Regression-based projection for learning Mori-Zwanzig operators
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Reflected entropy in random tensor networks. Part III. Triway cuts
For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S R = 2EW, where S R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.
AdS-CFT correspondence↗
Online MCMC Thinning with Kernelized Stein Discrepancy
A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many nonparametric approaches do so by sampling a large number of points using variants of Markov chain Monte Carlo (MCMC). Here, we propose an MCMC variant that retains only those posterior samples which exceed a kernelized Stein discrepancy (KSD) threshold, which we call KSD thinning. We establish the convergence and complexity trade-offs for several settings of KSD thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. We provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations. We observe superior consistency/complexity trade-offs across a range of settings including MCMC sampling on two Bayesian inference problems from the biological sciences, and 10 × inference speedup and storage reduction for Bayesian neural networks with no loss of accuracy and no increase in training time. Our code is available at https://github.com/colehawkins/KSD-Thinning.
Bayesian inference↗
Matrix Completion for Improved Observability in Low-Voltage Distribution Grids
This paper considers the problem of recovering missing entries in a partially observed matrix from relatively few measurements (i.e., the so-called matrix completion problem) with the aim of increasing the presently limited observability of low-voltage distribution grids. To this end, the partially observed matrix is formed using scarce voltage magnitude measurements while accounting for their spatial information. Voltage readings are assumed to be collected from distribution utility sensors and/or geographically-distributed cable television network sensors located in immediate proximity to distribution grid nodes. A matrix completion approach built on the parameter-less singular value shrinkage technique is used to estimate voltage magnitudes at otherwise non-observable low-voltage nodes using a small number of single- or multiple-snapshot data. The effectiveness of the proposed approach is demonstrated using a U.S.-style distribution test system from the synthetic SMART- DS data set under very low- to moderate-observability conditions.
low-rank matrix completion↗
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↗
Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo
As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. Furthermore, SGLD typically suffers from a slow convergence rate due to its large variance caused by the stochastic gradient. In order to alleviate these drawbacks, we leverage the recently developed Laplacian smoothing technique and propose a Laplacian smoothing stochastic gradient Langevin dynamics (LS-SGLD) algorithm. We prove that for sampling from both log-concave and non-log-concave densities, LS-SGLD achieves strictly smaller discretization error in 2-Wasserstein distance, although its mixing rate can be slightly slower. Experiments on both synthetic and real datasets verify our theoretical results and demonstrate the superior performance of LS-SGLD on different machine learning tasks including posterior sampling, Bayesian logistic regression, and training Bayesian convolutional neural networks.
97 MATHEMATICS AND COMPUTING↗
Deep generative models for vehicle speed trajectories
Generating realistic vehicle speed trajectories is a crucial component in evaluating vehicle fuel economy and in predictive control of self-driving cars. Traditional generative models rely on Markov chain methods and can produce accurate synthetic trajectories but are subject to the curse of dimensionality. They do not allow to include conditional input variables into the generation process. In this paper, we show how extensions to deep generative models allow accurate and scalable generation. Proposed architectures involve recurrent and feed-forward layers and are trained using adversarial techniques. Our models are shown to perform well on generating vehicle trajectories using a model trained on GPS data from Chicago metropolitan area.
33 ADVANCED PROPULSION SYSTEMS↗
Enriching Load Data Using Micro-PMUs and Smart Meters
In modern distribution systems, load uncertainty can be fully captured by micro-PMUs, which can record high-resolution data; however, in practice, micro-PMUs are installed at limited locations in distribution networks due to budgetary constraints. In contrast, smart meters are widely deployed but can only measure relatively low-resolution energy consumption, which cannot sufficiently reflect the actual instantaneous load volatility within each sampling interval. In this paper, we have proposed a novel approach for enriching load data for service transformers that only have low-resolution smart meters. The key to our approach is to statistically recover the high-resolution load data, which is masked by the low-resolution data, using trained probabilistic models of service transformers that have both high- and low-resolution data sources, i.e., micro-PMUs and smart meters. The overall framework consists of two steps: first, for the transformers with micro-PMUs, a Gaussian Process is leveraged to capture the relationship between the maximum/minimum load and average load within each low-resolution sampling interval of smart meters; a Markov chain model is employed to characterize the transition probability of known high-resolution load. Next, the trained models are used as teachers for the transformers with only smart meters to decompose known low-resolution load data into targeted high-resolution load data. The enriched data can recover instantaneous load uncertainty and significantly enhance distribution system observability and situational awareness. Here, we have verified the proposed approach using real high- and low-resolution load data.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Support for Reactor Operators in Case of Cyber-Security Threats (NEUP Final Report)
