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At least 55 records · Page 3

An analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

Barnett, Mark↗

Comparison of some biased estimation methods (including ordinary subset regression) in the linear model

Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.

Sidik, S. M.↗

Variance Decomposition of MEDLI2 Reconstructed Heating Using Neural Networks

The Mars Entry, Descent, and Landing Instrumentation (MEDLI2) sensor suite collected data during entry of the Mars 2020 Perseverance rover into Mars’ atmosphere. This suite included a network of MEDLI2 Instrumented Sensor Plugs (MISPs). Each MISP was comprised of a cylinder made of Thermal Protection System (TPS) material with 1-3 embedded thermocouples (TCs), and it was flush mounted into the heatshield or backshell. Data from these in-depth TCs were used to reconstruct the aeroheating environment of the vehicle throughout entry. Surface heating was posed as an inverse problem, with the goal of estimating the surface heating by minimizing an objective function of the difference between MISP temperature measurements during flight and the temperature predictions derived from the Fully Implicit Ablation and Thermal response (FIAT) program. Given an aerothermal environment, FIAT calculates the material response and provides in-depth temperatures throughout the TPS material. To achieve the reverse, an internal tool called FIAT_Opt runs through multiple different environments until the output temperature at the TC depth closely matches the flight data. 95% confidence intervals on the reconstructed surface heating were obtained using Monte Carlo analysis, in which uncertainties in the thermocouple depth and the TPS material properties (e.g., density, thermal conductivity, heat capacity, emissivity) based on flight-lot material testing were included. A variance decomposition method using Sobol indices was employed to assess the sensitivity of the reconstructed peak heating to the TC placement and material property uncertainties. Variance decomposition was found to require tens of thousands of FIAT_Opt runs in order for the Sobol indices to converge. With a single FIAT_Opt run taking on the order of 40 minutes, the required number of computations would take months to complete, even if using multiple CPUs. To mitigate this problem, three machine learning models (ridge regression with cross-validation, random forest regression, and a deep neural network) were trained and tested using the 2000 Monte Carlo runs that were already completed. A subset of 1600 runs were used to train the model (i.e., training set), while the remaining 400 runs were used as the test set. The predictions from the deep neural network (DNN) on the test set showed nearly perfect agreement to the actual values computed with FIAT_Opt (R2 > 0.99). Using the DNN as a surrogate model, the variance decomposition using 50,000 runs was completed within minutes. The resulting Sobol indices showed that the reconstructed peak surface heating was most sensitive to the uncertainties in the thermal conductivity (ST = 0.37) and heat capacity (ST = 0.26). This method can be leveraged to provide requirements for material property measurements needed to improve the accuracy of surface heating prediction and ultimately lead to the reduction of design margins in the future. This presentation will include background on the MEDLI2 suite; the method used for inverse heating estimation; the way that material property uncertainties were accounted for using Monte Carlo analysis; a brief background on variance decomposition; the motivation for using machine learning in this context; how a neural network was trained on the data to enable variance decomposition in a fraction of the time; and the variance decomposition results for one of the MISPs.

Hannah Alpert↗

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗

Control Effector Unsaturation Modification to the Cascading Generalized Inverse Control Allocation Algorithm

Control allocation has sufficiently progressed such that it is used in front-line fighter aircraft such as the F-18Superhornet and the F-35 Joint Strike Fighter. Published literature shows the F-35 utilizes Nonlinear Dynamic Inversion in conjunction with an Effector Blender that incorporates the Cascading Generalized Inverse control allocation algorithm. While the Cascading Generalized Inverse algorithm is one of the premier generalized inverse methods, it does suffer from three deficiencies. In particular, it suffers from an inability to achieve some desired outcomes, it intermittently provides non-optimal solutions and generally fails to preserve moment direction near maximal achievable moments. An effector unsaturation method based on a Scalar Difference Quadratic was first introduced and implemented on the iterative Prediction Method control allocation algorithm which was shown to consistently achieve optimal (weighted) control allocation solutions throughout the entire Attainable Moment Set while preserving desired moment direction. In this paper, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the baseline algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Numerical case studies demonstrate that the Modified Cascading Generalized Inverse algorithm resolves the aforementioned deficiencies.

