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DOE OSTI2024

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

DOE OSTI2023

Implicit learning of convective organization explains precipitation stochasticity

Accurate prediction of precipitation intensity is crucial for both human and natural systems, especially in a warming climate more prone to extreme precipitation. Yet, climate models fail to accurately predict precipitation intensity, particularly extremes. One missing piece of information in traditional climate model parameterizations is subgrid-scale cloud structure and organization, which affects precipitation intensity and stochasticity at coarse resolution. Here, using global storm-resolving simulations and machine learning, we show that, by implicitly learning subgrid organization, we can accurately predict precipitation variability and stochasticity with a low-dimensional set of latent variables. Using a neural network to parameterize coarse-grained precipitation, we find that the overall behavior of precipitation is reasonably predictable using large-scale quantities only; however, the neural network cannot predict the variability of precipitation (R 2 ~ 0.45) and underestimates precipitation extremes. The performance is significantly improved when the network is informed by our organization metric, correctly predicting precipitation extremes and spatial variability (R 2 ~ 0.9). The organization metric is implicitly learned by training the algorithm on a high-resolution precipitable water field, encoding the degree of subgrid organization. The organization metric shows large hysteresis, emphasizing the role of memory created by subgrid-scale structures. We demonstrate that this organization metric can be predicted as a simple memory process from information available at the previous time steps. These findings stress the role of organization and memory in accurate prediction of precipitation intensity and extremes and the necessity of parameterizing subgrid-scale convective organization in climate models to better project future changes of water cycle and extremes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Quantifying uncertainties on fission fragment mass yields with mixture density networks

Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we explore the use of one such probabilistic network, the mixture density network (MDN), to reproduce fission yields and their uncertainties. In this paper, we study mass yields for the spontaneous fission of 252 Cf, exploring the number of training samples needed for converged predictions, how different levels of uncertainty propagate from the training set to the MDN predictions, and how well physical constraints of the yields—such as normalization and symmetry—are upheld by the algorithm. Finally, we test the ability of the MDN to interpolate between and extrapolate beyond samples in the training set using energy-dependent mass yields for the neutron-induced fission on 235 U. The MDN provides a reliable way to include and predict uncertainties and is a promising path forward for supplementing sparse sets of nuclear data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Megahertz-compatible angular streaking with few-femtosecond resolution at x-ray free-electron lasers

Highly brilliant, coherent, femtosecond x-ray pulses delivered by free-electron lasers (FELs) constitute one of the pillars of modern ultrafast science. Next generation FEL facilities provide up to megahertz repetition rates and pulse durations down to the attosecond regime utilizing self-amplification of spontaneous emission. However, the stochastic nature of this generation mechanism demands single-shot pulse characterization to perform meaningful experiments. Here we demonstrate a fast yet robust online analysis technique capable of megahertz-rate mapping of the temporal intensity structure and arrival time of x-ray FEL pulses with few-femtosecond resolution. We performed angular streaking measurements of both neon photo- and Auger electrons and show their applicability for a direct time-domain feedback system during ongoing experiments. Here, the fidelity of the real-time pulse characterization algorithm is corroborated by resolving isolated x-ray pulses and double pulse trains with few-femtosecond substructure, thus paving the way for x-ray-pump–x-ray-probe FEL science at repetition rates compatible with the demands of LCLS-II and European XFEL.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Fast and scalable quantum Monte Carlo simulations of electron-phonon models

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly-bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. Here, these methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Elastic Stochastic Full Waveform Inversion (eSFWI)

This collaboration between Lawrence Livermore National Security, LLC (LLNS) as manager and operator of Lawrence Livermore National Laboratory (LLNL) and Chevron USA Inc., acting through its Chevron Technical Center division, aimed at developing next-generation computational methods for the Elastic Stochastic Full Waveform Inversion (eSFWI). Seismic imaging is heavily used in the oil and gas industry for identifying and operating subsurface reservoirs. Improved seismic imaging methods can improve productivity, lower costs, and improve operational and environmental safety. This CRADA demonstrated that new high-performance computing (HPC) architectures being rolled out over the next five years can enable unprecedented seismic imaging resolution when using eSFWI techniques to process active seismic data. An open-source computational mini-application was developed, capable of demonstrating near-peak performance for eSFWI algorithms on CPU and GPU enabled HPC platforms. Performance was demonstrated on LLNL HPC systems such as Lassen, as well as on Chevron systems. This project benefited Chevron USA Inc. by demonstrating the potential computational efficiency of their full waveform inversion capabilities used to characterize oil/gas reservoirs, which in turn benefits the public through potential increases in capabilities to perform analysis of leasing sites.

