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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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DOE OSTI2021

Probabilistic Voltage Sensitivity Analysis to Quantify Impact of High PV Penetration on Unbalanced Distribution System

From an operational and planning perspective, it is important to quantify the impact of increasing penetration of photovoltaics on the distribution system. Most existing impact assessment studies are scenario-based where derived results are scenario specific and not generalizable. Moreover, stochasticity in the temporal behavior of spatially distributed PVs requires a large number of scenarios that increase with the size of the network and the level of penetration. Therefore, we propose a new computationally efficient analytical framework of voltage sensitivity analysis that allows for stochastic analysis of voltage change due to random changes in PV generation. We first derive an analytical approximation for voltage change at any node of the network due to change in power at other nodes in an unbalanced distribution network. The quality of this approximation is reinforced via bounds on the approximation error. Then, we derive the probability distribution of voltage change at a certain node due to random changes in power injections/consumptions at multiple locations of the network. The accuracy of the proposed PVSA is illustrated using a modified version of the IEEE 37 bus test system. As a result, the proposed PVSA can serve as a powerful tool for proactive monitoring/control and ease the computational burden associated with perturbation based cybersecurity mechanisms.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Real-Time Distribution System State Estimation with Asynchronous Measurements

We report state estimation is a fundamental task in power systems. Although distribution systems are increasingly equipped with sensing devices and smart meters, measurements are typically reported at different rates and asynchronously; these aspects pose severe strains on workhorse state estimation algorithms, which are designed to process batches of data collected in a synchronous manner from all the measurement units. In this paper, we develop a novel state estimation algorithm to continuously update the estimate of the state based on measurements received in an asynchronous manner from measurement units. The synthesis of the algorithm hinges on a proximal-point type method, implemented in an online fashion, and capable of processing measurements received sequentially from sensors. A performance analysis is presented by providing bounds on the estimation error in terms of the mean and variance that hold at each iteration and asymptotically. The scheme is also compared with a more traditional Weighted Least Squares estimator that compensates for the lack of measurement data by using, as pseudo measurements, the measurement retrieved during a certain time window. Numerical simulations on the IEEE 37-bus feeder corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided.

differential inclusion↗
DOE OSTI2026

QEC-fidelity

Code for paper "Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction" https://doi.org/10.48550/arXiv.2607.24968

Wu, Jing [Fermi National Accelerator Laboratory (F↗
DOE OSTI2021

EFT asymptotics: the growth of operator degeneracy

We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of S-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series---partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Covariance operator estimation: Sparsity, lengthscale, and ensemble Kalman filters

This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the field. We prove that thresholded estimators enjoy an exponential improvement in sample complexity compared with the standard sample covariance estimator if the field has a small correlation lengthscale. As an application of the theory, we study thresholded estimation of covariance operators within ensemble Kalman filters.

Covariance operator estimation↗
DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗
DOE OSTI2022

Provably accurate simulation of gauge theories and bosonic systems

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ − 1 , an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ , obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog ( ϵ − 1 ) .

Tong, Yu↗
DOE OSTI2020

Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness

We report the accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory answers to the problems of approximation and optimization, much less is known about the theory of generalization. Most existing theoretical works for generalization fail to explain the performance of neural networks in practice. To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness. We introduce the cover complexity (CC) to measure the difficulty of learning a data set and the inverse of the modulus of continuity to quantify neural network smoothness. A quantitative bound for expected accuracy/error is derived by considering both the CC and neural network smoothness. Although most of the analysis is general and not specific to neural networks, we validate our theoretical assumptions and results numerically for neural networks by several data sets of images. The numerical results confirm that the expected error of trained networks scaled with the square root of the number of classes has a linear relationship with respect to the CC. We also observe a clear consistency between test loss and neural network smoothness during the training process. In addition, we demonstrate empirically that the neural network smoothness decreases when the network size increases whereas the smoothness is insensitive to training dataset size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Online and Scalable Data Compression Pipeline with Guarantees on Quantities of Interest

Data compression is becoming critical for data-intensive scientific applications. Scientists require compression techniques that accurately preserve derived quantities of interest (QoIs). Prior work has shown that a pipeline can be built to guarantee error on the primary data (PD) within user-defined bounds and achieve near-floating point QoI errors. In this paper, we present novel computational approaches for accelerating the pipeline and demonstrate results that enable concurrent execution of compression in parallel with the simulation nodes. This allows compression, including the writing of the required compression data, for the previous time step to be completed while the simulation proceeds with the current time step. Overall, the approach presented in this paper results in a 6–8 times improvement in computational overhead compared to previous work. These results were obtained using data generated by a large-scale fusion code called XGC, which produces hundreds of terabytes of data in a single day.

