for Computational Engin↗

NASA NTRS1992

Dynamic (computer) modelling of the particulate environment: Transformations from the LDEF reference frame to decode geocentric and interplanetary populations

The Long Duration Exposure Facility (LDEF) impact signature record and the size frequency distribution of craters and perforations offers a unique record of environmental data referenced conveniently to the geocentric reference frame. Chemical analysis of residues can offer only limited assistance. Hence, flux modeling has been developed to transform both geocentric orbital distributions and geocentrically unbounded interplanetary source distributions. This is applied to the foil and crater penetration records in the Ram (E), Trailing (W), and Space Pointing directions to offer the means of decoding the records. It shows that the mix of the components is size dependent. Parametric forms of the modeling transformations are presented for the orbital and unbounded populations.

Mcdonnell, J. A. M.↗

NASA NTRS1991

Dynamic (computer) modelling of the particulate environment: Transformations from the LDEF reference frame to decode geocentric and interplanetary populations

The Long Duration Exposure Facility's impact signature record and the size frequency distribution of craters and perforations offers a unique record of environmental data referenced conveniently to the geocentric reference frame. Chemical analysis of residues can offer only limited assistance. Hence, flux modelling has been developed to transform from both geocentric orbital distributions and geocentrically unbounded interplanetary source distributions. This is applied to the foil and crater penetration records in the Ram (E), Trailing (W), and Space Pointing directions to offer the means of decoding the records. It shows that the mix of the components is size dependent. Parametric forms of the modelling transformations are presented for the orbital and unbound populations.

Mcdonnell, J. A. M.↗

DOE OSTI2025

Direct local parametrization of nuclear state densities using the back-shifted Bethe formula

Level densities are often parametrized using the back-shifted Bethe formula (BBF) for nuclei that possess experimental data for s-wave neutron resonance average spacings and a complete discrete level sequence at low excitation energies. However, these parametrizations require the additional modeling of the dependence of the spin-cutoff parameter on excitation energy. Here, in this work, we avoid the need to model the spin distribution of level densities by using the experimental data to parametrize directly the state densities, for which the BBF does not depend on the spin-cutoff parameter. This approach allows for a local parameterization of state densities that is independent of the spin-cutoff parameter. We provide these parameters in a tabulated form for applications in nuclear reaction calculations and for testing microscopic approaches to state densities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1977

Modeling of spacecraft charging

Three types of modeling of spacecraft charging are discussed: statistical models, parametric models, and physical models. Local time dependence of circuit upset for DoD and communication satellites, and electron current to a sphere with an assumed Debye potential distribution are presented. Four regions were involved in spacecraft charging: (1) undisturbed plasma, (2) plasma sheath region, (3) spacecraft surface, and (4) spacecraft equivalent circuit.

Whipple, E. C., Jr.↗

NASA NTRS1998

Global Nonlinear Parametric Modeling with Application to F-16 Aerodynamics

A global nonlinear parametric modeling technique is described and demonstrated. The technique uses multivariate orthogonal modeling functions generated from the data to determine nonlinear model structure, then expands each retained modeling function into an ordinary multivariate polynomial. The final model form is a finite multivariate power series expansion for the dependent variable in terms of the independent variables. Partial derivatives of the identified models can be used to assemble globally valid linear parameter varying models. The technique is demonstrated by identifying global nonlinear parametric models for nondimensional aerodynamic force and moment coefficients from a subsonic wind tunnel database for the F-16 fighter aircraft. Results show less than 10% difference between wind tunnel aerodynamic data and the nonlinear parameterized model for a simulated doublet maneuver at moderate angle of attack. Analysis indicated that the global nonlinear parametric models adequately captured the multivariate nonlinear aerodynamic functional dependence.

Morelli, Eugene A.↗

NASA NTRS1997

Global Nonlinear Parametric Modeling with Application to F-16 Aerodynamics

A global nonlinear parametric modeling technique is described and demonstrated. The technique uses multivariate orthogonal modeling functions generated from the data to determine nonlinear model structure, then expands each retained modeling function into an ordinary multivariate polynomial. The final model form is a finite multivariate power series expansion for the dependent variable in terms of the independent variables. Partial derivatives of the identified models can be used to assemble globally valid linear parameter varying models. The technique is demonstrated by identifying global nonlinear parametric models for nondimensional aerodynamic force and moment coefficients from a subsonic wind tunnel database for the F-16 fighter aircraft. Results show less than 10% difference between wind tunnel aerodynamic data and the nonlinear parameterized model for a simulated doublet maneuver at moderate angle of attack. Analysis indicated that the global nonlinear parametric models adequately captured the multivariate nonlinear aerodynamic functional dependence.

