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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Saturation and Recurrence of Quantum Complexity in Random Local Quantum Dynamics

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. Published by the American Physical Society 2024

Oszmaniec, Michał (ORCID:0000000249466835)↗
DOE OSTI2021

Growing grasses in unprofitable areas of US Midwest croplands could increase species richness

The US has large potential to grow perennial energy crops, but because these crops are rarely grown in current agricultural landscapes, it is unclear how biodiversity may be affected. Over time, as agriculture has increased, many grassland species have declined. In addition, not all agricultural land is profitable for growing annual crops. Unprofitable areas were responsible for a loss of approximately $110 million USD per year from 2013 to 2016. Based on this, we want to know how converting less-profitable portions of agricultural fields to switchgrass, a native prairie grass, would influence species occurrence. To address this question, we developed an alternative landscape in which clustered corn/soy acres with a low return on investment (ROI) were replaced with grassland. We also developed and validated species distribution models to predict changes in species occurrence for 28 avian species in Iowa in response to landscape management. Furthermore, we compared results for three different models: Random forest (RF), Stochastic gradient boosting (GBM), and Neural network (Nnet) and found that all models performed well and predicted similar species distribution. Predicted species richness increased by 3.66% (RF), 2.79% (GBM), and 7.51% (Nnet) when we simulated a change in management for ~3% of Iowa's low ROI corn/soybean areas to grassland. If harvested, these areas could generate approximately 7.6 million dry tons/year of switchgrass for bioenergy, thereby increasing farmers earnings. Unprofitable areas tended to occur along streams, which suggest that incorporating partially harvested riparian buffers can benefit avian biodiversity, while improving water quality and reducing unnecessary costs for farmers.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Predicting demand for hydrogen station fueling

Full function hydrogen stations are a reality; fuel cell electric vehicle drivers can pull up to commercial fueling stations and receive 3–5 kg in less than 5 min, for an approximately 300-mile range. The demand for hydrogen is increasing, driven by an increase in the fueling of public and private fuel cell vehicles. This study describes the development and value of a model that simulates stochastic future demand at a hydrogen filling station. The predictive hydrogen demand model described in this article is trained from mathematical models constructed from actual hydrogen fill count, amount, and frequency data. Future fill probabilities inform the hour-by-hour demand profile and the station state of either “available, ready to fill” or “available, filling”. For example, a prediction for a station generally dispensing 5,000 kg a week on a Friday afternoon at 4 p.m. is 16 fills, totaling 48.7 kg, with a 0.52 proportion of time spent in “available, filling” state yielding 31 min of filling time. This is a first-of-its kind, published study on predicting future hydrogen demand by the time of day (e.g., hour-by-hour intervals) and day of week. This study can be used for hydrogen station requirements and operation and maintenance strategies and to assess the impact of demand variations and scenarios. Finally, this article presents the current status of hydrogen demand, the model development methods, a set of sample results. Discussion and conclusions concentrate on the value and use of the proposed model.

08 HYDROGEN↗
DOE OSTI2023

Emergency Asset Positioning for Resilient Transmission Grid Operation

In this paper we study a problem of hurricane emergency preparedness via placement of emergency storage assets prior to its strike. We present a two-stage stochastic model for choosing locations and quantities of emergency storage to help support the power grid through a hurricane event. The expectation of losses in our two-stage model is estimated using the sample average approximation. We construct damage scenarios for sample average approximation using WIND Toolkit meteorological data and fragility curves of various electric grid components. We demonstrate the efficacy of our two-stage planning model by simulating operations during Hurricane Dolly on the 2000-bus transmission test system. Our model, coupled with our scenario selection strategy, is effective at mitigating loss of load when compared to a model without emergency storage assets placed prior to an extreme event.

emergency preparedness↗
DOE OSTI2023

Emergency Asset Positioning for Resilient Transmission Grid Operation

In this paper we study a problem of hurricane emergency preparedness via placement of emergency generation assets prior to its strike. We present a two-stage stochastic model for choosing locations and quantities of emergency storage to help support the power grid through a hurricane event. The expectation of losses in our two-stage model is estimated using the sample average approximation. We construct damage scenarios for sample average approximation using WIND Toolkit meteorological data and fragility curves of various electric grid components. We demonstrate the efficacy of our two-stage planning model by simulating operations during Hurricane Dolly on the 2000-bus transmission test system. Our model, coupled with our scenario selection strategy, is effective at mitigating loss of load when compared to a model without emergency generation assets placed prior to an extreme event.