Banerjee, Tania↗
DOE OSTI2024

Towards optimal sensor placement for inverse problems in spaces of measures

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in the sensor configuration and robust with respect to the source, yet relatively easy to compute in practice, compared to a direct evaluation of the error by a large number of samples. In particular, we consider the identification of a measure consisting of an unknown linear combination of point sources from a finite number of measurements contaminated by Gaussian noise. The statistical framework for recovery relies on two main ingredients: first, a convex but non-smooth variational Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger–Kantorovich distance to the ground truth. To quantify the error, we employ a non-degenerate source condition as well as careful linearization arguments to derive a computable upper bound. This leads to asymptotically sharp error estimates in expectation that are explicit in the sensor configuration. Thus they can be used to estimate the expected reconstruction error for a given sensor configuration and guide the placement of sensors in sparse inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamic signal recovery in distribution grids using compressive lossy measurements

Distribution system state estimation requires reliable aggregation of the measured data. However, the large volume of the measured data imposes a significant stress on the underlying communication infrastructure. With the challenges associated with measurement availability, current distribution systems are typically unobservable. To cope with the unobservability issue, compressive sensing theory allows us to recover system state information from a small number of measurements provided the states of the distribution system exhibit sparsity. In this paper, we evaluate the robustness of an updated Kalman filtered modified compressive sensing (KF-ModCS) technique that dynamically estimates the grid states using a small fraction of measured data. In practice, measurements used for sparsity based state estimation may also be intermittent due to communication network induced losses. Further, to understand the effect of packet losses on KF-ModCS, we provide an upper bound for the expected variances of the state estimation error for a given rate of information loss. This upper bound is further improved if the support set of the sparse signal that characterizes the state dynamics does not change over time and/or the reduced model is observable. Simulations based on two practical data sets collected from actual customers in a distribution grid validate the theoretical results.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing

Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics U ( φ ) (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of φ even when the nonlinearities are applied for times much shorter than required to produce Schrödinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator n → · J → . We consider the following physical settings: all-to-all interactions generated by one-axis twisting J z 2 (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cramér-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of L without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an L layer quantum alternating operator ansatz.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

ZFP: A compressed array representation for numerical computations

HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.

Lindstrom, Peter↗
DOE OSTI2021

Spread Spectrum Time Domain Reflectometry and Steepest Descent Inversion to Measure Complex Impedance

In this paper, we present a method for estimating complex impedances using reflectometry and a modified steepest descent inversion algorithm. We simulate spread spectrum time domain reflectometry (SSTDR), which can measure complex impedances on energized systems for an experimental setup with resistive and capacitive loads. A parametric function, which includes both a misfit function and stabilizer function, is created. The misfit function is a least squares estimate of how close the model data matches observed data. The stabilizer function prevents the steepest descent algorithm from becoming unstable and diverging. Steepest descent iteratively identifies the model parameters that minimize the parametric function. We validate the algorithm by correctly identifying the model parameters (capacitance and resistance) associated with simulated SSTDR data, with added 3 dB white Gaussian noise. With the stabilizer function, the steepest descent algorithm estimates of the model parameters are bounded within a specified range. Furthermore, the errors for capacitance (220pF to 820pF) and resistance (50 Ω to 270 Ω) are < 10%, corresponding to a complex impedance magnitude |R +1/jωC| of 53 Ω to 510 Ω.

14 SOLAR ENERGY↗
DOE OSTI2020

Variational fast forwarding for quantum simulation beyond the coherence time

Abstract Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called variational fast forwarding (VFF), for decreasing the quantum circuit depth of QSs. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function’s operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. In addition, we implement VFF on Rigetti’s QC to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sources of error in detonation calorimeters and error analysis for neat 2,4,6-triamino-1,3,5- trinitrobenzene (TATB)

Here, a calorimeter for measuring heats of detonation at Lawrence Livermore National Laboratory is described. A calibration precision of 0.2 % at the 95 % confidence interval (CI) is reported. Sources of uncertainty are discussed, including nonequivalent sources, which are those arising from differences between calibration and experimental tests. The systematic error due to nonequivalent sources is bounded to 0.19–0.22 % of the measured heat for a standard detonation test where the confinement material is gold. The recommendation is to correct for the systematic error by adding 0.19 % to the reported value and adding 0.03 % to the uncertainty. It is demonstrated that the precision of a detonation test is variable with testing duration because a source of uncertainty resides in the thermodynamic correction factor k6, which accounts for the contribution to heat by stirring; the generated power is additive and therefore highly impacted by total test time. The relative proportion also varies with the magnitude of heat release and sample size, adding variance to the weight of the error arising from the correction factor. A full error analysis based on the described sources of uncertainty is developed. The methodology is applied to a test series on neat 2,4,6-triamino-1,3,5- trinitrobenzene (TATB), demonstrating an ultimate precision of 0.7 % (single test) for materials testing and a relative standard deviation of 1.8 %.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. Here, the computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.

97 MATHEMATICS AND COMPUTING↗