Michael J Acheson↗

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗

Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

Ganapol, Barry D.↗

Peak Wind Tool for General Forecasting

The expected peak wind speed of the day is an important forecast element in the 45th Weather Squadron's (45 WS) daily 24-Hour and Weekly Planning Forecasts. The forecasts are used for ground and space launch operations at the Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS). The 45 WS also issues wind advisories for KSC/CCAFS when they expect wind gusts to meet or exceed 25 kt, 35 kt and 50 kt thresholds at any level from the surface to 300 ft. The 45 WS forecasters have indicated peak wind speeds are challenging to forecast, particularly in the cool season months of October - April. In Phase I of this task, the Applied Meteorology Unit (AMU) developed a tool to help the 45 WS forecast non-convective winds at KSC/CCAFS for the 24-hour period of 0800 to 0800 local time. The tool was delivered as a Microsoft Excel graphical user interface (GUI). The GUI displayed the forecast of peak wind speed, 5-minute average wind speed at the time of the peak wind, timing of the peak wind and probability the peak speed would meet or exceed 25 kt, 35 kt and 50 kt. For the current task (Phase II ), the 45 WS requested additional observations be used for the creation of the forecast equations by expanding the period of record (POR). Additional parameters were evaluated as predictors, including wind speeds between 500 ft and 3000 ft, static stability classification, Bulk Richardson Number, mixing depth, vertical wind shear, temperature inversion strength and depth and wind direction. Using a verification data set, the AMU compared the performance of the Phase I and II prediction methods. Just as in Phase I, the tool was delivered as a Microsoft Excel GUI. The 45 WS requested the tool also be available in the Meteorological Interactive Data Display System (MIDDS). The AMU first expanded the POR by two years by adding tower observations, surface observations and CCAFS (XMR) soundings for the cool season months of March 2007 to April 2009. The POR was expanded again by six years, from October 1996 to April 2002, by interpolating 1000-ft sounding data to 100-ft increments. The Phase II developmental data set included observations for the cool season months of October 1996 to February 2007. The AMU calculated 68 candidate predictors from the XMR soundings, to include 19 stability parameters, 48 wind speed parameters and one wind shear parameter. Each day in the data set was stratified by synoptic weather pattern, low-level wind direction, precipitation and Richardson Number, for a total of 60 stratification methods. Linear regression equations, using the 68 predictors and 60 stratification methods, were created for the tool's three forecast parameters: the highest peak wind speed of the day (PWSD), 5-minute average speed at the same time (A WSD), and timing of the PWSD. For PWSD and A WSD, 30 Phase II methods were selected for evaluation in the verification data set. For timing of the PWSD, 12 Phase\I methods were selected for evaluation. The verification data set contained observations for the cool season months of March 2007 to April 2009. The data set was used to compare the Phase I and II forecast methods to climatology, model forecast winds and wind advisories issued by the 45 WS. The model forecast winds were derived from the 0000 and 1200 UTC runs of the 12-km North American Mesoscale (MesoNAM) model. The forecast methods that performed the best in the verification data set were selected for the Phase II version of the tool. For PWSD and A WSD, linear regression equations based on MesoNAM forecasts performed significantly better than the Phase I and II methods. For timing of the PWSD, none of the methods performed significantly bener than climatology. The AMU then developed the Microsoft Excel and MIDDS GUls. The GUIs display the forecasts for PWSD, AWSD and the probability the PWSD will meet or exceed 25 kt, 35 kt and 50 kt. Since none of the prediction methods for timing of the PWSD performed significantly better thanlimatology, the tool no longer displays this predictand. The Excel and MIDDS GUIs display forecasts for Day-I to Day-3 and Day-I to Day-5, respectively. The Excel GUI uses MesoNAM forecasts as input, while the MIDDS GUI uses input from the MesoNAM and Global Forecast System model. Based on feedback from the 45 WS, the AMU added the daily average wind speed from 30 ft to 60 ft to the tool, which is one of the parameters in the 24-Hour and Weekly Planning Forecasts issued by the 45 WS. In addition, the AMU expanded the MIDDS GUI to include forecasts out to Day-7.

