A Transfer Learning Framework for Power System Event Identification
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24 POWER TRANSMISSION AND DISTRIBUTION↗
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Results for “Kernel learning”
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.
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A GPU-Accelerated Population Generation, Sorting, and Mutation Kernel for an Optimization-Based Causal Inference Model
We develop a GPU-accelerated machine learning generative adversarial network model that can be used with observational data for the purpose of constructing causal inferences. The theoretical basis of our machine learning model is novel and is conceptualized to be operable and scalable for high performance computing platforms. Our GPU-accelerated code enables large-scale parallelization of the computation within a common and accessible computing environment. This will expand the reach of our model and empower research in new substantive domains while maintaining the underlying theoretical properties.
Cho, Wendy K. Tam↗
Physics-informed machine learning
Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.
97 MATHEMATICS AND COMPUTING↗
Data-driven learning of Mori–Zwanzig operators for isotropic turbulence
Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.
97 MATHEMATICS AND COMPUTING↗
Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.
97 MATHEMATICS AND COMPUTING↗
Optimization of the generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double- β decay: Ridge regression for nuclei with axial deformation
The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state 0νββ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76 Ge and 76 Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of 76 Ge and 76 Se, as well as the 0νββ-decay NME between their ground states, are computed. Furthermore, the results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.
59 ≤ A ≤ 89↗
Non-Gaussian estimates of tensions in cosmological parameters
We discuss how to efficiently and reliably estimate the level of agreement and disagreement on parameter determinations from different experiments, fully taking into account non-Gaussianities in the parameter posteriors. We develop two families of scalable algorithms that allow us to perform this type of calculations in increasing number of dimensions and for different levels of tensions. One family of algorithms rely on kernel density estimates of posterior distributions while the other relies on machine learning modeling of the posterior distribution with normalizing flows. We showcase their effectiveness and accuracy with a set of benchmark examples and find both methods agree with each other and the true tension within 0.5σ in difficult cases and generally to 0.2σ or better. This allows us to study the level of internal agreement between different measurements of the clustering of cosmological structures from the Dark Energy Survey and their agreement with measurements of the Cosmic Microwave Background from the Planck satellite.
79 ASTRONOMY AND ASTROPHYSICS↗
Ab initio generalized Langevin equation
We introduce a machine learning–based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori–Zwanzig formalism, under the constraint of the fluctuation–dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.
97 MATHEMATICS AND COMPUTING↗
Improved particle-flow event reconstruction with scalable neural networks for current and future particle detectors
Abstract Efficient and accurate algorithms are necessary to reconstruct particles in the highly granular detectors anticipated at the High-Luminosity Large Hadron Collider and the Future Circular Collider. We study scalable machine learning models for event reconstruction in electron-positron collisions based on a full detector simulation. Particle-flow reconstruction can be formulated as a supervised learning task using tracks and calorimeter clusters. We compare a graph neural network and kernel-based transformer and demonstrate that we can avoid quadratic operations while achieving realistic reconstruction. We show that hyperparameter tuning significantly improves the performance of the models. The best graph neural network model shows improvement in the jet transverse momentum resolution by up to 50% compared to the rule-based algorithm. The resulting model is portable across Nvidia, AMD and Habana hardware. Accurate and fast machine-learning based reconstruction can significantly improve future measurements at colliders.
Physics↗
Accurate parameterization of the kinetic energy functional
The absence of a reliable formulation of kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions which have been proposed in the literature and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals - a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since, the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H 2 , LiH, LiF and a one-dimensional chain of 8 hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures. For the ease of reproduction, codes used to generate the models are provided in the supporting materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Distributed Data-Driven Optimization for Voltage Regulation in Distribution Systems
Here, this paper proposes a distributed data-driven optimization framework for voltage regulation in distribution systems. The recursive kernel regression and alternating direction method of multipliers (ADMM) are selected to cover the system learning and distributed optimization tasks. The proposed distributed data-driven framework is capable of having a rapid response to system or load changes while considering the operation optimality. Besides, the distributed algorithm parallels the computation tasks and reduces the computational expense of a single agent. To validate the performance of the proposed method, a hypothetical 7-Bus system and the IEEE 123-Bus system are selected to show the effectiveness of the proposed data-driven framework. According to the numerical study results, the proposed method offers great flexibility for selecting customized kernel models for different regions and can effectively improve the system voltage profile in a distributed manner.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Compactly‐Supported Nonstationary Kernels for Computing Exact Gaussian Processes on Big Data
The Gaussian process (GP) is a widely used method for analyzing large-scale data sets, including spatio-temporal measurements of nonlinear processes that are now commonplace in the environmental sciences. Traditional implementations of GPs involve stationary kernels (also termed covariance functions) that limit their flexibility, and exact methods for inference that prevent application to data sets with more than about 10,000 points. Modern approaches to address stationarity assumptions generally fail to accommodate large data sets, while all attempts to address scalability focus on approximating the Gaussian likelihood, which can involve subjectivity and lead to inaccuracies. In this work, we explicitly derive an alternative kernel that can discover and encode both sparsity and nonstationarity. We embed the kernel within a fully Bayesian GP model and leverage high-performance computing resources to enable the analysis of massive data sets. We demonstrate the favorable performance of our novel kernel relative to existing exact and approximate GP methods across a variety of synthetic data examples. Furthermore, we conduct space–time prediction based on more than 1 million measurements of daily maximum temperature and verify that our results outperform state-of-the-art methods in the Earth sciences. More broadly, having access to exact GPs that use ultra-scalable, sparsity-discovering, nonstationary kernels allows GP methods to truly compete with a wide variety of machine learning methods.