04 OIL SHALES AND TAR SANDS↗

NASA NTRS1996

Integrated Control Using the SOFFT Control Structure

The need for integrated/constrained control systems has become clearer as advanced aircraft introduced new coupled subsystems such as new propulsion subsystems with thrust vectoring and new aerodynamic designs. In this study, we develop an integrated control design methodology which accomodates constraints among subsystem variables while using the Stochastic Optimal Feedforward/Feedback Control Technique (SOFFT) thus maintaining all the advantages of the SOFFT approach. The Integrated SOFFT Control methodology uses a centralized feedforward control and a constrained feedback control law. The control thus takes advantage of the known coupling among the subsystems while maintaining the identity of subsystems for validation purposes and the simplicity of the feedback law to understand the system response in complicated nonlinear scenarios. The Variable-Gain Output Feedback Control methodology (including constant gain output feedback) is extended to accommodate equality constraints. A gain computation algorithm is developed. The designer can set the cross-gains between two variables or subsystems to zero or another value and optimize the remaining gains subject to the constraint. An integrated control law is designed for a modified F-15 SMTD aircraft model with coupled airframe and propulsion subsystems using the Integrated SOFFT Control methodology to produce a set of desired flying qualities.

Halyo, Nesim↗

DOE OSTI2023

Benchmarking quantum logic operations relative to thresholds for fault tolerance

Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates—defined via the diamond norm—which can differ from average error rates by orders of magnitude. One method for resolving this discrepancy is to randomize the physical implementation of quantum gates, using techniques like randomized compiling (RC). In this work, we use gate set tomography to perform precision characterization of a set of two-qubit logic gates to study RC on a superconducting quantum processor. We find that, under RC, gate errors are accurately described by a stochastic Pauli noise model without coherent errors, and that spatially correlated coherent errors and non-Markovian errors are strongly suppressed. We further show that the average and worst-case error rates are equal for randomly compiled gates, and measure a maximum worst-case error of 0.0197(3) for our gate set. Our results show that randomized benchmarks are a viable route to both verifying that a quantum processor’s error rates are below a fault-tolerance threshold, and to bounding the failure rates of near-term algorithms, if—and only if—gates are implemented via randomization methods which tailor noise.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

Toward the modeling of land use change: A spatial analysis using remote sensing and historical data

It was hypothesized that the chronological observation of land use change could be shown to follow a predictable pattern and these patterns could be correlated with other statistical data to develop transition probabilities suitable for modeling purposes. A literature review and preliminary research, however, indicated a totally stochastic approach was not practical for simulating land use change and thus a more deterministic approach was adopted. The approach used assumes the determinants of the land use conversion process are found in the market place, where land transactions among buyers and sellers occur. Only one side of the market transaction process is studied, however, namely, the purchaser's desires in securing an ideal or suitable site. The problem was to identify the ideal qualities, quantities or attributes desired in an industrial site (or housing development), and to formulate a general algorithmic statement capable of identifying potential development sites. Research procedures involved developing a list of variables previously noted in the literature to be related to site selection and streamlining the list to a set suitable for statistical testing. A sample of 157 industries which have located (or relocated) in the 16-county Knoxville metropolitan region since 1950 was selected for industrial location analysis. Using NASA color infrared photography and Tennessee Valley Authority historical aerial photography, data were collected on the spatial characteristics of each industrial location event. These data were then subjected to factor analysis to determine the interrelations of variables.

Honea, R. B.↗

NASA NTRS1997

Computation of Reacting Flows in Combustion Processes

The main objective of this research was to develop an efficient three-dimensional computer code for chemically reacting flows. The main computer code developed is ALLSPD-3D. The ALLSPD-3D computer program is developed for the calculation of three-dimensional, chemically reacting flows with sprays. The ALL-SPD code employs a coupled, strongly implicit solution procedure for turbulent spray combustion flows. A stochastic droplet model and an efficient method for treatment of the spray source terms in the gas-phase equations are used to calculate the evaporating liquid sprays. The chemistry treatment in the code is general enough that an arbitrary number of reaction and species can be defined by the users. Also, it is written in generalized curvilinear coordinates with both multi-block and flexible internal blockage capabilities to handle complex geometries. In addition, for general industrial combustion applications, the code provides both dilution and transpiration cooling capabilities. The ALLSPD algorithm, which employs the preconditioning and eigenvalue rescaling techniques, is capable of providing efficient solution for flows with a wide range of Mach numbers. Although written for three-dimensional flows in general, the code can be used for two-dimensional and axisymmetric flow computations as well. The code is written in such a way that it can be run in various computer platforms (supercomputers, workstations and parallel processors) and the GUI (Graphical User Interface) should provide a user-friendly tool in setting up and running the code.

