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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Banks, H. T.↗
NASA NTRS1980

A rapid method for the approximate determination of nonlinear solutions Application to aerodynamic flows

A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.

Stahara, S. S.↗
DOE OSTI2023

Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Recent advances in modeling large-scale, complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult. For these systems, often computationally inexpensive, but in general inaccurate models, known as the low-fidelity models, are available. Here in this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system's response and a low-fidelity response in the presence of a small training dataset from the true system's response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown physical systems.

MATHEMATICS AND COMPUTING↗
DOE OSTI2020

hp -VPINNs: Variational physics-informed neural networks with domain decomposition

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto the space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the entire computational domain, while the test space contains piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with a local learning algorithm that can efficiently localize the network parameter optimization. Here, we demonstrate the advantages of hp-VPINNs in both accuracy and training cost for several numerical examples of function approximation and in solving differential equations.

42 ENGINEERING↗
DOE OSTI2023

DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories

This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Bilinear dynamic mode decomposition for quantum control

Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian, Multifidelity Operator Learning for Complex Engineering Systems–A Position Paper

Abstract Deep learning has significantly improved the state-of-the-art in computer vision and natural language processing, and holds great potential to design effective tools for predicting and simulating complex engineering systems. In particular, scientific machine learning seeks to apply the power of deep learning to scientific and engineering tasks, with operator learning (OL) emerging as a particularly effective tool. OL can approximate nonlinear operators arising in complex engineering systems, making it useful for simulating, designing, and controlling those systems. In this position paper, we provide a comprehensive overview of OL, including its potential applications to complex engineering domains. We cover three variations of OL approaches: deterministic OL for modeling nonautonomous systems, OL with uncertainty quantification (UQ) capabilities, and multifidelity OL. For each variation, we discuss drawbacks and potential applications to engineering, in addition to providing a detailed explanation. We also highlight how multifidelity OL approaches with UQ capabilities can be used to design, optimize, and control engineering systems. Finally, we outline some potential challenges for OL within the engineering domain.

Computer Science↗
DOE OSTI2021

HAIMOS Ensemble Forecasts for Intra-day and Day- Ahead GHI, DNI and Ramps

The objective of this research is to develop a hybrid physics-based/data-driven forecast model to improve direct normal and global horizontal irradiance (DNI and GHI) prediction for horizons ranging from 1 to 72 hours. Project objectives also address key gaps in state-of-the-art solar forecasting: accurate probabilistic solar forecasts and the forecasting of large irradiance ramps (ramp onset and magnitude). The proposed model ensembles Numerical Weather Prediction (NWP) forecasts, determinist physics-based algorithms, and new-generation cloud cover products (high-resolution rapid refresh satellite images and Large Eddy Simulations). The result is the Hybrid Adaptive Input Model Objective Selection (HAIMOS) ensemble model. HAIMOS blends state of the art machine learning methodologies with physics-based models for cloud cover and cloud optical depth forecasts. The technical activities followed a two-pronged strategy. First, the preprocessing of data, the selection of inputs to the nonlinear approximators, the type of approximator and objective functions, and post-processing ensembling techniques included in HAIMOS were all optimized adaptively to find the best model for a specific goal (reduce DNI/GHI forecast error, improve the prediction of ramp onset, etc.). Second, a large effort was put in improving cloud identification and the forecast of cloud cover and cloud optical depth. To this end, new-generation cloud parametrization products were developed in this work. These include improved algorithms to assist in cloud identification, cloud classification and cloud parametrization from satellite images – three key factors in the accuracy of 1 to 6-hours irradiance forecasts and prediction of ramp onset. Furthermore, we also included cloud information extracted from high resolution rapid refresh satellite images (GOES-16) and Large Eddy Simulations (LES). LES was used to model the atmosphere in detail over locations of interest and produce cloud optical depth forecasts. Once these data streams were validated, they were used as input data to the HAIMOS forecast. The model was developed using data from several climatologically distinct locations with potential for high solar penetration. In the last year of the project, we conducted a validation campaign according to the guidelines stipulated by the Topic Area 1 project as described in the FOA. This effort brings, for the first time, proven machine-learning methodologies for generating state-of-the-art solar forecasts interweaved with detailed physics-based models for cloud detection, and cloud optical depth forecasts. HAIMOS will generate accurate irradiance probabilistic forecast to assist in reducing solar generation prediction error. Globally optimized solar forecast models are more likely to impact solar energy stakeholders. The goal of this project was to increase the state-of-the-art forecast skill from their present values of 10 to 35%. At the end of the project, we achieved between 30% and 50% forecast skill across a wide range of horizons for both GHI and DNI.

14 SOLAR ENERGY↗
DOE OSTI2022

Preconditioning for Hyper-reduction in Reduced Order Models

Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments

There is an increasing aspiration to utilize machine learning (ML) for various tasks of relevance to national security. ML models have thus far been mostly applied to tasks and domains that, while impactful, have sufficient volume of data. For predictive tasks of national security relevance, ML models of great capacity (ability to approximate nonlinear trends in input-output maps) are often needed to capture the complex underlying physics. However, scientific problems of relevance to national security are often accompanied by various sources of sparse and/or incomplete data, including experiments and simulations, across different regimes of operation, of varying degrees of fidelity, and include noise with different characteristics and/or intensity. State-of-the-art ML models, despite exhibiting superior performance on the task and domain they were trained on, may suffer detrimental loss in performance in such sparse data environments. This report summarizes the results of the Laboratory Directed Research and Development project entitled Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments. The objective of the project was to develop a new transfer learning (TL) framework that aims to adaptively blend the data across different sources in tackling one task of interest, resulting in enhanced trustworthiness of ML models for mission- and safety-critical systems. The proposed framework determines when it is worth applying TL and how much knowledge is to be transferred, despite uncontrollable uncertainties. The framework accomplishes this by leveraging concepts and techniques from the fields of Bayesian inverse modeling and uncertainty quantification, relying on strong mathematical foundations of probability and measure theories to devise new uncertainty-aware TL workflows.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Near optimum digital phase locked loops.

