Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable order”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Development and Calibration of an Online Energy Model for AHU Fan

The model development is necessary for the study of the energy consumption of Heating, Ventilation, and Air Conditioning (HVAC) systems. To predict the HVAC energy consumption accurately, one needs to model the individual HVAC components either from the measured data or based on the knowledge of the underlying physical phenomenon. Online model characterization is critical for improving the performance of real-time model-based fault detection and diagnosis (FDD) strategies. For HVAC control, models can be used to optimize the supervisory and local feedback control strategies to improve the energy consumption efficiency, or for providing ancillary services to the grid. It has been reported that, fans in HVAC systems of commercial buildings alone can provide substantial frequency regulation service, with little change in the indoor environment. In this paper, a real-time data-driven Air Handling Unit (AHU) fan model was developed based on recursive multi regression model. A generic nonlinear polynomial model has been studied to cover scenarios with different combinations of measurement variables, variable orders as well as different training and prediction horizons. Typical measurements including static pressure, mass flow rate, and damper positions are utilized as inputs to model the power consumption of the fan. The developed models have been validated both with simulation data from EnergyPlus-Dymola co-simulation model and with field measurement data for small to medium commercial buildings. The validation results show that the online model proposed can provide an effective prediction of the AHU fan power consumption.

Dong, Jin↗
DOE OSTI2022

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Parameterization of Large Variability Using the Hyper-Dual Meta-Model

One major problem in the design of aerospace components is the nonlinear changes in the response due to a change in the geometry and material properties. Many of these components have small nominal values and any change can lead to a large variability. In order to characterize this large variability, traditional methods require either many simulation runs or the calculations of many higher order derivatives. Each of these paths requires a large amount of computational power to evaluate the response curve. In order to perform uncertainty quantification analysis, even more simulation runs are required. The hyper-dual meta-model is introduced and used to characterize the response curve with the use of basis functions. The information of the response is generated with the utilization of the hyper-dual step to determine the sensitivities at a few number of simulation runs to greatly enrich the response space. This study shows the accuracy of this method for two different systems with parameterizations at different stages in the design analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimal renormalization of multiscale systems

While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have recently developed a time-dependent renormalization approach to stabilize such reduced models. In the current work, we extend this framework by introducing a parameter that controls the time-decay of the memory of such models and optimally selecting this parameter based on limited fully resolved simulations. First, we demonstrate our framework on the inviscid Burgers equation whose solution develops a finite-time singularity. Our renormalized reduced order models are stable and accurate for long times while using for their calibration only data from a full order simulation before the occurrence of the singularity. Furthermore, we apply this framework to the 3D Euler equations of incompressible fluid flow, where the problem of finite-time singularity formation is still open and where brute force simulation is only feasible for short times. Our approach allows us to obtain for the first time a perturbatively renormalizable model which is stable for long times and includes all the complex effects present in the 3D Euler dynamics. We find that, in each application, the renormalization coefficients display algebraic decay with increasing resolution, and that the parameter which controls the time-decay of the memory is problem-dependent.

Price, Jacob↗
DOE OSTI2018

An improved consistent, conservative, non-oscillatory and high order finite difference scheme for variable density low Mach number turbulent flow simulation

A consistent, conservative and truly high order finite difference scheme for low Mach number turbulent variable density flow simulation is presented. In the present scheme, the scalar transport equation is discretized with the explicit weighted compact nonlinear scheme (WCNS) while the continuity and momentum equations are discretized with a conservative centered high order finite difference scheme on a staggered grid. Bounded hybrid high order upwind interpolation is proposed for the evaluation of density on the cell faces of the staggered grid. The use of explicit WCNS along with the bounded density interpolation resolves the issue of degraded order of accuracy in the existing high order finite difference schemes where the centered finite difference scheme for mass and momentum conservation is combined with a total variation stable scheme for scalar transport. With the same difference operator used for the continuity and scalar transport equations, the present scheme is consistent naturally, and resolves the inconsistency problem reported in Trisjono et al. (J. Comp. Phys., 327, 612-628, 2016) without employing any modification to a scheme. Such improvements are demonstrated for several test cases.

02 PETROLEUM↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

iRF v2.0

A predictive, stable, and interpretable machine learning tool: the iterative random forest algorithm (iRF). iRF discovers high-order interactions among variables with the same order of computational cost as random forests (RF). We have demonstrated the utility of iRF in several applications in the biological and environmental sciences. It is a general purpose machine learning framework for building "explainable" predictive engines.

