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NASA NTRS2007

Automated Knowledge Discovery From Simulators

A computational method, SimLearn, has been devised to facilitate efficient knowledge discovery from simulators. Simulators are complex computer programs used in science and engineering to model diverse phenomena such as fluid flow, gravitational interactions, coupled mechanical systems, and nuclear, chemical, and biological processes. SimLearn uses active-learning techniques to efficiently address the "landscape characterization problem." In particular, SimLearn tries to determine which regions in "input space" lead to a given output from the simulator, where "input space" refers to an abstraction of all the variables going into the simulator, e.g., initial conditions, parameters, and interaction equations. Landscape characterization can be viewed as an attempt to invert the forward mapping of the simulator and recover the inputs that produce a particular output. Given that a single simulation run can take days or weeks to complete even on a large computing cluster, SimLearn attempts to reduce costs by reducing the number of simulations needed to effect discoveries. Unlike conventional data-mining methods that are applied to static predefined datasets, SimLearn involves an iterative process in which a most informative dataset is constructed dynamically by using the simulator as an oracle. On each iteration, the algorithm models the knowledge it has gained through previous simulation trials and then chooses which simulation trials to run next. Running these trials through the simulator produces new data in the form of input-output pairs. The overall process is embodied in an algorithm that combines support vector machines (SVMs) with active learning. SVMs use learning from examples (the examples are the input-output pairs generated by running the simulator) and a principle called maximum margin to derive predictors that generalize well to new inputs. In SimLearn, the SVM plays the role of modeling the knowledge that has been gained through previous simulation trials. Active learning is used to determine which new input points would be most informative if their output were known. The selected input points are run through the simulator to generate new information that can be used to refine the SVM. The process is then repeated. SimLearn carefully balances exploration (semi-randomly searching around the input space) versus exploitation (using the current state of knowledge to conduct a tightly focused search). During each iteration, SimLearn uses not one, but an ensemble of SVMs. Each SVM in the ensemble is characterized by different hyper-parameters that control various aspects of the learned predictor - for example, whether the predictor is constrained to be very smooth (nearby points in input space lead to similar output predictions) or whether the predictor is allowed to be "bumpy." The various SVMs will have different preferences about which input points they would like to run through the simulator next. SimLearn includes a formal mechanism for balancing the ensemble SVM preferences so that a single choice can be made for the next set of trials.

Burl, Michael↗
NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Memarsadeghi, Nargess↗
NASA NTRS2004

Simulating Virtual Terminal Area Weather Data Bases for Use in the Wake Vortex Avoidance System (Wake VAS) Prediction Algorithm

During the research project, sounding datasets were generated for the region surrounding 9 major airports, including Dallas, TX, Boston, MA, New York, NY, Chicago, IL, St. Louis, MO, Atlanta, GA, Miami, FL, San Francico, CA, and Los Angeles, CA. The numerical simulation of winter and summer environments during which no instrument flight rule impact was occurring at these 9 terminals was performed using the most contemporary version of the Terminal Area PBL Prediction System (TAPPS) model nested from 36 km to 6 km to 1 km horizontal resolution and very detailed vertical resolution in the planetary boundary layer. The soundings from the 1 km model were archived at 30 minute time intervals for a 24 hour period and the vertical dependent variables as well as derived quantities, i.e., 3-dimensional wind components, temperatures, pressures, mixing ratios, turbulence kinetic energy and eddy dissipation rates were then interpolated to 5 m vertical resolution up to 1000 m elevation above ground level. After partial validation against field experiment datasets for Dallas as well as larger scale and much coarser resolution observations at the other 8 airports, these sounding datasets were sent to NASA for use in the Virtual Air Space and Modeling program. The application of these datasets being to determine representative airport weather environments to diagnose the response of simulated wake vortices to realistic atmospheric environments. These virtual datasets are based on large scale observed atmospheric initial conditions that are dynamically interpolated in space and time. The 1 km nested-grid simulated datasets providing a very coarse and highly smoothed representation of airport environment meteorological conditions. Details concerning the airport surface forcing are virtually absent from these simulated datasets although the observed background atmospheric processes have been compared to the simulated fields and the fields were found to accurately replicate the flows surrounding the airport where coarse verification data were available as well as where airport scale datasets were available.

