Search NASA⌕ Search

SEARCH · Search NASA

Results for “variance”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Technical Note: Introduction of variance component analysis to setup error analysis in radiotherapy

Purpose: The purpose of this technical note is to introduce variance component analysis to the estimation of systematic and random components in setup error of radiotherapy. Methods: Balanced data according to the one-factor random effect model were assumed. Results: Analysis-of-variance (ANOVA)-based computation was applied to estimate the values and their confidence intervals (CIs) for systematic and random errors and the population mean of setup errors. The conventional method overestimates systematic error, especially in hypofractionated settings. The CI for systematic error becomes much wider than that for random error. The ANOVA-based estimation can be extended to a multifactor model considering multiple causes of setup errors (e.g., interpatient, interfraction, and intrafraction). Conclusions: Variance component analysis may lead to novel applications to setup error analysis in radiotherapy.

60 APPLIED LIFE SCIENCES↗

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations

This paper presents a hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for more than a decade to very effectively improve the efficiency of Monte Carlo calculations of localized quantities (e.g., flux, dose, or reaction rate at a specific location). The basis of this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space-and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain more uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented and demonstrated within the MAVRIC (Monaco with Automated Variance Reduction using Importance Calculations) sequence of SCALE and the ADVANTG (Automated Deterministic Variance Reduction Generator)/MCNP framework. Application of the method to representative real-world problems, including calculation of dose rate and energy-dependent flux throughout the problem space, dose rates in specific areas, and energy spectra at multiple detectors, is presented and discussed. Results of the FW-CADIS method and other recently developed global variance-reduction approaches are also compared, and the FW-CADIS method outperformed the other methods in all cases considered.

Wagner, John C↗

ADVANTG An Automated Variance Reduction Parameter Generator

The AutomateD VAriaNce reducTion Generator (ADVANTG) software automates the generation of variance reduction (VR) parameters for continuous-energy Monte Carlo simulations of fixed-source neutron, photon, and coupled neutron-photon transport problems using MCNP5 (X-5 Monte Carlo Team 2003). ADVANTG generates space- and energy dependent mesh-based weight-window bounds and biased source distributions from three dimensional (3-D) discrete ordinates (SN) calculations that are performed by the Denovo package (Evans et al. 2010). The deterministic calculations can be performed using multiple cores and/or processors (e.g., on multi-core desktop systems and clusters). The final variance reduction parameters are output in a format that can be used with unmodified versions of MCNP. The primary objective of the development of ADVANTG has been to reduce both the user effort and the computational time required to obtain accurate and precise tally estimates across a broad range of challenging transport application areas.

ADVANTG↗

A Minimum Variance Algorithm for Overdetermined TOA Equations with an Altitude Constraint.

We present a direct (non-iterative) method for solving for the location of a radio frequency (RF) emitter, or an RF navigation receiver, using four or more time of arrival (TOA) measurements and an assumed altitude above an ellipsoidal earth. Both the emitter tracking problem and the navigation application are governed by the same equations, but with slightly different interpreta- tions of several variables. We treat the assumed altitude as a soft constraint, with a specified noise level, just as the TOA measurements are handled, with their respective noise levels. With 4 or more TOA measurements and the assumed altitude, the problem is overdetermined and is solved in the weighted least squares sense for the 4 unknowns, the 3-dimensional position and time. We call the new technique the TAQMV (TOA Altitude Quartic Minimum Variance) algorithm, and it achieves the minimum possible error variance for given levels of TOA and altitude estimate noise. The method algebraically produces four solutions, the least-squares solution, and potentially three other low residual solutions, if they exist. In the lightly overdermined cases where multiple local minima in the residual error surface are more likely to occur, this algebraic approach can produce all of the minima even when an iterative approach fails to converge. Algorithm performance in terms of solution error variance and divergence rate for bas eline (iterative) and proposed approach are given in tables.

97 MATHEMATICS AND COMPUTING↗

Cost-optimized Automated Variance Reduction for Highly Angle-dependent Radiation Transport Analyses [Dissertation]

Monte Carlo variance-reduction techniques that directly bias particle direction have historically received limited attention despite being useful for many radiation transport applications such as those in which radiation travels through large regions with a low probability of colliding. One such technique is known as DXTRAN (short for deterministic transport) in the MCNP Monte Carlo radiation transport code. Until now, effectively applying DXTRAN in calculations is largely based on empirical observations of computational performance. Optimal DXTRAN parameters are identified through manual iteration. This work develops new mathematical descriptions of the DXTRAN variance-reduction process and demonstrates a new automated variance-reduction method that applies these mathematical formulations to determine the optimal application of DXTRAN in a given problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

LLNS Request for Variance from 10 CFR 851 for Construction of LLNL Digital Infrastructure Capabilities Expansion Project