Brown, JamesB.↗
DOE OSTI2021

A novel approach to partitioning evapotranspiration into evaporation and transpiration in flooded ecosystems

Reliable partitioning of micrometeorologically measured evapotranspiration (ET) into evaporation (E) and transpiration (T) would greatly enhance our understanding of the water cycle and its response to climate change related shifts in local-to-regional climate conditions and rising global levels of vapor pressure deficit (VPD). While some methods on ET partitioning have been developed, their underlying assumptions make them difficult to apply more generally, especially in sites with large contributions of E. Here, we report a novel ET partitioning method using artificial neural networks (ANNs) in combination with a range of environmental input variables to predict daytime E from nighttime ET measurements. The study uses eddy covariance data from four restored wetlands in the Sacramento-San Joaquin Delta, California, USA, as well as leaf-level T data for validation. The four wetlands vary in their vegetation make-up and structure, representing a range of ET conditions. The ANNs were built with increasing complexity by adding the input variable that resulted in the next highest average value of model testing R 2 across all sites. The order of variable inclusion (and importance) was: VPD > gap-filled sensible heat flux (H_gf) > air temperature (T air ) > friction velocity (u * ) > other variables. The model using VPD, H_gf, T air , and u * showed the best performance during validation with independent data and had a mean testing R 2 value of 0.853 (averaged across all sites, range from 0.728 to 0.910). In comparison to other methods, our ANN method generated T/ET partitioning results which were more consistent with CO 2 exchange data especially for more heterogeneous sites with large E contributions. Further, our method improves the understanding of T/ET partitioning. While it may be particularly suited to flooded ecosystems, it can also improve T/ET partitioning in other systems, increasing our knowledge of the global water cycle and ecosystem functioning.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Modeling Si/SiGe quantum dot variability induced by interface disorder reconstructed from multiperspective microscopy

SiGe heteroepitaxial growth yields pristine host material for quantum dot qubits, but residual interface disorder can lead to qubit-to-qubit variability that might pose an obstacle to reliable SiGe-based quantum computing. By convolving data from scanning tunneling microscopy and high-angle annular dark field scanning transmission electron microscopy, we reconstruct 3D interfacial atomic structure and employ an atomistic multi-valley effective mass theory to quantify qubit spectral variability. The results indicate (1) appreciable valley splitting (VS) variability of ~50% owing to alloy disorder and (2) roughness-induced double-dot detuning bias energy variability of order 1–10 meV depending on well thickness. For measured intermixing, atomic steps have negligible influence on VS, and uncorrelated roughness causes spatially fluctuating energy biases in double-dot detunings potentially incorrectly attributed to charge disorder. Our approach yields atomic structure spanning orders of magnitude larger areas than post-growth microscopy or tomography alone, enabling more holistic predictions of disorder-induced qubit variability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Leveraging Extremal Dependence to Better Characterize the 2021 Pacific Northwest Heatwave

Abstract In late June, 2021, a devastating heatwave affected the US Pacific Northwest and western Canada, breaking numerous all-time temperature records by large margins and directly causing hundreds of fatalities. The observed 2021 daily maximum temperature across much of the U.S. Pacific Northwest exceeded upper bound estimates obtained from single-station temperature records even after accounting for anthropogenic climate change, meaning that the event could not have been predicted under standard univariate extreme value analysis assumptions. In this work, we utilize a flexible spatial extremes model that considers all stations across the Pacific Northwest domain and accounts for the fact that many stations simultaneously experience extreme temperatures. Our analysis incorporates the effects of anthropogenic forcing and natural climate variability in order to better characterize time-varying changes in the distribution of daily temperature extremes. We show that greenhouse gas forcing, drought conditions and large-scale atmospheric modes of variability all have significant impact on summertime maximum temperatures in this region. Our model represents a significant improvement over corresponding single-station analysis, and our posterior medians of the upper bounds are able to anticipate more than 96% of the observed 2021 high station temperatures after properly accounting for extremal dependence. Supplementary materials accompanying this paper appear online.

Zhang, Likun (ORCID:0000000154584556)↗
DOE OSTI2020

Systems and methods for control of polymer reactions and processing using automatic continuous online monitoring

Manual and automatic methods and devices using a ACOMP system for active control of polymerization reaction processes. An ideal desired trajectory of one or more reaction and polymer characteristics can be established to produce a desired final polymer product with specified characteristics from a polymerization reaction process. A current reaction trajectory of a polymerization reaction process can be driven to an ideal or desired reaction trajectory. In a manual embodiment an operator can use ACOMP data to adjust process variables in order to drive the current reaction trajectory toward the ideal or desired reaction trajectory. In an automated mode a control program can use ACOMP data to make adjustments to process variables to drive the polymerization reaction process toward the desired trajectory as closely as possible either empirically or by solving the governing equations for the polymerization reaction process.