Near optimum digital phase locked loops are derived utilizing nonlinear estimation theory. Nonlinear approximations are employed to yield realizable loop structures. Baseband equivalent loop gains are derived which under high signal to noise ratio conditions may be calculated off-line. Additional simplifications are made which permit the application of the Kalman filter algorithms to determine the optimum loop filter. Performance is evaluated by a theoretical analysis and by simulation. Theoretical and simulated results are discussed and a comparison to analog results is made.

Polk, D. R.↗
NASA NTRS1973

An application of a linear programing technique to nonlinear minimax problems

A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.

Schiess, J. R.↗
NASA NTRS1979

A critical examination of stresses in an elastic single lap joint

The results of an approximate nonlinear finite-element analysis of a single lap joint are presented and compared with the results of a linear finite-element analysis, and the geometric nonlinear effects caused by the load-path eccentricity on the adhesive stress distributions are determined. The results from finite-element, Goland-Reissner, and photoelastic analyses show that for a single lap joint the effect of the geometric nonlinear behavior of the joint has a sizable effect on the stresses in the adhesive. The Goland-Reissner analysis is sufficiently accurate in the prediction of stresses along the midsurface of the adhesive bond to be used for qualitative evaluation of the influence of geometric or material parametric variations. Detailed stress distributions in both the adherend and adhesive obtained from the finite-element analysis are presented to provide a basis for comparison with other solution techniques.

Cooper, P. A.↗
NASA NTRS1979

Wave theory for microwave remote sensing of a half-space random medium with three-dimensional variations

The two-variable expansion technique is used to solve for the mean Green's functions from the Dyson equation under the nonlinear approximation for a half-space random medium with three-dimensional correlation functions. The Bethe-Salpeter equations are then solved under the ladder approximation. The radiative transfer equations, which have been applied extensively in the study of microwave remote sensing problems, are derived under these approximations. The limiting cases of large and small horizontal correlation lengths are discussed. It is found that there is only one propagation constant except for the case of large horizontal correlation lengths, in which there are two propagation constants. It is shown that boundary layer appears in first-order solutions and does not appear in zeroth-order solutions.

Tsang, L.↗
NASA NTRS1981

Mean dyadic Green's function for a two layer random medium

The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.

Zuniga, M. A.↗
NASA NTRS1983

Nonlinear effects of elastic coupling in unsymmetric laminates

Classical lamination theory predicts the room-temperature shape of all unsymmetrically laminated, elevated-temperature cure composites to be a saddle shape. Experimental observation indicates, however, that in many cases the room-temperature shape is cylindrical. In addition, a second cylindrical shape can often be obtained from the first by a simple snap-through action. It is the elastic couplings between inplane and out-of-plane deformations which are inherent in unsymmetric laminates that are responsible for the room-temperature shape. However, the couplings are so strong that geometrically nonlinear effects are produced. These are not accounted for in the classical theory. This paper reviews a theory developed to explain the effects of the coupling on laminate shape. The theory is based on a minimization of the laminate's total potential energy. The theory accounts for geometric nonlinearities. Because the problem is nonlinear, approximate solutions are sought by using a Rayleigh-Ritz procedure. Because of the observed snap-through of some laminates, stability of the predicted shapes is examined. Numerical results and some limited experimental data are presented for several laminates.

Hyer, M. W.↗
NASA NTRS1986

Soil/Structure Interactions in Earthquakes

In effort to improve design of Earthquake-resistant structures, mathematical study undertaken to simulate interactions among soil, foundation, and superstructure during various kinds of vibrational excitation. System modeled as three lumped masses connected vertically by springs, with lowest mass connected to horizontal vibrator (representing ground) through springs and dashpot. Behavior of springs described by elastic or elastoplastic force/deformation relationships. Relationships used to approximate nonlinear system behavior and soil/foundation-interface behavior.

Ramey, G. W.↗
NASA NTRS1985

Remote sensing of earth terrain

Progress on the investigation of the anisotropy of the terrain media, such as vegetation canopy and sea ice, and the study of the fluctuation-dissipation theorem in conjunction with the application of strong fluctuation theory for passive remote sensing of snowpacks is reported. The Feynman diagrammatic technique is used to derive the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field for electromagnetic wave propagation and scattering in an anisotropic random medium. With the random permittivity expressed in a general form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation and the ladder approximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a two layer anisotropic random medium with arbitrary three dimensional correlation function was investigated with the zeroth-order solutions to the Dyson equation under the four characteristic waves associated with the coherent vector fields propagating in an anisotropic random medium layer, which are the ordinary and extraordinary waves with upward and downward propagating vectors.

Kong, J. A.↗