Lawrence Livermore National Security, LLC (LLNS) requests variance to 10 CFR 851 (the Rule) for the construction of the Digital Infrastructure Capabilities Expansion (DICE) project. The request isin continued support of the National Nuclear Security Administration (NNSA) “pilot” to streamline the delivery of commercial-like line-item construction projects under $50 million. This pilot is aligned with the approved NA-50 safety approach. Experience gained in the construction of the new Lawrence Livermore National Laboratory (LLNL) Emergency Operations Facility (EOC) under the variance granted in June 2020 is very encouraging. While detailed analysis will be forthcoming after that project is completed, there are strong indicators that a benefit has been realized by the subcontractors executing the work. The variance has permitted local/regional construction businesses contracted to Management & Operation contractor operated facilities and lower tier subcontractors to bid, operate, execute, and comply with safety and health standards they utilize in their business outside of the Department of Energy (DOE) Complex. While compliance to standards that are as safe and healthful as those in 10 CFR 851: confusion, additional cost, and inefficiencies associated with the burden of compliance to an unfamiliar regulatory spectrum has been avoided. Safety and health performance on the EOC construction project including the number of inspection and surveillance issues is comparable to other subcontractors and projects at LLNL executed under 10 CFR 851.

99 GENERAL AND MISCELLANEOUS↗

Density variance dynamics in disparate shock tubes

This report discusses two experiments which investigate thin layer, heavy curtain fragmentation from the perspective of a Reynolds-Averaged mix model, in drastically disparate experimental regimes. The first, the centimeter/millisecond-scale “Horizontal Shock Tube” (HST) is a compressed-gas piston-driven shock tube experiment. The second, the “Multishock thin layer” (Mshock) experiment performed at the National Ignition Facility, is a micrometer/nanosecond-scale laser-driven shock tube experiment. Both are situations in which a heavy plane layer (a ‘curtain’) is initially suspended in a lighter medium. After being shocked from at least one side, the layer translates while its interfaces evolve due to the excitation of the Richtmyer-Meshkov instability at its surfaces. The evolution of density variance, which initially exists only on the surface of the layer, as it comes to encompass the whole layer interior is used as a description of layer fragmentation and dissolution. These experiments have each been simulated in the Los Alamos National Laboratory multi-physics code xRAGE, which includes fundamental hydrodynamics, extended plasma physics and radiation effects which are important to drive the high-energy density experiment, and the Besnard-Harlow-Rauenzahn (BHR) turbulence model. In each, the principal diagnostic for comparison is an experimental metric for the density (co)variance, b, which tracks the moments of the density field at the curtain interfaces and body. Due to experimental constraints in different regimes (i.e. optical diagnostics can be deployed on conventional shock tubes, while the plasma shock tubes must be imaged by x-rays; interfaces can be imposed to specification on laser-driven experiments, which are stored in the solid phase, while conventional experiments have imperfect control of the flow fields which separate the layer, etc.) the experiments are not designed to be perfect scaled cognates of one another. However, despite the separation of six orders of magnitude of scaling in time, and four in space, we are able to demonstrate that the same turbulence model, operating in the same fashion in the same computer code, is able to reproduce results in each experiment, by tracking evolution due to common relevant physics. Additionally, we will present preliminary work toward density variance comparisons in a single-interface Richtmyer-Meshkov configuration, the conventional fluid “Vertical Shock Tube” (VST) experiment, and the Modal Initial Conditions (ModCons) campaign fielded at the OMEGA-EP laser facility.

42 ENGINEERING↗

Allan Variance is Bootstrap Aggregation for Spectral Estimation

Characterization of clocks and inertial sensors, such as accelerometers and gyroscopes, typically includes Allan variance analysis. Allan variance is ubiquitous in timing and navigation communities which may appear niche compared with generalized spectral analysis. This note provides some motivation for Allan Variance for audiences more familiar with spectral analysis.

Walker, Michael Ray [Sandia National Laboratories ↗

Online Control of Process Variance Using Feedback

For many stochastic control problem formulations, design objectives typically include constraining the covariance of the outputs of the system. Recent engineering challenges have demonstrated an interest in controlling system output covariances to a setpoint. However, open-loop control of system output covariance can be exceptionally challenging when the system has significant plant uncertainties. This paper explores closed-loop control of the system’s output covariance using a windowed variance function. The stochastic nature of the windowed variance feedback means that root locus and other classical control design techniques cannot be immediately used. Expected value analysis is used to generate transfer functions for the average response of such systems, and the results are used to design controllers. Stochastic simulations are presented to verify the analytical results and make other observations concerning closed-loop variance control.

Bieniek, Mitchell↗

A method for transporting cloud-resolving model variance in a multiscale modeling framework

Abstract. An unphysical checkerboard pattern has recently been identified in the multiscale modeling framework configuration of the Energy Exascale Earth System Model (E3SM-MMF) that is hypothesized to be associated with the inability of large-scale dynamics to transport fluctuations within the embedded cloud-resolving model (CRM) on the global grid. To address this issue, a method is presented to facilitate the large-scale transport of CRM variance in E3SM-MMF. Simulation results show that the method is effective at reducing the occurrence of unphysical checkerboard patterns on a range of timescales from days to years. This result is confirmed both subjectively through visual inspection and quantitatively with a previously developed pattern categorization technique. The CRM variance transport does not significantly alter the model climate, although it does tend to reduce temporal variance on fields associated with convection on the global grid.

