Results for “Gaussian process model” — Page 23

DOE OSTI2019

Application and Evaluation of Surrogate Models for Radiation Source Search

Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.

Cook, Jared A.↗

DOE OSTI2022

Machine Learning with Gradient-Based Optimization of Nuclear Waste Vitrification with Uncertainties and Constraints

Gekko is an optimization suite in Python that solves optimization problems involving mixed-integer, nonlinear, and differential equations. The purpose of this study is to integrate common Machine Learning (ML) algorithms such as Gaussian Process Regression (GPR), support vector regression (SVR), and artificial neural network (ANN) models into Gekko to solve data based optimization problems. Uncertainty quantification (UQ) is used alongside ML for better decision making. These methods include ensemble methods, model-specific methods, conformal predictions, and the delta method. An optimization problem involving nuclear waste vitrification is presented to demonstrate the benefit of ML in this field. ML models are compared against the current partial quadratic mixture (PQM) model in an optimization problem in Gekko. GPR with conformal uncertainty was chosen as the best substitute model as it had a lower mean squared error of 0.0025 compared to 0.018 and more confidently predicted a higher waste loading of 37.5 wt% compared to 34 wt%. The example problem shows that these tools can be used in similar industry settings where easier use and better performance is needed over classical approaches. Future works with these tools include expanding them with other regression models and UQ methods, and exploration into other optimization problems or dynamic control.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1974

A curvature-corrected Kirchhoff formulation for radar sea-return from the near vertical

A new theoretical treatment of the problem of electromagnetic wave scattering from a randomly rough surface is given. A high frequency correction to the Kirchhoff approximation is derived from a field integral equation for a perfectly conducting surface. The correction, which accounts for the effect of local surface curvature, is seen to be identical with an asymptotic form found by Fock (1945) for diffraction by a paraboloid. The corrected boundary values are substituted into the far field Stratton-Chu integral, and average backscattered powers are computed assuming the scattering surface is a homogeneous Gaussian process. Preliminary calculations for K(-4) ocean wave spectrum indicate a resonable modelling of polarization effects near the vertical, theta 45 deg. Correspondence with the results of small perturbation theory is shown.

Jackson, F. C.↗

DOE OSTI2021

A practical extension of the recursive multi-fidelity model for the emulation of hole closure experiments

We report in regimes of high strain rate, the strength of materials often cannot be measured directly in experiments. Instead, the strength is inferred based on an experimental observable, such as a change in shape, that is matched by simulations supported by a known strength model. In hole closure experiments, the rate and degree to which a central hole in a plate of material closes during a dynamic loading event are used to infer material strength parameters. Due to the complexity of the experiment, many computationally expensive, three-dimensional simulations are necessary to train an emulator for calibration or other analyses. These simulations can be run at multiple grid resolutions, where dense grids are slower but more accurate. In an effort to reduce the computational cost, a combination of simulations with different resolutions can be combined to develop an accurate emulator within a limited training time. We explore the novel design and construction of an appropriate functional recursive multi-fidelity emulator of a strength model for tantalum in hole closure experiments that can be applied to arbitrarily large training data. Hence, by formulating a multi-fidelity model to employ low-fidelity simulations, we were able to reduce the error of our emulator by approximately 81% with only an approximately 1.6% increase in computing resource utilization.

36 MATERIALS SCIENCE↗

NASA NTRS2011

Prognostics of Power Mosfets Under Thermal Stress Accelerated Aging Using Data-Driven and Model-Based Methodologies

An approach for predicting remaining useful life of power MOSFETs (metal oxide field effect transistor) devices has been developed. Power MOSFETs are semiconductor switching devices that are instrumental in electronics equipment such as those used in operation and control of modern aircraft and spacecraft. The MOSFETs examined here were aged under thermal overstress in a controlled experiment and continuous performance degradation data were collected from the accelerated aging experiment. Dieattach degradation was determined to be the primary failure mode. The collected run-to-failure data were analyzed and it was revealed that ON-state resistance increased as die-attach degraded under high thermal stresses. Results from finite element simulation analysis support the observations from the experimental data. Data-driven and model based prognostics algorithms were investigated where ON-state resistance was used as the primary precursor of failure feature. A Gaussian process regression algorithm was explored as an example for a data-driven technique and an extended Kalman filter and a particle filter were used as examples for model-based techniques. Both methods were able to provide valid results. Prognostic performance metrics were employed to evaluate and compare the algorithms.

