Search NASA⌕ Search

SEARCH · Search NASA

Results for “nonlinear mappings”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗
DOE OSTI2024

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗
DOE OSTI2024

Accelerating uncertainty quantification in incremental dynamic analysis using dimension reduction-based surrogate modeling

We propose a surrogate modeling framework based on dimension reduction to facilitate the quantification of seismic risk of structural systems in performance-based earthquake engineering. The framework adopts incremental dynamic analysis (IDA) for addressing hazard variability, and promotes significant computational efficiency improvement for propagating epistemic uncertainties associated with the structural models. It utilizes both linear and nonlinear dimension reduction approaches, equipped with inverse mappings, to learn a functional between the input parameter space (e.g., the epistemic uncertainties of the structure) to the high-dimensional output space created through the IDA implementation across different ground motions and seismic intensity levels. Polynomial chaos expansion is adopted as the surrogate model to learn this functional in the reduced space. A nine-story steel moment-resisting frame with uncertain structural properties is used as a testbed. Furthermore, we select the seismic fragility curves as a measure of the structure’s seismic performance, since it provides an estimate of the probability of entering specified damage states for given levels of ground shaking.

42 ENGINEERING↗
DOE OSTI2021

Nonlinear nanoelectrodynamics of a Weyl metal

Chiral Weyl fermions with linear energy-momentum dispersion in the bulk accompanied by Fermi-arc states on the surfaces prompt a host of enticing optical effects. While new Weyl semimetal materials keep emerging, the available optical probes are limited. In particular, isolating bulk and surface electrodynamics in Weyl conductors remains a challenge. We devised an approach to the problem based on near-field photocurrent imaging at the nanoscale and applied this technique to a prototypical Weyl semimetal TaIrTe 4 . As a first step, we visualized nano-photocurrent patterns in real space and demonstrated their connection to bulk nonlinear conductivity tensors through extensive modeling augmented with density functional theory calculations. Notably, our nanoscale probe gives access to not only the in-plane but also the out-of-plane electric fields so that it is feasible to interrogate all allowed nonlinear tensors including those that remained dormant in conventional far-field optics. Surface- and bulk-related nonlinear contributions are distinguished through their “symmetry fingerprints” in the photocurrent maps. Robust photocurrents also appear at mirror-symmetry breaking edges of TaIrTe 4 single crystals that we assign to nonlinear conductivity tensors forbidden in the bulk. Here, nano-photocurrent spectroscopy at the boundary reveals a strong resonance structure absent in the interior of the sample, providing evidence for elusive surface states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum computing for fusion energy science applications

This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron–Frobenius evolution operator, and the Koopman–von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendixes. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave–particle interactions through the simulation of quantum maps and of wave–wave interactions important in nonlinear plasma dynamics.

Joseph, I. (ORCID:0000000255400840)↗
DOE OSTI2020

Inversion of Time-Lapse Seismic Reservoir Monitoring Data Using CycleGAN: A Deep Learning-Based Approach for Estimating Dynamic Reservoir Property Changes

Carbon capture and storage is being pursued globally as a geoengineering measure for reducing the emission of anthropogenic CO 2 the atmosphere. Comprehensive monitoring, verification, and accounting programs must be established for demonstrating the safe storage of injected CO 2 . One of the most commonly deployed monitoring techniques is time-lapse seismic reservoir monitoring (also known as 4-D seismic), which involves comparing 3-D seismic survey data taken at the same study site but over different times. Analyses of 4-D seismic data volumes can help improve the quality of storage reservoir characterization, track the movement of injected CO 2 plume, and identify potential CO 2 spillover/leakage from the storage reservoirblue. However, the derivation of high-resolution CO 2 saturation maps from 4-D seismic data is a highly nonlinear and ill-posed inverse problem, often requiring significant computational effort. In this research, we apply a physics-based deep learning method to facilitate the solution of both the forward and inverse problems in seismic inversion while honoring physical constraints. A cycle generative adversarial neural network (CycleGAN) model is trained to learn the bidirectional functional mappings between the reservoir dynamic property changes and seismic attribute changes, such that both forward and inverse solutions can be obtained efficiently from the trained model. We show that our CycleGAN-based approach not only improves the reliability of 4-D seismic inversion but also expedites the quantitative interpretation. Our deep learning-based workflow is generic and can be readily used for reservoir characterization and reservoir model updates involving the use of 4-D seismic data.