Barrett, Joe H., III↗

Automatic Determination of the Conic Coronal Mass Ejection Model Parameters

Characterization of the three-dimensional structure of solar transients using incomplete plane of sky data is a difficult problem whose solutions have potential for societal benefit in terms of space weather applications. In this paper transients are characterized in three dimensions by means of conic coronal mass ejection (CME) approximation. A novel method for the automatic determination of cone model parameters from observed halo CMEs is introduced. The method uses both standard image processing techniques to extract the CME mass from white-light coronagraph images and a novel inversion routine providing the final cone parameters. A bootstrap technique is used to provide model parameter distributions. When combined with heliospheric modeling, the cone model parameter distributions will provide direct means for ensemble predictions of transient propagation in the heliosphere. An initial validation of the automatic method is carried by comparison to manually determined cone model parameters. It is shown using 14 halo CME events that there is reasonable agreement, especially between the heliocentric locations of the cones derived with the two methods. It is argued that both the heliocentric locations and the opening half-angles of the automatically determined cones may be more realistic than those obtained from the manual analysis

Pulkkinen, A.↗

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

Application of a viscous-inviscid interaction method to predict transonic separated flows

A viscous-inviscid interaction numerical procedure is used to predict turbulent transonic separated flows over axisymmetric bodies. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is determined by a finite-difference solution to the full-potential equation in conservative form. Parameters affecting the convergence rate of the interaction procedure are discussed. The predictions of a new turbulence model proposed by Johnson and King are compared with experimental data and numerical solutions to the Navier-Stokes equations for flows with large regions of separation.

Lee, D. S.↗

Bayesian retrieval of optically relevant properties from hyperspectral water-leaving reflectances

Current methods to retrieve optically relevant properties from ocean color observations do not explicitly make use of prior knowledge about property distributions. Here we implement a simplified Bayesian approach that takes into account prior probability distributions on two sets of five optically relevant parameters, and conduct a retrieval of these parameters using hyperspectral simulated water-leaving reflectances. We focus specifically on the ability of the model to distinguish between two optically similar phytoplankton taxa, diatoms and Noctiluca scintillans. The inversion retrieval gives most-likely concentrations and uncertainty estimates, and we find that the model is able to probabilistically predict the occurrence of Noctiluca scintillans blooms using these metrics. We discuss how this method can be expanded to include a priori covariances between different parameters, and show the effect of varying measurement uncertainty and spectral resolution on Noctiluca scintillans bloom predictions.

