SEARCH · Search NASA
Results for “Kernel function”
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.
On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model
We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.
Application of mixed kernels function (MKF) based support vector regression model (SVR) for CO 2 – Reservoir oil minimum miscibility pressure prediction
Carbon dioxide (CO 2 ) injection into oil reservoirs is considered a mature enhanced oil recovery (EOR) technique for conventional reservoirs. The local displacement efficiency of the CO 2 -EOR process is highly dependent on the minimum miscibility pressure (MMP), estimating this parameter is critical to design of the CO 2 injection process. Traditional empirical methods to test the CO 2 -oil MMP are time consuming and expensive; derived correlations are fast but not accurate. Therefore, an efficient and reliable method to determine MMP is beneficial. Here in this study, a mixed kernels function (MKF) based support vector regression (SVR) model was developed and used to predict the MMP for both pure and impure CO 2 injection cases. Four parameters were chosen as input parameters: (1) reservoir temperature; (2) average critical temperature; (3) molecular weight of pentane plus (C 5+ ) fraction of crude oil, and; (4) the ratio of volatile components to intermediate components in crude oil. MMP was selected as the desired output parameter to train and test this newly developed model. The performance of basic kernels function based SVR model is compared with that of this newly developed MKF-SVR model. The well-trained MFK-SVR was compared with three well-established published correlations, demonstrated the highest correlation coefficient (R of 0.9381), lowest root mean square error (RMSE of 1.9151), smallest average absolute error (AAE of 1.1406) and maximum absolute error (MAE of 4.6291). We believe that the proposed MFK-SVM model is a more reliable and stable regression model to predict MMP. In addition, a sensitivity analysis was conducted to evaluate the physical correctness. It indicates that the predicted results from the newly developed model are in excellent agreement with previous empirical work.
Smoothing Lexis diagrams using kernel functions: A contemporary approach
Lexis diagrams are rectangular arrays of event rates indexed by age and period. Analysis of Lexis diagrams is a cornerstone of cancer surveillance research. Typically, population-based descriptive studies analyze multiple Lexis diagrams defined by sex, tumor characteristics, race/ethnicity, geographic region, etc. Inevitably the amount of information per Lexis diminishes with increasing stratification. Several methods have been proposed to smooth observed Lexis diagrams up front to clarify salient patterns and improve summary estimates of averages, gradients, and trends. In this article, we develop a novel bivariate kernel-based smoother that incorporates two key innovations. First, for any given kernel, we calculate its singular values decomposition, and select an optimal truncation point—the number of leading singular vectors to retain—based on the bias-corrected Akaike information criterion. Second, we model-average over a panel of candidate kernels with diverse shapes and bandwidths. The truncated model averaging approach is fast, automatic, has excellent performance, and provides a variance-covariance matrix that takes model selection into account. We present an in-depth case study (invasive estrogen receptor-negative breast cancer incidence among non-Hispanic white women in the United States) and simulate operating characteristics for 20 representative cancers. The truncated model averaging approach consistently outperforms any fixed kernel. Our results support the routine use of the truncated model averaging approach in descriptive studies of cancer.
Physics Model Calibration via Functional Kernel Regression and Multilevel Modeling
Explore the source record for details and available documents.
Gaussian kernel density functions for compositional quantification in atom probe tomography
Highlights: • A methodology for compositional quantification from atom probe tomography is proposed. • A probability density function p(x) given discrete data points is constructed. • Each atom approximated by a Gaussian function with a particular smoothing parameter. • Density Kernel functions are used to find the optimum smoothing parameter. • The method is validated by using simulated data of semiconductor materials. - Abstract: Atom probe tomography (APT) has the ability to identify the nature and position of single atoms in a material with an almost 3D atomic resolution. However, the quantification of the material composition requires an appropriate treatment of the discrete APT data. When the amount of atoms selected to quantify the composition is relatively small, the spatial resolution is enhanced but the statistical error worsens. Conversely, the increase in the number of atoms considered reduces the spatial resolution, but improving the statistics. We have developed a methodology to reach an optimum equilibrium between the positional and the statistical error in an unsupervised form using Gaussian Kernel density functions. The validity of the method has been tested using APT simulated data of semiconductor materials. It has been proved that the chemical quantification in these materials requires the appropriate selection of the smoothing parameter, obtained without user intervention. In addition, the results have been compared to the usual techniques for composition measurement from APT data (voxelization and proximity histograms), showing better precision for high spatial resolution. This work supplies a data driven methodology based in Gaussian Kernel density functions for the accurate quantification of the composition from APT data.