58 GEOSCIENCES↗
DOE OSTI2023

Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons

We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton–polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light–matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton–phonon coupling among polariton states due to the strong light–matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Spectral interferometry-based microwave-frequency vibrometry for integrated acoustic wave devices

Microwave phononics is a promising platform for sensing, computing, and quantum information science; thus, sensitive and high-throughput characterization tools are needed not only for device verification and optimization but also for revealing transient and nonlinear dynamics. Existing interferometric optical vibrometers for 2D mapping are challenged by operating point stabilization, surface reflectivity contrast, and long acquisition time. Here, we use spectral interferometry, which is insensitive to these factors and utilizes a continuous raster scanning scheme for vibration mapping with high throughput. We intensity-modulate our broadband light source with an electro-optic modulator to resolve vibrations at microwave frequencies. Our system requires no fast photodetector or digitizer operating in the microwave frequency range. We image the 1 GHz vibration field of a 300 × 150 µm 2 area of an entire surface acoustic wave device in 10 min with simultaneous surface profilometry. Our system has a vibration sensitivity of 120 fm/sqrt(Hz) and a linear throughput of 0.77 mm/s on the chip surface. The technique offers capabilities for characterizing a wide range of acoustic wave and micromechanical devices to better understand their behavior and performance.

47 OTHER INSTRUMENTATION↗
NASA NTRS1988

Effects of joints in truss structures

The response of truss-type structures for future space applications, such as Large Deployable Reflector (LDR), will be directly affected by joint performance. Some of the objectives of research at BAC were to characterize structural joints, establish analytical approaches that incorporate joint characteristics, and experimentally establish the validity of the analytical approaches. The test approach to characterize joints for both erectable and deployable-type structures was based upon a Force State Mapping Technique. The approach pictorially shows how the nonlinear joint results can be used for equivalent linear analysis. Testing of the Space Station joints developed at LaRC (a hinged joint at 2 Hz and a clevis joint at 2 Hz) successfully revealed the nonlinear characteristics of the joints. The Space Station joints were effectively linear when loaded to plus or minus 500 pounds with a corresponding displacement of about plus or minus 0.0015 inch. It was indicated that good linear joints exist which are compatible with errected structures, but that difficulty may be encountered if nonlinear-type joints are incorporated in the structure.

Ikegami, R.↗
NASA NTRS1988

System Turns SAR Images Into Maps

Postprocessing system for synthetic-aperture radar (SAR) transforms raw images from natural rotated and distorted SAR reference frame into geocoded images. Images automatically corrected to remove slant-range nonlinearities and Doppler skew. Produces multiple-frame mosaics for large-scale mapping. Does not require tedious manual registration of representative "tie" points in raw SAR imagery with known locations on Earth.

Curlander, J. C.↗
NASA NTRS2008

Tide Corrections for Coastal Altimetry: Status and Prospects

Knowledge of global oceanic tides has markedly advanced over the last two decades, in no small part because of the near-global measurements provided by satellite altimeters, and especially the long and precise Topex/Poseidon time series e.g. [2]. Satellite altimetry in turn places very severe demands on the accuracy of tidal models. The reason is clear: tides are by far the largest contributor to the variance of sea-surface elevation, so any study of non-tidal ocean signals requires removal of this dominant tidal component. Efforts toward improving models for altimetric tide corrections have understandably focused on deep-water, open-ocean regions. These efforts have produced models thought to be generally accurate to about 2 cm rms. Corresponding tide predictions in shelf and near-coastal regions, however, are far less accurate. This paper discusses the status of our current abilities to provide near-global tidal predictions in shelf and near-coastal waters, highlights some of the difficulties that must be overcome, and attempts to divine a path toward some degree of progress. There are, of course, many groups worldwide who model tides over fairly localized shallow-water regions, and such work is extremely valuable for any altimeter study limited to those regions, but this paper considers the more global models necessary for the general user. There have indeed been efforts to patch local and global models together, but such work is difficult to maintain over many updates and can often encounter problems of proprietary or political nature. Such a path, however, might yet prove the most fruitful, and there are now new plans afoot to try again. As is well known, tides in shallow waters tend to be large, possibly nonlinear, and high wavenumber. The short spatial scales mean that current mapping capabilities with (multiple) nadir-oriented altimeters often yield inadequate coverage. This necessitates added reliance on numerical hydrodynamic models and data assimilation, which in turn necessitates very accurate bathymetry with high spatial resolution. Nonlinearity means that many additional compound tides and overtides must be accounted for in our predictions, which increases the degree of modeling effort and increases the amounts of data required to disentangle closely aliased tides.