Kaplan, Michael L.↗
NASA NTRS1996

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗
DOE OSTI2024

EFIT-Prime: Probabilistic and physics-constrained reduced-order neural network model for equilibrium reconstruction in DIII-D

We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A spatially regularized detector for emergent/re-emergent disease outbreaks

Early detection of outbreaks caused by emergent pathogens, using epidemiological surveillance data i.e., daily case counts, is difficult. This is because the data tend to be noisy during the early epoch of the outbreak. In contrast, the spread-rate of the disease tends to be well-behaved, as it depends only on the mixing patterns of the population and the characteristics of the pathogen, neither of which behave erratically in space-time. In this report, we explore whether the spread-rate can be used for epidemiological surveillance, conditional on case count data. Estimating the spread-rate from case count data allows us to exploit exogenous information, e.g., incubation period distributions etc., which can considerably smooth out any erratic temporal behavior. Further, epidemiological dynamics are spatially correlated, and if case counts are available for multiple areal units e.g., counties, these correlations could potentially be used to suppress noise in the early epoch data. These exogenous information and structure are not exploited by conventional syndromic surveillance detectors to extract a well-behaved latent variable for monitoring purposes. The technical challenge lies in the estimation of the spread-rate field jointly over a collection of areal units; further, the spread-rate varies over time. We develop a method based on mean-field variational inference to approximately estimate the spread-rate field, using a Gaussian Random Field Model for spatial regularization. The method is tested on the estimation of spread-rate in the thirty-three counties of New Mexico and detect the arrival of the Fall 2020 COVID-19 wave in September 2020. We find that the method is scalable, but underestimates the uncertainty in the estimated spread-rate field. We detect the arrival of the Fall 2020 wave a week ahead of conventional syndromic surveillance algorithms, but our simplistic detection algorithm, based on simple anomaly detection, suffers from a high false positive rate, similar to conventional detectors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
DOE OSTI2020

Optimization of Geometric Perturbations on a Rod Moving Through a High Explosive Target

After completing a study to ensure the simulation results were converged, several high resolution 3D Smoothed Particle Hydrodynamic (SPH) simulations of copper rods impacting a high explosive (LX14) target were performed. This was then formulated into an optimization problem: I wanted to find the optimum shape and location of a perturbation on the rod that would maximize its erosion after it left the target. The shape of the perturbation was modeled as a 2D Gaussian bump and parameterized by its location along the rod axis (z 0 ) and amplitude (A). The final mass of the coherent part of the rod as it leaves the target was used as a metric to represent the erosion of the rod, and the optimization was formulated to maximize this metric with respect to the aforementioned design variables. Due to the expensive nature of the high-fidelity 3D SPH simulations, a surrogate model needed to be chosen so that many function calls to the optimizer would be feasible. Thus, a strategic full factorial sampling plan was chosen to build a dataset, which consisted of 24 high-fidelity simulations. Two surrogate models, a third order polynomial regression model and a Gaussian Process Model, were analyzed using a 14%/86% test/train holdout technique. The root mean square and R2 score of the test set was used to determine the best model, and the third order polynomial regression model was chosen as the surrogate model. Finally, the Nelder-Mead Simplex and Basin-hopping optimization algorithms were implemented, and it was found that the two algorithms gave slightly different optimum values. Nelder-Mead gave an optimum point of [z* 0 ;A*] = [9:9;0:4] and Basin-Hopping gave an optimum value of x* = [z* 0 ;A*] = [9:2;0:1].