Application of a new hybrid particle swarm optimization-mixed kernels function-based support vector machine model for reservoir porosity prediction: A case study in Jacksonburg-Stringtown oil field, West Virginia, USA
Porosity is a fundamental property that characterizes the storage capability of fluid and gas-bearing formations in a reservoir. An accurate porosity value can be measured from core samples in the laboratory; however, core analysis is expensive and time consuming. Well-log data can be used to calculate porosity, but the availability of log suites is often limited in mature fields. Therefore, robust porosity prediction requires integration of core-measured porosity with available well-log suites to control for changes in lithology and fluid content. A support vector machine (SVM) model with mixed kernel function (MKF) is used to construct the relationship between limited conventional well-log suites and sparse core data. Porosity is the desired output, and two conventional well-log responses (gamma ray [GR] and bulk density) and three well-log-derived parameters (the slope of GR, the slope of density, and [Formula: see text]) are input parameters. A global stochastic searching algorithm, particle swarm optimization (PSO), is applied to improve the efficiency of locating the appropriate values of five control parameters in MKF-SVM model. The results of SVM with different traditional kernel functions were compared, and the MKF-SVM model provided an improvement over the traditional SVM model. To confirm the advantage of the hybrid PSO-MKF-SVM model, the results from three models: (1) radial basis function (RBF)-based least-squares SVM, (2) multilayer perceptron artificial neural network (ANN), and (3) RBF ANN, are compared with the result of the hybrid PSO-MKF-SVM model. The results indicate that the hybrid PSO-MKF-SVM model improves porosity prediction with the highest correlation coefficient ([Formula: see text] of 0.9560), the highest coefficient of determination ([Formula: see text] of 0.9140), the lowest root-mean-square error (1.6505), average absolute error value (1.4050), and maximum absolute error (2.717).
Machine Learning Optimization of p-Type Transparent Conducting Films
p-Type transparent conducting materials (p-TCMs) are important components of optoelectronic devices including solar cells, photodetectors, displays, and flexible sensors. Cu–Zn–S thin films prepared by chemical bath deposition (CBD) can have both high transparency in the visible range (>80%) as well as excellent hole conductivity (>1000 S cm –1 ). However, the interplay between the deposition parameters in the CBD process (metal and sulfur precursor concentrations, temperature, pH, complexing agents, etc.) creates a multidimensional parameter space such that optimization for a specific application is challenging and time-consuming. Here we show that strategic design of experiment combined with machine learning (ML) allows for the efficient optimization of p-TCM performance. The approach is guided by a figure of merit (FOM) calculated from the film conductivity and optical transmission in the desired spectral range. A specific example is shown using two steps of optimization using a selected subset of four experimental CBD factors. The ML model is based on support vector regression employing a radial basis function as the kernel function. 10-fold cross-validation was performed to mitigate overfitting. After the first round of optimization, predicted areas in the parameter space with maximal FOMs were selected for a second round of optimization. Films with optimal FOMs were incorporated into heterojunction solar cells and transparent photodiodes. Here, the optimization approach shown here will be generally applicable to any materials synthesis process with multiple parameters.
StOKeDMD: Streaming Occupation kernel dynamic mode decomposition
Dynamic mode decomposition (DMD) has become a common technique for constructing surrogate models for dynamical systems from observed system states. The Occupation Kernel DMD (OKDMD) method proposed in (Rosenfeld et al., 2022) and (Rosenfeld et al., 2024) is a Liouville operator based method that builds surrogate models from system state trajectories. Here, this paper proposes an extension of OKDMD to the case when the system states are observed in a streaming fashion, i.e., only a small fraction of the state trajectory is available at a given time. The developed method, Streaming Occupation Kernel DMD (StOKeDMD), accommodates the streaming data input by leveraging properties of specific choices of kernel functions and occupation kernels. We apply the StoKeDMD method as a compression method for streaming data, analyze the memory complexity, and demonstrate the performance of StoKeDMD in the compression of streaming data generated from a Lorenz system and a fluid flow simulation.
An Immersed Boundary method with divergence-free velocity interpolation and force spreading
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least $\mathscr{C}$ 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. Finally, the method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.
Determining the memory kernel from a fixed point measurement data for a parabolic equation with memory effect
We consider an inverse problem for a parabolic equation with memory effect. This inverse problem aims to identify the memory kernel function from a fixed point measurement data. Based on the fixed point arguments, we derive the global in time existence and uniqueness of our inverse problem. Moreover, we present a numerical algorithm to reconstruct the memory kernel function. Numerical simulations show the effectiveness of the proposed method.
Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method
Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.
A Diethylene Glycol Condensation Particle Counter for Rapid Sizing of sub-3 nm Atmospheric Clusters
AbstractThis paper describes the modification of a laminar flow, thermally diffusive universal-fluid condensation particle counter (standard operation: 50% detection efficiency at 5 nm) to rapidly measure the size distribution of sub 3 nm aerosol. Sub 3 nm detection was achieved by using diethylene glycol as the working fluid, which enabled high instrument super-saturations while minimizing homogenous nucleation of the working fluid; a detection efficiency of 50% was achieved at 1.6 nm with laboratory-generated ammonium sulfate aerosol. Rapid aerosol sizing beneath 3 nm was achieved by inverting the measured grown droplet size distribution (1 second sampling) to recover the sampled aerosol size distribution. The developed inversion algorithm utilizes analytical kernel functions determined from the instrument response to pseudo-monodisperse ammonium sulfate aerosol from 1.5 nm to 20 nm, generated by a high resolution DMA and a nano DMA. The inversion algorithm was tested numerically with assumed, idealized aerosol size distributions consistent with observed new particle formation events, yielding reasonable agreement between inverted and assumed aerosol size distributions below 3 nm. Furthermore, this technique provides a measure of the aerosol size assuming an aerosol composition identical to that of the aerosol used to generate the experimentally determined kernel function.
Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.
Parallel hybrid quantum-classical machine learning for kernelized time-series classification
Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. Here, in this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a timeseries Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.
On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation
The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.
Snake River Plain Geothermal Play Fairway Analysis Heat, Permeability, and Seal CRS Map Raster Files
Snake River Plain Play Fairway Analysis - Phase 1 CRS Raster Files. This dataset contains raster files created in ArcGIS. These raster images depict Common Risk Segment (CRS) maps for HEAT, PERMEABILITY, AND SEAL, as well as selected maps of Evidence Layers. These evidence layers consist of either Bayesian krige functions or kernel density functions, and include: (1) HEAT: Heat flow (Bayesian krige map), Heat flow standard error on the krige function (data confidence), volcanic vent distribution as function of age and size, groundwater temperature (equivalue interval and natural breaks bins), and groundwater T standard error. (2) PERMEABILTY: Fault and lineament maps, both as mapped and as kernel density functions, processed for both dilational tendency (TD) and slip tendency (ST), along with data confidence maps for each data type. Data types include mapped surface faults from USGS and Idaho Geological Survey data bases, as well as unpublished mapping; lineations derived from maximum gradients in magnetic, deep gravity, and intermediate depth gravity anomalies. (3) SEAL: Seal maps based on presence and thickness of lacustrine sediments and base of SRP aquifer. Raster size is 2 km. All files generated in ArcGIS.
Projecting the Thermal Response in a HTGR-Type System during Conduction Cooldown Using Graph-Laplacian Based Machine Learning
Accurate prediction of an off-normal event in a nuclear reactor is dependent upon the availability of sensory data, reactor core physical condition, and understanding of the underlying phenomenon. This work presents a method to project the data from some discrete sensory locations to the overall reactor domain during conduction cooldown scenarios similar to High Temperature Gas-cooled Reactors (HTGRs). The existing models for conductive cooldown in a heterogeneous multi-body system, such as an assembly of prismatic blocks or pebble beds relies on knowledge of the thermal contact conductance, requiring significant knowledge of local thermal contacts and heat transport possibilities across those contacts. With a priori knowledge of bulk geometry features and some discrete sensors, a machine learning approach was devised. The presented work uses an experimental facility to mimic conduction cooldown with an assembly of 68 cylindrical rods initially heated to 1200 K. High-fidelity temperature data were collected using an infrared (IR) camera to provide training data to the model and validate the predicted temperature data. The machine learning approach used here first converts the macroscopic bulk geometry information into Graph-Laplacian, and then uses the eigenvectors of the Graph-Laplacian to develop Kernel functions. Support vector regression (SVR) was implemented on the obtained Kernels and used to predict the thermal response in a packed rod assembly during a conduction cooldown experiment. The usage of SVR modeling differs from most models today because of its representation of thermal coupling between rods in the core. When trained with thermographic data, the average normalized error is less than 2% over 400 s, during which temperatures of the assembly have dropped by more than 500 K. The rod temperature prediction performance was significantly better for rods in the interior of the assembly compared to those near the exterior, likely due to the model simplification of the surroundings.