Ray, Richard D.↗
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

Control of the NASA Langley 16-Foot Transonic Tunnel with the Self-Organizing Map

A predictive, multiple model control strategy is developed based on an ensemble of local linear models of the nonlinear system dynamics for a transonic wind tunnel. The local linear models are estimated directly from the weights of a self-organizing map (SOM). Multiple self-organizing maps collectively model the global response of the wind tunnel to a finite set of representative prototype controls. These prototype controls partition the control space and incorporate experiential knowledge gained from decades of operation. Each SOM models the combination of the tunnel with one of the representative controls, over the entire range of operation. The SOM based linear models are used to predict the tunnel response to a larger family of control sequences which are clustered on the representative prototypes. The control sequence which corresponds to the prediction that best satisfies the requirements on the system output is applied as the external driving signal.

Mark A. Motter↗
DOE OSTI2022

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO 2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10 6 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

Nonlinear Internal Waves in the South China Sea During ASIAEX

Internal wave distribution maps have been compiled from more than one hundred ERS-1/2, RADARSAT and Space Shuttle SAR images in the South China Sea (SCS) from 1993 to 2000. Based on these distribution maps, most of internal waves in the northeast part of SCS were propagating westward. The wave crest can be as long as 200 km with amplitude of 100 m, due to strong current from the Kuroshio branching out into the SCS. In recent Asian Seas International Acoustics Experiment (ASIAEX), moorings have been deployed in April 2000 and May 2001. Simultaneous RADARSAT ScanSAR images have been collected during the field test to integrate with the model and the in-situ measurements in the SCS. During ASIAEX in May 2001, many large internal waves were observed at the test area and were the major features for acoustic volume interaction. The environmental parameters have been calculated based on extensive CTD castings and mooring data. Nonlinear internal wave models have been applied to simulate the wave evolution on the continental shelf and the results compare reasonably with mooring measurements. The evolution and dissipation of huge internal waves on the shelf break, mode-two waves, elevation waves, and wave-wave interaction are very important issues for acoustic propagation. The implication of internal wave effects on acoustic propagation will also be discussed.

ACOUSTIC PROPAGATION↗
DOE OSTI2025

Neural operators for stochastic modeling of nonlinear structural system response to natural hazards

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators capable of mapping infinite-dimensional function spaces. Here, in this work, we employ two state-of-the-art neural operators, the deep operator network (DeepONet) and the Fourier neural operator (FNO) for the prediction of the nonlinear time history response of structural systems exposed to natural hazards, such as earthquakes and windstorms. Specifically, we propose two architectures, a self-adaptive FNO and a fast Fourier transform-based DeepONet (DeepFNOnet), where we employ a FNO beyond the DeepONet to learn the discrepancy between the ground truth and the solution predicted by the DeepONet. To demonstrate the efficiency and applicability of the architectures, two problems are considered. In the first, we use the proposed model to predict the seismic nonlinear dynamic response of a six-story shear building subject to stochastic ground motions. In the second problem, we employ the operators to predict the wind-induced nonlinear dynamic response of a high-rise building while explicitly accounting for the stochastic nature of the wind excitation. In both cases, the trained metamodels achieve high accuracy while being orders of magnitude faster than their corresponding high-fidelity models.

DeepONet↗
DOE OSTI2024

A nonlinear journey from structural phase transitions to quantum annealing

Motivated by an exact mapping between equilibrium properties of a one-dimensional chain of quantum Ising spins in a transverse field (the transverse field Ising (TFI) model) and a two-dimensional classical array of particles in double-well potentials (the “$\phi$ 4 model”) with weak inter-chain coupling, we explore connections between the driven variants of the two systems. Here, we argue that coupling between the fundamental topological solitary waves in the form of kinks between neighboring chains in the classical $\phi$ 4 system is the analog of the competing effect of the transverse field on spin flips in the quantum TFI model. As an example application, we mimic simplified measurement protocols in a closed quantum model system by studying the classical $\phi$ 4 model subjected to periodic perturbations. This reveals memory/loss of memory and coherence/decoherence regimes, whose quantum analogs are essential in annealing phenomena. In particular, we examine regimes where the topological excitations control the thermal equilibration following perturbations. This paves the way for further explorations of the analogy between lower-dimensional linear quantum and higher-dimensional classical nonlinear systems.

74 ATOMIC AND MOLECULAR PHYSICS↗