Electrolytic capacitors↗

DOE OSTI2023

$\text{GPLaSDI}$: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. Here we demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Integrated top-down process and voxel-based microstructure modeling for Ti-6Al-4V in laser wire direct energy deposition process

Laser-wire metal additive manufacturing (AM) is one of the ideal direct energy deposition (DED) processes for creating large-scale parts with a medium level of complexity. However, the DED process involves complex thermal signatures and wide length scales making the fabrication of realistic AM components and part qualification often reliant on experimental trial-and-error optimization. While experimental measurements over the full volume of a part are valuable and necessary, measuring the entire area of a part is significantly laborious and practically infeasible, particularly for large parts in terms of cost and rapid qualification. Therefore, in this work, we developed an effective thermal and microstructure modeling framework based on the Johnson–Mehl-Avrami-Kolmogorov (JMAK) and Koistinen & Marburger (KM) models through a top-down approach that considers plate distortion-affected thermal profiles. A voxel-by-voxel simulation method is used to predict individual phase fractions of Ti-6Al-4 V. The predicted results were validated through detailed metallurgical measurements. A combined voxel-by-voxel approach with a sparse data reconstruction technique produced a near-perfect reconstruction of the original data. This approach anticipates a significant reduction in data points and computation time and resources. Lastly, we conclude with potential extensions of this work to other modeling efforts.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Machine learning enables national assessment of wind plant controls with implications for land use

Summary As deployment of wind energy continues to expand, computationally efficient tools for predicting wind plant performance over a wide range of layout designs, technology innovations, and spatial locations are increasingly important for policy and investment decisions. We demonstrate two approaches to training a surrogate model to predict annual energy production (AEP) of parameterized wind plant layouts: one using a Gaussian process (GP) and the other using a fully convolutional neural network (FCNN). We leverage the powerful FCNN architecture by encoding wind plant design parameters and output response surface as an image. The FCNN produces more accurate results than the GP with mean absolute errors equivalent to 1% and 1.9% of plant rated power, respectively, although the GP performs well under limited training data and provides useful uncertainty information. We also evaluate a surrogate model for wake steering, enabling a nationwide assessment of the impact of plant control strategies and plant layout decisions. Across two million locations, we find that wake steering strategies boost AEP with relative gains upwards of 3%. Gains are most pronounced at sites without a dominant wind direction and where layout optimization is less fruitful. Additionally, we perform a nationwide sensitivity analysis showing that wake steering can mitigate wake losses from higher density plant layouts. Our results suggest that regions which have not been previously viable for wind deployment due to moderate wind resources are especially well enhanced by wake steering strategies that could help overcome land constraints and inflexible layout options, potentially identifying new deployment opportunities.

17 WIND ENERGY↗

DOE OSTI2020

Gaussian process regression and conditional polynomial chaos for parameter estimation

Not Available

Li, Jing↗

NASA NTRSDate not supplied

Discriminative Methodology using the Unscented Transform in Special Euclidean Group SE(3) for Autonomous GN&C

Kalman filtering techniques usually compare a known dynamic model with some process noise to an updated, noisy measurement. Both sources of noise are generally assumed to be Gaussian and are filtered to obtain a more accurate estimate of the state of the system of interest. However, these methods assume that a relatively accurate dynamical model already exists. By including discriminative methodology to interpret differences in the predictive model and the measured states over time, an incorrect model can be corrected overtime, allowing a spacecraft to learn about its environment and adapt to changing conditions. In this paper, a discriminative unscented Kalman filter (DUKF) is introduced on the special Euclidean group SE(3) formulation framework. A spacecraft is initialized near a small body with no knowledge of its parameters, and using several consecutive conditional models the environment is studied and the filter is updated. The case study of a spacecraft in a slightly elliptical, inclined, relatively tight orbit around the irregular moon Phobos is simulated and discussed. The accuracy of this approach is quantifying the differences between the true state, the UKF with a poor model, and the DUKF.

