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Results for “Linearity preservation”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Extraordinary Magnetic Response of an Anisotropic 2D Antiferromagnet via Site Dilution

A prominent characteristic of 2D magnetic systems is the enhanced spin fluctuations, which reduce the ordering temperature. We report that a magnetic field of only 1000th of the Heisenberg superexchange interaction can induce a crossover, which for practical purposes is the effective ordering transition, at temperatures about 6 times the Néel transition in a site-diluted two-dimensional anisotropic quantum antiferromagnet. Such a strong magnetic response is enabled because the system directly enters the antiferromagnetically ordered state from the isotropic disordered state, skipping the intermediate anisotropic stage. The underlying mechanism is achieved on a pseudospin-half square lattice realized in the [(SrIrO3)1/(SrTiO3)2] superlattice thin film that is designed to linearly couple the staggered magnetization to external magnetic fields by virtue of the rotational symmetry-preserving Dzyaloshinskii–Moriya interaction. Furthermore, our model analysis shows that the skipping of the anisotropic regime despite finite anisotropy is due to the enhanced isotropic fluctuations under moderate dilution.

2D antiferromagnet↗
DOE OSTI2021

Adiabatic matching of particle bunches in a plasma-based accelerator in the presence of ion motion

Witness beam stability and preservation of its ultra-low emittance have been identified as critical challenges toward realizing a TeV-class, plasma-based linear collider. In fact, the witness bunch parameters required by a future TeV-class collider have been expected to trigger hosing instability and background ion motion, leading to emittance degradation and, potentially, to bunch loss. Recently, it has been shown that ion motion suppresses the hosing instability, and proper longitudinal bunch shaping can eliminate the ion-motion-induced emittance growth. Here, we propose and analyze a plasma-based method to generate the shaped bunches that enable emittance preservation in the presence of ion motion. The method is based on an adiabatic matching procedure, where a bunch with an initially untapered profile is injected in the plasma accelerator stage with an energy low enough that ion motion effects are initially small. As the bunch accelerates, it is adiabatically compressed, ion motion is gradually triggered, and the bunch slowly but continuously readjusts itself in the ion motion-perturbed wakefield acquiring the desired taper. The production of tapered witness bunch profiles that minimize energy spread and preserve emittance for collider-relevant parameters could enable the use of plasma-based accelerators for high-energy physics applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗
DOE OSTI2022

Local bilinear computation of Jacobi sets

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Canonical and noncanonical Hamiltonian operator inference

Here, a method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems

Here, we propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Correspondingly, we prove two new universal approximation theorems that demonstrate that SympNets can approximate arbitrary symplectic maps based on appropriate activation functions. We then perform several experiments including the pendulum, double pendulum and three-body problems to investigate the expressivity and the generalization ability of SympNets. The simulation results show that even very small size SympNets can generalize well, and are able to handle both separable and non-separable Hamiltonian systems with data points resulting from short or long time steps. In all the test cases, SympNets outperform the baseline models, and are much faster in training and prediction. We also develop an extended version of SympNets to learn the dynamics from irregularly sampled data. This extended version of SympNets can be thought of as a universal model representing the solution to an arbitrary Hamiltonian system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Site-controlled telecom-wavelength single-photon emitters in atomically-thin MoTe2

Abstract Quantum emitters (QEs) in two-dimensional transition metal dichalcogenides (2D TMDCs) have advanced to the forefront of quantum communication and transduction research. To date, QEs capable of operating in O-C telecommunication bands have not been demonstrated in TMDCs. Here we report site-controlled creation of telecom QEs emitting over the 1080 to 1550 nm telecommunication wavelength range via coupling of 2D molybdenum ditelluride (MoTe 2 ) to strain inducing nano-pillar arrays. Hanbury Brown and Twiss experiments conducted at 10 K reveal clear photon antibunching with 90% single-photon purity. The photon antibunching can be observed up to liquid nitrogen temperature (77 K). Polarization analysis further reveals that while some QEs display cross-linearly polarized doublets with ~1 meV splitting resulting from the strain induced anisotropic exchange interaction, valley degeneracy is preserved in other QEs. Valley Zeeman splitting as well as restoring of valley symmetry in cross-polarized doublets are observed under 8 T magnetic field.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Transfer learning nonlinear plasma dynamic transitions in low dimensional embeddings via deep neural networks

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel, data-driven model reduction methods, coupled with detection of abnormal modes with plasma physics, opens a unique opportunity to identify plasma instabilities through automated construction of parsimonious models that can be tuned to balance accuracy and cost. Our fusion transfer learning (FTL) model demonstrates success in rapidly reconstructing nonlinear kink mode structures by learning from a limited amount of nonlinear simulation data. The knowledge transfer process leverages a pre-trained neural encoder–decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL’s capacity to capture transitional behaviors and dynamical features in plasma dynamics—a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

FTL: Transfer Learning Nonlinear Plasma Dynamic Transitions in Low Dimensional Embeddings (FTL) v1.0

Fusion Transfer Learning (FTL) model provides a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. The knowledge transfer process leverages a pre-trained neural encoder-decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL's capacity to capture transitional behaviors and dynamical features in plasma dynamics -- a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics (MHD) modes.