emergency preparedness↗
DOE OSTI2023

Emergency Generation Asset Positioning for Resilient Transmission Grid Operation: Preprint

In this paper we study a problem of hurricane emergency preparedness via placement of emergency generation assets prior to its strike. We present a two-stage stochastic model for choosing locations and quantities of emergency storage to help support the power grid through a hurricane event. The expectation of losses in our two-stage model is estimated using the sample average approximation. We construct damage scenarios for sample average approximation using WIND Toolkit meteorological data and fragility curves of various electric grid components. We demonstrate the efficacy of our two-stage planning model by simulating operations during Hurricane Dolly on the 2000-bus transmission test system. Our model, coupled with our scenario selection strategy, is effective at mitigating loss of load when compared to a model without emergency generation assets placed prior to an extreme event.

emergency preparedness↗
DOE OSTI2024

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Uncertainty Quantification of Geophysical Inversion Using Stochastic Partial Differential Equations (LDRD #218329)

This report summarizes work completed under the Laboratory Directed Research and Development (LDRD) project "Uncertainty Quantification of Geophysical Inversion Using Stochastic Differential Equations." Geophysical inversions often require computationally expensive algorithms to find even one solution, let alone propagating uncertainties through to the solution domain. The primary purpose of this project was to find more computationally efficient means to approximate solution uncertainty in geophysical inversions. We found multiple computationally efficient methods of propagating Earth model uncertainty into uncertainties in solutions of full waveform seismic moment tensor inversions. However, the optimum method of approximating the uncertainty in these seismic source solutions was to use the Karhunen-Love theorem with data misfit residuals. This method was orders of magnitude more computationally efficient than traditional Monte Carlo methods and yielded estimates of uncertainty that closely approximated those of Monte Carlo. We will summarize the various methods we evaluated for estimating uncertainty in seismic source inversions as well as work toward this goal in the realm of 3-D seismic tomographic inversion uncertainty.

58 GEOSCIENCES↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

High-throughput bend-strengths of ultra-small polysilicon MEMS components

The strength distribution of polysilicon bend specimens, approximately 10 μm in size, is measured using a high-throughput microelectromechanical system fabrication and testing method. The distribution is predicted from reference tests on tensile specimens and finite element analysis of the bend specimen geometry incorporated into a stochastic extreme-value strength framework. Agreement between experiment and prediction suggests that the ultra-small specimens may be at the limit of extreme-value scaling and contain only one strength-controlling flaw/specimen.

Cook, Robert F. (ORCID:0000000304228881)↗
DOE OSTI2021

Optimization models for integrated biorefinery operations

Variations of physical and chemical characteristics of biomass lead to an uneven flow of biomass in a biorefinery, which reduces equipment utilization and increases operational costs. Uncertainty of biomass supply and high processing costs increase the risk of investing in the US’s cellulosic biofuel industry. We propose a stochastic programming model to streamline processes within a biorefinery. A chance constraint models system’s reliability requirement that the reactor is operating at a high utilization rate given uncertain biomass moisture content, particle size distribution, and equipment failure. The model identifies operating conditions of equipment and inventory level to maintain a continuous flow of biomass to the reactor. Furthermore, the sample average approximation method approximates the chance constraint and a bisection search-based heuristic solves this approximation. A case study is developed using real-life data collected at Idaho National Laboratory’s biomass processing facility. An extensive computational analysis indicates that sequencing of biomass bales based on moisture level, increasing storage capacity, and managing particle size distribution, increases utilization of the reactor and reduces operational costs.

09 BIOMASS FUELS↗
DOE OSTI2023

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. Here, this type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k × k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