54 ENVIRONMENTAL SCIENCES↗

Global variance decomposition of downscaled and bias-corrected CMIP6 climate projections

This dataset provides the results of a global variance decomposition of downscaled and bias-corrected CMIP6 climate projections. The total projection variance for a set of climate metrics is partitioned into contributions from: scenario uncertainty, model/GCM uncertainty, downscaling and bias-correction uncertainty, and interannual variability. The contribution from each source is expressed as a percentage of the total variance. Seven climate metrics are analyzed: Annual average temperature (avg_tas.nc) Annual total precipitation (tot_pr.nc) Annual maximum of daily maximum temperature (max_tasmax.nc) Annual maximum 1-day precipitation (max_pr.nc) Annual number of extremely hot days (hot_days.nc) Annual number of extremely wet days (wet_days.nc) Annual number of dry days (dry_days.nc) Extremely hot/wet days are defined to occur when temperature/precipitation exceeds the local 99th percentile defined over 1980-2014. Dry days are defined to occur when daily precipitation is less than 1mm. all_metrics_timesliced.nc gives the results for all metrics averaged over three 20-year periods: 2020-2039, 2050-2069, 2080-2099. For more details on the methods, see: Lafferty & Sriver, Downscaling and bias-correction contribute considerable uncertainty to local climate projections in CMIP6, npj Climate & Atmospheric Science (2023) An interactive visualization of this data can be found at: https://lafferty-sriver-2023-downscaling-uncertainty.msdlive.org

Lafferty, David↗

The human as a detector of changes in variance and bandwidth

The detection of changes in random process variance and bandwidth was studied. Psychophysical thresholds for these two parameters were determined using an adaptive staircase technique for second order random processes at two nominal periods (1 and 3 seconds) and damping ratios (0.2 and 0.707). Thresholds for bandwidth changes were approximately 9% of nominal except for the (3sec,0.2) process which yielded thresholds of 12%. Variance thresholds averaged 17% of nominal except for the (3sec,0.2) process in which they were 32%. Detection times for suprathreshold changes in the parameters may be roughly described by the changes in RMS velocity of the process. A more complex model is presented which consists of a Kalman filter designed for the nominal process using velocity as the input, and a modified Wald sequential test for changes in the variance of the residual. The model predictions agree moderately well with the experimental data. Models using heuristics, e.g. level crossing counters, were also examined and are found to be descriptive but do not afford the unification of the Kalman filter/sequential test model used for changes in mean.

Curry, R. E.↗

Cross-bispectrum computation and variance estimation

A method for the estimation of cross-bispectra of discrete real time series is developed. The asymptotic variance properties of the bispectrum are reviewed, and a method for the direct estimation of bispectral variance is given. The symmetry properties are described which minimize the computations necessary to obtain a complete estimate of the cross-bispectrum in the right-half-plane. A procedure is given for computing the cross-bispectrum by subdividing the domain into rectangular averaging regions which help reduce the variance of the estimates and allow easy application of the symmetry relationships to minimize the computational effort. As an example of the procedure, the cross-bispectrum of a numerically generated, exponentially distributed time series is computed and compared with theory.

Lii, K. S.↗

Spectral variance of aeroacoustic data

An asymptotic technique for estimating the variance of power spectra is applied to aircraft flyover noise data. The results are compared with directly estimated variances and they are in reasonable agreement. The basic time series need not be Gaussian for asymptotic theory to apply. The asymptotic variance formulae can be useful tools both in the design and analysis phase of experiments of this type.

Rao, K. V.↗

Estimation of parameters in linear structural relationships: Sensitivity to the choice of the ratio of error variances

Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. The use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio is investigated.

Lakshminarayanan, M. Y.↗

Image variance and spatial structure in remotely sensed scenes

Digital images derived by scanning air photos and through acquiring aircraft and spcecraft scanner data were studied. Results show that spatial structure in scenes can be measured and logically related to texture and image variance. Imagery data were used of a South Dakota forest; a housing development in Canoga Park, California; an agricltural area in Mississppi, Louisiana, Kentucky, and Tennessee; the city of Washington, D.C.; and the Klamath National Forest. Local variance, measured as the average standard deviation of brightness values within a three-by-three moving window, reaches a peak at a resolution cell size about two-thirds to three-fourths the size of the objects within the scene. If objects are smaller than the resolution cell size of the image, this peak does not occur and local variance simply decreases with increasing resolution as spatial averaging occurs. Variograms can also reveal the size, shape, and density of objects in the scene.

Woodcock, C. E.↗