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2023

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

Engineering↗
NASA NTRS2003

EVA Robotic Assistant Project: Platform Attitude Prediction

The Robotic Systems Technology Branch is currently working on the development of an EVA Robotic Assistant under the sponsorship of the Surface Systems Thrust of the NASA Cross Enterprise Technology Development Program (CETDP). This will be a mobile robot that can follow a field geologist during planetary surface exploration, carry his tools and the samples that he collects, and provide video coverage of his activity. Prior experiments have shown that for such a robot to be useful it must be able to follow the geologist at walking speed over any terrain of interest. Geologically interesting terrain tends to be rough rather than smooth. The commercial mobile robot that was recently purchased as an initial testbed for the EVA Robotic Assistant Project, an ATRV Jr., is capable of faster than walking speed outside but it has no suspension. Its wheels with inflated rubber tires are attached to axles that are connected directly to the robot body. Any angular motion of the robot produced by driving over rough terrain will directly affect the pointing of the on-board stereo cameras. The resulting image motion is expected to make tracking of the geologist more difficult. This will either require the tracker to search a larger part of the image to find the target from frame to frame or to search mechanically in pan and tilt whenever the image motion is large enough to put the target outside the image in the next frame. This project consists of the design and implementation of a Kalman filter that combines the output of the angular rate sensors and linear accelerometers on the robot to estimate the motion of the robot base. The motion of the stereo camera pair mounted on the robot that results from this motion as the robot drives over rough terrain is then straightforward to compute. The estimates may then be used, for example, to command the robot s on-board pan-tilt unit to compensate for the camera motion induced by the base movement. This has been accomplished in two ways: first, a standalone head stabilizer has been implemented and second, the estimates have been used to influence the search algorithm of the stereo tracking algorithm. Studies of the image motion of a tracked object indicate that the image motion of objects is suppressed while the robot crossing rough terrain. This work expands the range of speed and surface roughness over which the robot should be able to track and follow a field geologist and accept arm gesture commands from the geologist.

Nickels, Kevin M.↗
NASA NTRS2011

A New Inversion Routine to Produce Vertical Electron-Density Profiles from Ionospheric Topside-Sounder Data

Two software applications have been produced specifically for the analysis of some million digital topside ionograms produced by a recent analog-to-digital conversion effort of selected analog telemetry tapes from the Alouette-2, ISIS-1 and ISIS-2 satellites. One, TOPIST (TOPside Ionogram Scalar with True-height algorithm) from the University of Massachusetts Lowell, is designed for the automatic identification of the topside-ionogram ionospheric-reflection traces and their inversion into vertical electron-density profiles Ne(h). TOPIST also has the capability of manual intervention. The other application, from the Goddard Space Flight Center based on the FORTRAN code of John E. Jackson from the 1960s, is designed as an IDL-based interactive program for the scaling of selected digital topside-sounder ionograms. The Jackson code has also been modified, with some effort, so as to run on modern computers. This modification was motivated by the need to scale selected ionograms from the millions of Alouette/ISIS topside-sounder ionograms that only exist on 35-mm film. During this modification, it became evident that it would be more efficient to design a new code, based on the capabilities of present-day computers, than to continue to modify the old code. Such a new code has been produced and here we will describe its capabilities and compare Ne(h) profiles produced from it with those produced by the Jackson code. The concept of the new code is to assume an initial Ne(h) and derive a final Ne(h) through an iteration process that makes the resulting apparent-height profile fir the scaled values within a certain error range. The new code can be used on the X-, O-, and Z-mode traces. It does not assume any predefined profile shape between two contiguous points, like the exponential rule used in Jackson s program. Instead, Monotone Piecewise Cubic Interpolation is applied in the global profile to keep the monotone nature of the profile, which also ensures better smoothness in the final profile than in Jackson s program. The new code uses the complete refractive index expression for a cold collisionless plasma and can accommodate the IGRF, T96, and other geomagnetic field models.