Bai, Zhe↗
DOE OSTI2022

Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis

ABSTRACT Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On non-linear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scalable Gaussian Processes, GPyTorch Application Benchmarking, and Targeted Adaptive Design (TAD) on ThetaGPU

We aim at showcasing the scalability of Gaussian Process (GP). The naive GP implementation scales cubically with data size, which can be prohibitive, so GP has not heretofore been considered suitable for very large-scale problem settings. We take advantage of GPyTorch, a library for scalable GPs built on top of PyTorch that incorporates GPU acceleration. With GPyTorch, one can achieve nearly linear scaling with structured kernel interpolation (SKI) and constant-time predictive covariances computation with LanczOs Variance Estimates (LOVE) while preserving accuracy. We also take advantage of the computational power of ThetaGPU, a supercomputer of Argonne Leadership Computing Facility (ALCF). In addition, we implement a scalable, GPU-ready version of Targeted Adaptive Design (TAD), a GP-based data-driven algorithm that efficiently searches the control space of an advanced manufacturing experiment for settings capable of producing a required design within a specified tolerance, despite the poorly known mapping from control settings to design. We finally show our benchmarking for GPyTorch and TAD performance on CPU vs. ThetaGPU and discuss the results and implications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Mass Spectrometer Transient Analysis

This software implements a complete preprocessing pipeline for transient mass spectrometry (MS) data collected during TAP (Temporal Analysis of Products) experiments. It is designed to extract chemically meaningful fluxes from overlapping ion signals by applying a calibrated defragmentation matrix and solving the resulting linear system using non-negative least squares (NNLS) regression. The core script, preprocess_mass_spec.py, performs the following operations: Gain correction: Applies amplifier gain scalars derived from inert-packed calibration pulses to normalize signal intensities across AMUs and acquisition settings. Background subtraction: Removes experiment baselines using user-defined time windows, ensuring compatibility with slow-diffusing species and preventing negative values that would interfere with NNLS. Options to subtract before and after defragmentation. Defragmentation: Constructs a fragmentation matrix A from zeroth moments of calibration pulses (equal molar gas:inert mixtures) and solves Ax=b at each time point, where b is the raw MS signal and x is the estimated species flux. The matrix is normalized to inert signals and accounts for instrument-specific fragmentation behavior. Pulse-mode handling: Supports both averaged and individual pulse modes, enabling statistical treatment of fluxes and calculation of standard deviations. Integration and output: Computes zeroth moments (integrated fluxes) and exports time-resolved and integrated data in CSV format, suitable for downstream kinetic modeling. The software is validated using both virtual TAP simulations (VTAP) and experimental data from propane dehydrogenation (PDH) on CrOx/Al2O3 catalysts. It preserves temporal resolution by applying NNLS point-by-point across the pulse duration (typically 6,000+ time slices per pulse), leveraging the linear superposition principle to reconstruct full flux profiles. The defragmented outputs are compatible with kinetic extraction methods such as the G and Y procedures, which are used to derive rate–concentration relationships from TAP data. The details of these validations are discussed in detail in the supporting manuscript and supporting information. Example data and output files are also included. The methodology is robust to experimental noise and drift, with calibration protocols that account for pulse size effects, MS aging, and inert gas normalization. The software is modular, reproducible, and tailored for high-throughput TAP-MS workflows in catalysis research.

Kristy, Stephen [Idaho National Laboratory (INL), ↗
DOE OSTI2023

Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering

A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other quantum critical systems. Here, we propose a one-dimensional (1D) model to capture key aspects of the 2D Dirac fluid while including lattice effects and being amenable to nonperturbative computation. When interactions are added to the Dirac-like 1D dispersion without opening a gap, we show that this kind of irrelevant interaction is able to preserve Fermi-liquid-like quasiparticle features while relaxing a zero-momentum charge current via collisions between particle-hole excitations, leading to resistivity that is linear in temperature via a mechanism previously discussed for large-diameter metallic carbon nanotubes. We further provide a microscopic lattice model and obtain numerical results via density-matrix renormalization group simulations, which support the above physical picture. The limits on such fast relaxation at strong coupling are of considerable interest because of the ubiquity of bad metals in experiments.

1-dimensional systems↗
DOE OSTI2025

Creation of Self-Semi-Interpenetrating Network Structures in PIM-1 Membranes for Enhanced Physical Aging Resistance

A series of self-semi-interpenetrating network (ssIPN) thin films based on PIM-1 structure were developed by end-cross-linking telechelic PIM-1 oligomers end-capped with curable carboxylic acid groups to form model networks, which are penetrated by linear high-molecular-weight PIM-1 chains. ssIPN films with systematically varied network content ranging from 10 to 30 wt % were comprehensively examined on their microstructure and gas permeation properties. Fresh PIM-1 ssIPN films exhibited gas separation performances close to those of as-cast linear PIM-1, where the films closely followed the upper bound trade-off line, gaining as much selectivity as they lose gas permeability as the network content increases. This indicates that gas permeability is largely preserved despite cross-linking. Wide-angle X-ray scattering supported this observation, with peaks shifting toward lower d-spacing as oligomer content increased, suggesting tighter chain packing with higher cross-linkable oligomer loading. In physical aging studies over two months, all ssIPN films outperform linear PIM-1 for H 2 /CH 4 and O 2 /N 2 separations. Notably, the PIM-1 ssIPN with 10 wt % network content showed the best physical aging resistance, with negligible permeability loss even after one month. Finally, these findings highlight a promising macromolecular strategy for enhancing the physical aging resistance of microporous polymer membranes for gas separation.

PIM-1↗