Gaussian processes↗
Gamma-ray Spectrum Explanations (GRSE) v0.1
This code repository provides tools for producing various types of machine learning model explanations trained on gamma-ray spectra. It includes implementations of saliency mapping, Grad-CAM, LIME, and Kernel SHAP, including improvements and clarifications to some of the approaches that are specific to their use with gamma-ray spectral data. These tools are in support of the manuscript M.S. Bandstra et al., "Explaining machine-learning models for gamma-ray detection and identification," under review at PLOS ONE.
Bandstra, Mark↗
Feature learning and generalization in deep networks with orthogonal weights
Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width—which govern the evolution of observables during training—saturate at a depth of ~20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed in deep networks with depth comparable to width. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep non-linear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.
97 MATHEMATICS AND COMPUTING↗
Model Residuals as Shields: A Two-Level Formulation to Defend Smart Grids From Poisoning Attacks
The advancement of smart grids presents both vast opportunities and heightened cybersecurity risks. Data-driven defense mechanisms, though designed as a shield against these threats, can fall prey to poisoning attacks. We delve into regression settings, underscoring the imperative to fortify defenses against a spectrum of poison ratios, notably those above 0.5—an issue scarcely addressed in prior studies. Recognizing the susceptibilities of smart grids and their manipulable sensors, we exploit the very intent of poisoning attacks, compromising model accuracy, as our defense mechanism. Our proposed two-level optimization framework discerns between poisoned and authentic data based on model residuals, outperforming or matching existing methods in 72% to 77% of precision and 75% to 80% of recalls across various poisoning attacks, poison ratios, and datasets. Once the authentic data are identified, the trained model is adaptable for a variety of applications. Comprehensive evaluations on different smart grid datasets, pitted against myriad poisoning schemes, validate our methodology’s edge over existing methods. Here, we also shed light on the implications of model misspecification originating from temporal auto-correlation, a common feature in Internet of Things and smart grid data.
Adversarial machine learning (ML)↗
Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra
This work investigates and applies machine learning paradigms seldom seen in analytical spectroscopy for quantification of gallium in cerium matrices via processing of laser-plasma spectra. Ensemble regressions, support vector machine regressions, Gaussian kernel regressions, and artificial neural network techniques are trained and tested on cerium-gallium pellet spectra. A thorough hyperparameter optimization experiment is conducted initially to determine the best design features for each model. The optimized models are evaluated for sensitivity and precision using the limit of detection (LoD) and root mean-squared error of prediction (RMSEP) metrics, respectively. Gaussian kernel regression yields the superlative predictive model with an RMSEP of 0.33% and an LoD of 0.015% for quantification of Ga in a Ce matrix. This study concludes that these machine learning methods could yield robust prediction models for rapid quality control analysis of plutonium alloys.
Rao, Ashwin P. (ORCID:0000000319312568)↗
MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities
The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Neural Network-Enhanced Reproducing Kernel Particle Method for Image-Based Multiphysics Damage Modeling of Energy Storage Materials
Energy storage materials undergo significant stresses during charge/discharge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), image-based modeling techniques are used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electrochemical-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in capturing crack propagation due to mesh dependency. Additionally, commonly used damage models, such as the continuous damage model and the cohesive zone model, often have steep tradeoffs between discontinuous field accuracy and computational expense. In this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022.
damage modeling↗