Wang, Yongli↗
NASA NTRS1993

The three-dimensional structure of cumulus clouds over the ocean. 1: Structural analysis

Thermal channel (channel 6, 10.4-12.5 micrometers) images of five Landsat thematic mapper cumulus scenes over the ocean are examined. These images are thresholded using the standard International Satellite Cloud Climatology Project (ISCCP) thermal threshold algorithm. The individual clouds in the cloud fields are segmented to obtain their structural statistics which include size distribution, orientation angle, horizontal aspect ratio, and perimeter-to-area (PtA) relationship. The cloud size distributions exhibit a double power law with the smaller clouds having a smaller absolute exponent. The cloud orientation angles, horizontal aspect ratios, and PtA exponents are found in good agreement with earlier studies. A technique also is developed to recognize individual cells within a cloud so that statistics of cloud cellular structure can be obtained. Cell structural statistics are computed for each cloud. Unicellular clouds are generally smaller (less than or equal to 1 km) and have smaller PtA exponents, while multicellular clouds are larger (greater than or equal to 1 km) and have larger PtA exponents. Cell structural statistics are similar to those of the smaller clouds. When each cell is approximated as a quadric surface using a linear least squares fit, most cells have the shape of a hyperboloid of one sheet, but about 15% of the cells are best modeled by a hyperboloid of two sheets. Less than 1% of the clouds are ellipsoidal. The number of cells in a cloud increases slightly faster than linearly with increasing cloud size. The mean nearest neighbor distance between cells in a cloud, however, appears to increase linearly with increasing cloud size and to reach a maximum when the cloud effective diameter is about 10 km; then it decreases with increasing cloud size. Sensitivity studies of threshold and lapse rate show that neither has a significant impact upon the results. A goodness-of-fit ratio is used to provide a quantitative measure of the individual cloud results. Significantly improved results are obtained after applying a smoothing operator, suggesting the eliminating subresolution scale variations with higher spatial resolution may yield even better shape analyses.

Kuo, Kwo-Sen↗
NASA NTRS2009

Adaptive Morphological Feature-Based Object Classifier for a Color Imaging System

Utilizing a Compact Color Microscope Imaging System (CCMIS), a unique algorithm has been developed that combines human intelligence along with machine vision techniques to produce an autonomous microscope tool for biomedical, industrial, and space applications. This technique is based on an adaptive, morphological, feature-based mapping function comprising 24 mutually inclusive feature metrics that are used to determine the metrics for complex cell/objects derived from color image analysis. Some of the features include: Area (total numbers of non-background pixels inside and including the perimeter), Bounding Box (smallest rectangle that bounds and object), centerX (x-coordinate of intensity-weighted, center-of-mass of an entire object or multi-object blob), centerY (y-coordinate of intensity-weighted, center-of-mass, of an entire object or multi-object blob), Circumference (a measure of circumference that takes into account whether neighboring pixels are diagonal, which is a longer distance than horizontally or vertically joined pixels), . Elongation (measure of particle elongation given as a number between 0 and 1. If equal to 1, the particle bounding box is square. As the elongation decreases from 1, the particle becomes more elongated), . Ext_vector (extremal vector), . Major Axis (the length of a major axis of a smallest ellipse encompassing an object), . Minor Axis (the length of a minor axis of a smallest ellipse encompassing an object), . Partial (indicates if the particle extends beyond the field of view), . Perimeter Points (points that make up a particle perimeter), . Roundness [(4(pi) x area)/perimeter(squared)) the result is a measure of object roundness, or compactness, given as a value between 0 and 1. The greater the ratio, the rounder the object.], . Thin in center (determines if an object becomes thin in the center, (figure-eight-shaped), . Theta (orientation of the major axis), . Smoothness and color metrics for each component (red, green, blue) the minimum, maximum, average, and standard deviation within the particle are tracked. These metrics can be used for autonomous analysis of color images from a microscope, video camera, or digital, still image. It can also automatically identify tumor morphology of stained images and has been used to detect stained cell phenomena (see figure).

McDowell, Mark↗