GN&C↗

DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗

DOE OSTI2023

Bayesian inference of in-medium baryon-baryon scattering cross sections from HADES proton flow data

Within a Bayesian statistical framework using a Gaussian Process emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate energies, we infer from the HADES proton flow data the posterior probability distribution functions of in-medium baryon-baryon scattering cross section modification factor X with respect to free-space and the corresponding incompressibility K of nuclear matter as well as their correlation function. In conclusion, the mean value of X is found to be $X$ = $1.32_ {+0.28} ^ {-0.40} $ at 68% confidence level assuming the nuclear incompressibility K will not exceed 400 MeV, providing circumstantial evidence for enhanced baryon-braryon scattering cross sections in hot and dense nuclear matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Bayesian inference of nuclear incompressibility from collective flow in mid-central Au+Au collisions at 400–1500 MeV/nucleon

The incompressibility K of symmetric nuclear matter (SNM) is determined through a Bayesian analysis of collective flow data from Au + Au collisions at beam energies $E = 400 -1500$ MeV/nucleon. This analysis utilizes a Gaussian process (GP) emulator applied to the isospin-dependent quantum molecular dynamics (IQMD) model for heavy-ion collisions, both with and without incorporating the momentum dependence of the single-nucleon potentials. Specifically, at the 68% confidence level, using rapidity and transverse velocity dependence of proton elliptic flow data with and without consideration of the momentum dependence, the inferred incompressibility values are $K=188.9^{+2.9}_{-4.5}$ MeV and $256.1^{+8.2}_{-8.7}$ MeV at $E = 400$ MeV/nucleon, respectively. When the transverse momentum dependence of proton-like directed flow data is included, the inferred incompressibility values become $K=222.3^{+9.0}_{-9.9}$ MeV and $K=285.5^{+6.7}_{-7.3}$ MeV, respectively. Furthermore, we found that the value of K derived from observables of proton elliptic flow increases with beam energy. Finally, this indicates that the equation of state (EoS) of nuclear matter hardens at higher densities and temperatures in reactions with higher beam energies.

Bayesian inference↗

DOE OSTI2022

The Chocolate Chip Cookie Model: Dust Geometry of Milky Way–like Disk Galaxies

We present a new two-component dust geometry model, the Chocolate Chip Cookie model, where the clumpy nebular regions are embedded in a diffuse stellar/interstellar medium disk, like chocolate chips in a cookie. By approximating the binomial distribution of the clumpy nebular regions with a continuous Gaussian distribution and omitting the dust scattering effect, our model solves the dust attenuation process for both the emission lines and stellar continua via analytical approaches. Our Chocolate Chip Cookie model successfully fits the inclination dependence of both the effective dust reddening of the stellar components derived from stellar population synthesis and that of the emission lines characterized by the Balmer decrement for a large sample of Milky Way–like (MW-like) disk galaxies selected from the main galaxy sample of the Sloan Digital Sky Survey. Our model shows that the clumpy nebular disk is about 0.55 times thinner and 1.6 times larger than the stellar disk for MW-like galaxies, whereas each clumpy region has a typical optical depth of τ cl,V ~ 0.5 in the V band. After considering the aperture effect, our model prediction on the inclination dependence of dust attenuation is also consistent with observations. Not only that, in our model, the dust attenuation curve of the stellar population naturally depends on the inclination, and its median case is consistent with the classical Calzetti law. As the modeling constraints are from the optical wavelengths, our model is unaffected by the optically thick dust component, which however could bias the model's prediction of the infrared emissions.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1999

Transonic Flutter Suppression Control Law Design Using Classical and Optimal Techniques with Wind-Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Mukhopadhyay, Vivek↗

NASA NTRS1999

Transonic Flutter Suppression Control Law Design, Analysis and Wind Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Mukhopadhyay, Vivek↗

NASA NTRS1999

Transonic Flutter Suppression Control Law Design, Analysis and Wind-Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Mukhopadhyay, Vivek↗

NASA NTRS1999

Transonic Flutter Suppression Control Law Design Using Classical and Optimal Techniques with Wind-Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Mukhopadhyay, Vivek↗