Increasing use of digital technology in nuclear power plants (NPPs) poses cyber-security as a crucial threat to public safety and to continuous energy production. Cyber-security risks are comprised of complex known and unknown interactions between various entities, system vulnerabilities, network protocols, human users and malicious attacks. There is little understanding or research geared towards plant operators’ response under cyber-security threats and operational procedures to cope with such threats. This is particularly critical when a cyber-security event masquerades as a safety incident or an evolving accident. Instead of leading operators to the remediation of the accident, the masked cyber event may lead them to circumvent the safety mechanisms of the plant. Given these challenges, the objective of this project is to develop a tool to characterize abnormal NPP events as “cyber” or “safety” incidents, and to further develop this tool as a real-time operator aid to assist in response to the incident. This NEUP Final Report summarizes the research efforts towards the above goals and the results in the following three aspects. First, a methodology for classifying abnormal NPP events as cyber-attacks or safety incidents was developed. This provides the basis for responding to potential cyber-attacks. In this methodology, the causal relationships between various variables (i.e., physical variables, network variables, and control variables) for a nuclear system under consideration are modeled using dynamic Bayesian networks. Based on observations of certain variables (i.e., the evidence), inference is performed to identify the state of hidden variables, which helps indicate the occurrence of cyber-attacks or safety incidents. The proposed methodology was applied to the full scope NPP simulator system at The Ohio State University as a case study. The result shows that the proposed methodology is capable of distinguishing between cyber-attacks and safety incidents. Second, a game-theoretic approach for responding to cyber-attacks on nuclear power plants was developed. This is the second major goal of the project, and the method is used to recommend optimal responses to reactor operators in the case of cyber-attacks. We consider two cases in this research. In the first case, the interaction between the defender (i.e., the reactor operator) and the attacker is modeled as a two-player, nonzero-sum, Markov game with an infinite time horizon. In the second case, we consider a semi-Markov game between the defender and the attacker within a finite time horizon. The model in the second case enables us to consider the time sensitive response of the defender. In each case, the method for deriving the Nash equilibrium is developed. The Nash Equilibrium of the game provides the valid prediction of both players’ actions because no single player can benefit from unilaterally deviating from the equilibrium policy if the other player adheres to his/hers, hence it provides the best response of the defender to cyber-attacks. The proposed method in each case is demonstrated through a simplified benchmark digital feedwater control system. Third, a prototype display is developed to integrate the above information. The prototype display depicts the communication information to the operator and incorporates the cyber-security tool developed by the team into the interface. It consists of the regular display in current control rooms, as well as a panel used to indicate the occurrence of cyber-attacks or safety events and a panel used to guide the operator’s response to detected cyber-attacks.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Neural-Network Inverse Design of SRF Cavities and Transmons for Bosonic Quantum Computation
Three-dimensional superconducting radio-frequency (SRF) cavities provide exceptionally long-lived electromagnetic modes and, when coupled to nonlinear elements such as transmon qubits, become promising architectures for bosonic quantum information processing. The inverse design of such systems, i.e., recovering device geometries that produce specified electromagnetic and coupling targets, is generally a one-to-many problem. The qubit-cavity coupling strength depends sensitively on both the transmon geometry and its position within the cavity's electromagnetic field. As these systems scale up and their design parameter spaces grow, the cost of conventional iterative simulation becomes prohibitive. We present two deep neural network (DNN) approaches that address this inverse-design problem at complementary levels of the design stack. The first proposes SRF cavity geometries that produce target cavity observables. The second proposes transmon qubit designs that produce target qubit-cavity parameters - the coupling rate, qubit frequency, and anharmonicity $(g, ν_q, α)$. The recovered candidate designs match the targets to within ~5% (cavity) and ~2% (transmon), confirmed by end-to-end re-simulation. Both approaches map desired device behavior directly to candidate designs, a fast alternative to the iterative simulation studies usually required.
Yaker, Joseph [Fermilab; Northwestern U.]↗
Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)
With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.
97 MATHEMATICS AND COMPUTING↗
CLASS Survey Description: Coronal-line Needles in the SDSS Haystack
Coronal lines are a powerful, yet poorly understood, tool to identify and characterize active galactic nuclei. There have been few large-scale surveys of coronal lines in the general galaxy population in the literature so far. Using a novel preselection technique with a flux-to-rms ratio $\mathcal{F}$, followed by Markov Chain Monte Carlo fitting, we searched for the full suite of 20 coronal lines in the optical spectra of almost 1 million galaxies from the Sloan Digital Sky Survey Data Release 8. We present a catalog of the emission-line parameters for the resulting 258 galaxies with detections. The Coronal Line Activity Spectroscopic Survey includes line properties, host-galaxy properties, and selection criteria for all galaxies in which at least one line is detected. This comprehensive study reveals that a significant fraction of coronal-line activity is missed in past surveys based on a more limited set of coronal lines; ~60% of our sample do not display the more widely surveyed [Fe x] λ6374. In addition, we discover a strong correlation between coronal-line and Wide-field Infrared Survey Explorer W2 luminosities, suggesting that the mid-infrared flux can be used to predict coronal-line fluxes. For each line we also provide a confidence level that the line is present, generated by a novel neural network, trained on fully simulated data. We find that after training the network to detect individual lines using 100,000 simulated spectra, we achieve an overall true-positive rate of 75.49% and a false-positive rate of only 3.96%.
79 ASTRONOMY AND ASTROPHYSICS↗