Zachary K Erickson↗

Adaptive Inverse Control for Rotorcraft Vibration Reduction

This thesis extends the Least Mean Square (LMS) algorithm to solve the mult!ple-input, multiple-output problem of alleviating N/Rev (revolutions per minute by number of blades) helicopter fuselage vibration by means of adaptive inverse control. A frequency domain locally linear model is used to represent the transfer matrix relating the higher harmonic pitch control inputs to the harmonic vibration outputs to be controlled. By using the inverse matrix as the controller gain matrix, an adaptive inverse regulator is formed to alleviate the N/Rev vibration. The stability and rate of convergence properties of the extended LMS algorithm are discussed. It is shown that the stability ranges for the elements of the stability gain matrix are directly related to the eigenvalues of the vibration signal information matrix for the learning phase, but not for the control phase. The overall conclusion is that the LMS adaptive inverse control method can form a robust vibration control system, but will require some tuning of the input sensor gains, the stability gain matrix, and the amount of control relaxation to be used. The learning curve of the controller during the learning phase is shown to be quantitatively close to that predicted by averaging the learning curves of the normal modes. For higher order transfer matrices, a rough estimate of the inverse is needed to start the algorithm efficiently. The simulation results indicate that the factor which most influences LMS adaptive inverse control is the product of the control relaxation and the the stability gain matrix. A small stability gain matrix makes the controller less sensitive to relaxation selection, and permits faster and more stable vibration reduction, than by choosing the stability gain matrix large and the control relaxation term small. It is shown that the best selections of the stability gain matrix elements and the amount of control relaxation is basically a compromise between slow, stable convergence and fast convergence with increased possibility of unstable identification. In the simulation studies, the LMS adaptive inverse control algorithm is shown to be capable of adapting the inverse (controller) matrix to track changes in the flight conditions. The algorithm converges quickly for moderate disturbances, while taking longer for larger disturbances. Perfect knowledge of the inverse matrix is not required for good control of the N/Rev vibration. However it is shown that measurement noise will prevent the LMS adaptive inverse control technique from controlling the vibration, unless the signal averaging method presented is incorporated into the algorithm.

Jacklin, Stephen A.↗

Application of a viscous-inviscid interaction procedure to predict separated flows with heat transfer

A viscous-inviscid interaction procedure is described for predicting heat transfer in separated flows. The separating flow in a rearward-facing step/asymmetric channel expansion is considered. For viscous regions, the boundary-layer momentum and continuity equations are solved inversely in a coupled manner by a finite-difference numerical scheme. The streamwise convective term is altered to permit marching the solution through regions of reversed flow. The inviscid flow is computed by numerically solving the Laplace equation for stream-function in the region bounded by the displacement surfaces used in the inverse boundary-layer solution. The viscous and inviscid solutions are repeated iteratively until the edge velocities obtained from both solutions are in agreement. Predictions using this method compare favorably with experimental data and other predictions.

Hall, E. J.↗

ML-Based Rock Properties and Seismic Volume Enhancement

This project aims to improve field-scale Carbon Capture and Storage (CCS) assessments by enhancing petrophysical and geophysical log predictions through machine learning and neural networks. In our work during EY23, we applied Conditional Variational Autoencoders (CVAEs) to predict compressional velocity (Vp) and assess CO2 saturation levels in geological formations at the Illinois Basin Decatur Project (IBDP). In another task, we improved full-waveform inversion (FWI) methods with machine-learning approaches using lithological constraints. Full-waveform inversion (FWI) of seismic data estimates the elastic properties of subsurface rocks with high spatial resolution.

Nathanail, Athanasios↗

Contamination and Surface Preparation Effects on Composite Bonding

Results presented here demonstrate the effect of several prebond surface contaminants (hydrocarbon, machining fluid, latex, silicone, peel ply residue, release film) on bond quality, as measured by fracture toughness and failure modes of carbon fiber reinforced epoxy substrates bonded in secondary and co-bond configurations with paste and film adhesives. Additionally, the capability of various prebond surface property measurement tools to detect contaminants and potentially predict subsequent bond performance of three different adhesives is also shown. Surface measurement methods included water contact angle, Dyne solution wettability, optically stimulated electron emission spectroscopy, surface free energy, inverse gas chromatography, and Fourier transform infrared spectroscopy with chemometrics analysis. Information will also be provided on the effectiveness of mechanical and energetic surface treatments to recover a bondable surface after contamination. The benefits and drawbacks of the various surface analysis tools to detect contaminants and evaluate prebond surfaces after surface treatment were assessed as well as their ability to correlate to bond performance. Surface analysis tools were also evaluated for their potential use as in-line quality control of adhesive bonding parameters in the manufacturing environment.

Kutscha, Eileen O.↗

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