LANL studies of ESD spark energy discharge through September 2019

Two concentric-sphere apparatuses were used to measure the energies deposited by electric sparks through air to calibrated loads. Both sets of spheres had clean, uninsulated metal surfaces. The 127-mm diameter pair of spheres had a gap of 10 mm and a capacitance of 52 pF. The maximum energy stored on these spheres was 12 mJ and the maximum energy delivered to the 50-mΩ load was 11 µJ, with or without inductance. This load energy amounted to 0.09% of the available input energy; the remainder of the input energy was expended in forming the spark. The second set of spheres was 330 mm in diameter with a gap of 14 mm and a capacitance of 240 pF. The maximum energy stored on these spheres was 71 mJ and the maximum energy delivered to the 50-mΩ load was 150 µJ without added inductance. This load energy was 0.27% of the input energy; again, the remainder of the input energy was expended in forming the spark. The inclusion of 250 nH and 500 nH inductances in the discharge path of the smaller spheres caused the current discharges to resonate, but had little effect on the maximum energies deposited in the loads. At the time of writing, inductances had not yet been added to the larger spheres. The magnitudes of the observed spark discharges were stochastic, so more than 1200 tests were required to develop the statistical bounds of the spark behavior, i.e., to estimate the worst case (highest likely) energy depositions in the loads. The action integrals of the current discharges $∫ i^2dt$ were found to be approximately independent of the load resistances for loads of less than ~1 Ω. Hence the energy deposition scaled with resistance as 207 µJ/Ω and 2.93 mJ/Ω for the two apparatuses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2026

Near-Optimal Performance of Stochastic Model Predictive Control

Here, this article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

93E20, 93B45↗
DOE OSTI2024

A Data-Driven Methodology for Contextual Unit Commitment Using Regression Residuals

Day after day, system operators are faced with the challenge of taking unit commitment (UC) decisions under uncertain net load conditions. The standard operating procedure for taking UC decisions begins by leveraging auxiliary data on covariates (such as the day of the week or latest weather information) to generate a point prediction for net load, which is used in solving a deterministic UC problem. Such an approach, however, is known to deliver a notoriously poor out-of-sample (OOS) performance, as it completely disregards the stochastic nature of net load. While stochastic programming models explicitly represent uncertainty, they mostly do so using a generic set of scenarios that neglect covariate observations, squandering useful auxiliary data that could be harnessed to glean insights into uncertainty. In this article, we discuss a contextual stochastic optimization approach to UC, which effectively exploits covariate observations while explicitly assessing uncertainty so as to boost the OOS performance of UC decisions. The key thrust of our approach is to leverage regression models, along with their empirical residuals, to set up and solve sample average approximation problems. Not only do we prove that our approach satisfies the requisite conditions for asymptotic optimality and consistency laid out in (Kannan et al., 2022), but we also assess its performance on several case studies conducted using real-world data collected in California ISO and New York ISO grids. In conclusion, results show that the proposed approach can significantly improve OOS performance compared to alternative methods proposed in the literature under varying dataset sizes.

Yurdakul, Ogun↗
DOE OSTI2021

Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance

The ability of neural networks to provide ‘best in class’ approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train (choose) the parameters defining the network. In general, neural networks are trained by gradient descent type optimization methods,a stochastic variant thereof. In practice, such methods result in the loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down. The loss may even appear to stagnate over the period of a large number of epochs, only to then suddenly start to decrease fast again for no apparent reason. This so-called plateau phenomenon manifests itself in many learning tasks. The present work aims to identify and quantify the root causes of plateau phenomenon.analysis is carried out in the setting of univariate ReLU networks. No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes. Here, the main findings are: plateaux correspond to periods during which activation patterns remain constant, where activation pattern refers to the number of data points that activate a given neuron; quantification of convergence of the gradient flow dynamics; and, characterization stationary points in terms solutions of local least squares regression lines over subsets of the training data. Based on these conclusions, we propose a new iterative training method, the Active Neuron Least Squares (ANLS), characterised by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau. Illustrative numerical examples are included throughout.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A test of gravity with Pulsar Timing Arrays

Abstract A successful measurement of the Stochastic Gravitational Wave Background (SGWB) in Pulsar Timing Arrays (PTAs) would open up a new window through which to test the predictions of General Relativity (GR). We consider how these measurements might reveal deviations from GR by studying the overlap reduction function — the quantity that in GR is approximated by the Hellings-Downs curve — in some sample modifications of gravity, focusing on the generic prediction of a modified dispersion relation for gravitational waves. We find a distinct signature of such modifications to GR — a shift in the minimum angle of the angular distribution — and demonstrate that this shift is quantitatively sensitive to any change in the phase velocity. In a given modification of gravity, this result can be used, in some regions of parameter space, to distinguish the effect of a modified dispersion relation from that due to the presence of extra polarization modes.

Astronomy & Astrophysics↗