Morelli, Eugene A.↗

DOE OSTI2026

Coherent and Dynamic Small Polaron Delocalization in CuFeO 2

Small polarons remain a bottleneck in realizing efficient transition metal oxide devices. Routes to engineer small polaron coupling to electronic states and lattice modes to control carrier localization remain unclear. Here, we measure small polaron formation in CuFeO 2 using transient extreme ultraviolet reflection spectroscopy and compare to theoretical predictions in realistically parametrized Holstein models, demonstrating that polaron localization depends on coupling to high-frequency versus low-frequency phonon bath components. We measure small polaron formation on a comparable ∼100 fs timescale to other Fe(III) compounds. Dynamic delocalization of the polaron follows formation through a coherent lattice expansion between Fe–O layers and charge-sharing with surrounding Fe(IV) states. Simulations reveal two major factors dictate polaron formation timescales: phonon density and reorganization energy distributions between acoustic and optical modes, matching experimental findings. Our work shows how electronic-structural coupling in a polaron-host material can be leveraged to suppress polaronic effects for various applications.

Hematite↗

NASA NTRS2015

Exploring Life Support Architectures for Evolution of Deep Space Human Exploration

Life support system architectures for long duration space missions are often explored analytically in the human spaceflight community to find optimum solutions for mass, performance, and reliability. But in reality, many other constraints can guide the design when the life support system is examined within the context of an overall vehicle, as well as specific programmatic goals and needs. Between the end of the Constellation program and the development of the "Evolvable Mars Campaign", NASA explored a broad range of mission possibilities. Most of these missions will never be implemented but the lessons learned during these concept development phases may color and guide future analytical studies and eventual life support system architectures. This paper discusses several iterations of design studies from the life support system perspective to examine which requirements and assumptions, programmatic needs, or interfaces drive design. When doing early concept studies, many assumptions have to be made about technology and operations. Data can be pulled from a variety of sources depending on the study needs, including parametric models, historical data, new technologies, and even predictive analysis. In the end, assumptions must be made in the face of uncertainty. Some of these may introduce more risk as to whether the solution for the conceptual design study will still work when designs mature and data becomes available.

Anderson, Molly↗

NASA NTRS2015

Exploring Life Support Architectures for Evolution of Deep Space Human Exploration

Life support system architectures for long duration space missions are often explored analytically in the human spaceflight community to find optimum solutions for mass, performance, and reliability. But in reality, many other constraints can guide the design when the life support system is examined within the context of an overall vehicle, as well as specific programmatic goals and needs. Between the end of the Constellation program and the development of the "Evolvable Mars Campaign", NASA explored a broad range of mission possibilities. Most of these missions will never be implemented but the lessons learned during these concept development phases may color and guide future analytical studies and eventual life support system architectures. This paper discusses several iterations of design studies from the life support system perspective to examine which requirements and assumptions, programmatic needs, or interfaces drive design. When doing early concept studies, many assumptions have to be made about technology and operations. Data can be pulled from a variety of sources depending on the study needs, including parametric models, historical data, new technologies, and even predictive analysis. In the end, assumptions must be made in the face of uncertainty. Some of these may introduce more risk as to whether the solution for the conceptual design study will still work when designs mature and data becomes available.

Anderson, Molly S.↗

NASA NTRS2012

The Effects of B/L-Dependent Heating on the Formation and Evolution of a Multi-Threaded Prominence

We have developed a comprehensive, multi-threaded, three-dimensional model of the plasma dynamics and energetics of a prominence and its overlying arcade (Luna et al. 2012). In this model, the basic magnetic structure is that of two interacting sheared arcades, while the cool condensations composing the prominence are formed by the well-studied thermal nonequilibrium mechanism. In a given filament-channel flux tube, the mass is evaporated from the chromosphere by heating localized near the footpoints, and condenses in the form of transient blobs or a persistent thread. Our previous studies of thermal nonequilibrium used steady or impulsive heating functions with no dependence on local physical. However, parametric active-region models with steady heating proportional to B/L, where B is the flux-tube magnetic field strength at each footpoint and L is the flux-tube length, yield the best agreement with observations (e.g., Schrijver et al. 2008). We have determined the effects of this active-region heating function on our model for the formation and evolution of prominence mass. We have also expanded the range of our computational domain to include more ofthe overlying arcade (the so-called "cavity") than in Luna et al. (2012), and have increased the number of selected flux tubes from 125 to 533. We will illustrate the time-dependent plasma behavior produced by the B/L heating function with synthetic images in several ALA passbands, and compare the resulting prominence properties with those predicted by our model with steady heating.

Karpen, Judith T.↗