Keith, Theo G., Jr.↗

DOE OSTI2019

ADP-Based Home Energy Management System: A Case Study Using Dynamo: Preprint

This paper explores Home Energy Management System (HEMS) algorithms to minimize household cost while maintaining comfort when faced with uncertain weather, and demand. Specifically, we consider a HEMS that optimizes forward looking schedules for a home's heating, ventilation, and air conditioning (HVAC); water heater (WH); and electric vehicle (EV) charging while considering uncertainty in outside temperature, hot water usage, and non-controllable load (NCL). We adopt a Dynamic Programming (DP) formulation and utilize the Dynamic programming for Adaptive Modeling and Optimization (DYNAMO) toolkit to implement DP and approximate dynamic programming (ADP) algorithms. Simulation results under a single tariff plan compare the quality of the solution generated by ADP to that of DP, and show significant improvement in computation time while maintaining acceptable solution accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2019

Unified probabilistic energy flow analysis for electricity–gas coupled systems with integrated demand response

Under a multi-energy environment, the conventional demand response programmes in smart-grid will be evolving to the concept of integrated demand response (IDR). In order to examine such an effect, this study presents a new methodological framework to conduct the probabilistic energy flow (PEF) analysis of integrated energy systems, while considering the potential effects of IDR. For this aim, a new price-elasticity-based IDR model is developed. As distinct from existing works, this study explicitly focuses on the stochastic characteristics of IDR programme and a novel Z-number-based technique is introduced to handle the relevant uncertainties that involved. The proposed Z-number model can not only capture the inherent randomness in demand-side performance but also account for the potential impact of information availability/reliability on the representation of IDR. Since the presence of Z-numbers makes the authors model include different types of uncertain representations, the fuzzy expectation technique and centroid method are jointly used to make them manageable under the same framework. A comprehensive algorithm based on the cumulant method and an optimisation scheme is employed to solve this PEF problem with consideration of IDR. The proposed framework is illustrated through numerical studies and simulation results confirm its effectiveness in actual implementations.

Zeng, Bo↗

NASA NTRS1972

Earth-based navigation capabilities for outer planet missions.

The role of new Earth-based radio metric data types and of advanced estimation algorithms in navigating an outer planet spacecraft in the vicinity of Saturn has been analyzed. The data types included in the study consist of conventional range and range-rate measurements taken from a single station and simultaneous and nearly simultaneous measurements obtained from pairs of stations during overlapping viewing periods. The utility of a third data set that is produced by explicitly differencing the simultaneous points has also been investigated. The data was processed with a conventional least squares batch filter and with a sequential filter that estimated parameters describing small stochastic accelerations (process noise) acting on the spacecraft. It was found that process noise can produce large errors in the estimates obtained from batch filtering conventional and simultaneous data, and that the only batch filtered estimates that were reliable were those obtained from differenced data. The performance of the simultaneous data in the presence of process noise is greatly improved by sequential filtering.

Hildebrand, C. E.↗

NASA NTRS2010

An Aircraft Separation Algorithm with Feedback and Perturbation

A separation algorithm is a set of rules that tell aircraft how to maneuver in order to maintain a minimum distance between them. This paper investigates demonstrating that separation algorithms satisfy the FAA requirement for the occurrence of incidents by means of simulation. Any demonstration that a separation algorithm, or any other aspect of flight, satisfies the FAA requirement is a challenge because of the stringent nature of the requirement and the complexity of airspace operations. The paper begins with a probability and statistical analysis of both the FAA requirement and demonstrating meeting it by a Monte Carlo approach. It considers the geometry of maintaining separation when one plane must change its flight path. It then develops a simple feedback control law that guides the planes on their paths. The presence of feedback control permits the introduction of perturbations, and the stochastic nature of the chosen perturbation is examined. The simulation program is described. This paper is an early effort in the realistic demonstration of a stringent requirement. Much remains to be done.

White, Allan L.↗

DOE OSTI2023

Binary operations on neuromorphic hardware with application to linear algebraic operations and stochastic equations

Abstract Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Stochastic Virtual Battery Modeling of Uncertain Electrical Loads using Variational Autoencoder

Effective utilization of flexible loads for grid services, while satisfying end-user preferences and constraints, requires an accurate estimation of the aggregated predictive flexibility offered by the electrical loads. Recently, there have been efforts to quantify the predictive flexibility of thermostatic loads (e.g. residential air-conditioners, electric water-heaters) using the notion of virtual battery (VB), whose state evolution is governed by a first order dynamics including self-dissipation rate, and power and energy capacities. Identifying the VB model parameters for a collection of thermostatic loads, however, is challenging primarily due to uncertainties and lack of information regarding the end-user behavior, underlying device models and parameters. In this paper, we propose a \textit{variational autoencoder}-based deep learning algorithm to identify the parameters of the VB model. Using available sensors and meters data, the proposed algorithm generates not only point estimates of the VB parameters, but also confidence intervals around those values. Effectiveness of the proposed frameworks is demonstrated on a collection of electric water-heater loads, whose operation is driven by uncertain water usage profiles.

virtual battery, deep learning algorithms↗

DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