Reed, Wayne Frederick↗
DOE OSTI2021

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders n ϵ R> 0 and exact solutions are also constructed for reaction orders n ϵ N : n ≤ 3. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Ongoing solution reproducibility of earth system models as they progress toward exascale computing

We present a methodology for solution reproducibility for the Energy Exascale Earth System Model during its ongoing software infrastructure development to prepare for exascale computers. The nonlinear chaotic nature of climate system simulations precludes traditional model verification approaches since machine precision differences—resulting from code refactoring, changes in software environment, and so on—grow exponentially to a different weather state. Here, we leverage the nature of climate as a statistical description of the atmosphere in order to establish model reproducibility. We evaluate the degree to which two-sample equality of distribution tests can confidently detect the change in climate from minor tuning parameter changes on model output variables in order to establish the level of difference that indicates a new climate. To apply this (baselined test), we target a section of the model’s development cycle wherein no intentional science changes have been applied to its source code. We compare an ensemble of short simulations that were conducted using a verified model configuration against a new ensemble with the same configuration but with the latest software infrastructure (Common Infrastructure for Modeling the Earth, CIME5.0), compiler versions, and software libraries. We also compare these against ensemble simulations conducted using the original version of the software infrastructure (CIME4.0) of the earlier model configuration, but with the latest compilers and software libraries, to test the impact of new compilers and libraries in isolation from additional software infrastructure. The two-sample equality of distribution tests indicates that these ensembles indeed represent the same climate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stockpile Assessment (Quad Chart)

Our goal was to characterize certain aspects of shaped charges. In order to determine the pressure field created by the jet and the jet velocity, I worked with and modified simulations using CTH, a code developed at Sandia. I was able to manipulate and modify certain variables in order to observe their effects and measure the pressure and velocities at different points in the simulation.

42 ENGINEERING↗
DOE OSTI2021

Physical, resource supply, and biological controls on nutrient processing along the river continuum

Nutrient impairment has led to damages to US surface and groundwater systems in excess of 100 billion dollars per year. Therefore, there is a strong need to develop methods to predict the transport, uptake, and export of nutrients along fluvial networks. We present results that are based on a data-driven mechanistic understanding of three factors that largely control nutrient uptake and export: 1) interactions between transport-related processes (mass transfer to metabolically active zones), 2) resource supply dynamics (nutrient concentration, stoichiometric constraints, etc.), and 3) biological controls (microbial community structure and function). Our results were generated from column experiments conducted along the Jemez River-Rio Grande continuum, which spans four orders of magnitude in mean annual discharge, more than 2000 m in altitude, and more than 500 km of stream longitude. Two resource supply injections were performed on each of the columns, i.e., a nitrate only addition, followed by a stoichiometrically ‘balanced’ 106Carbon:16Nitrogen:1Phosphorus addition. We quantified NO3-N uptake kinetics while constraining three variables: stream order, sediment type and type of injection (N vs stoichiometrically ‘balanced’ C:N:P). Following the laboratory nutrient uptake experiments, the columns were destructively sampled and the contents were homogenized to collect subsamples for DNA sequencing. Amplicon analysis was carried out as described by the Earth Microbiome Protocol for 16s and ITS sequencing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Observation of multiple-muon seasonal variations in the NOνA Near Detector

The interaction of a cosmic ray particle with an element of the atmosphere results in a cascade of particles, known as extensive air showers, which can be divided into three main branches, known as the hadronic, the electromagnetic, and the muonic component. As for the latter, since muons can reach high depths underground, they are generally used to study cosmic rays at different underground depths. The dynamics of extensive air showers is directly connected to the density of the atmosphere, as it defines the probability of particles to decay or interact. As muons are mainly produced from the decay of pions and kaons, and a warmer atmosphere results in higher number of meson decays, such particles are prone to suffer a seasonality effect that is directly correlated to the yearly seasonal variations of the atmosphere, an effect that has been verified by a large number of experiments over the past six decades. In 2015 the MINOS experiment presented an anti-correlation between the effective temperature of the atmosphere and the seasonality of the muon flux for multiplicities higher than one (i.e. more than one muon track per cosmic ray event). Said anti-correlation is not yet fully understood, counting with only a qualitative hypothesis as a probable mechanism. As such, the main goals of this study are to verify the MINOS anti-correlation effect and extend the study to verify the seasonality of the effect as a function of different variables in order to improve the understanding of the phenomenon and possible corroborations with the known hypothesis. Two full years of the NO$\nu$A Near Detector, ranging from April 2015 to April 2017, were used as the dataset for the analysis. The anti-correlation between the multiple muon flux and the effective temperature of the atmosphere is confirmed by the NO$\nu$A Near Detector, being in full agreement with the results presented by the MINOS Collaboration. The seasonal effect is also broken down by different variables: i) track separation, ii) zenith angle, iii) track angular separation, and iv) multiplicity. Different regions of these variables represent different energy ranges for the detected underground muons, their hadron parents or the primary particles that originated the cosmic ray shower, being a way to verify any particular dependency with energy. The results show that there are no clear trends in any of the studied variables, except for the multiplicity, in which the intensity of the seasonal variation increases for higher multiplicities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