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Results for “algorithmic differentiation”

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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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Numerical simulation of photoexcited polaron states in water

We consider the dynamic polaron model of the hydrated electron state on the basis of a system of three nonlinear partial differential equations with appropriate initial and boundary conditions. A parallel numerical algorithm for the numerical solution of this system has been developed. Its effectiveness has been tested on a few multi-processor systems. A numerical simulation of the polaron states formation in water under the action of the ultraviolet range laser irradiation has been performed. The numerical results are shown to be in a reasonable agreement with experimental data and theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Vibration suppression in flexible structures via the sliding-mode control approach

Sliding mode control became very popular recently because it makes the closed loop system highly insensitive to external disturbances and parameter variations. Sliding algorithms for flexible structures have been used previously, but these were based on finite-dimensional models. An extension of this approach for differential-difference systems is obtained. That makes if possible to apply sliding-mode control algorithms to the variety of nondispersive flexible structures which can be described as differential-difference systems. The main idea of using this technique for dispersive structures is to reduce the order of the controlled part of the system by applying an integral transformation. We can say that transformation 'absorbs' the dispersive properties of the flexible structure as the controlled part becomes dispersive.

Drakunov, S.↗
DOE OSTI2022

Differentiable Predictions for Large Scale Structure with SHAMNet

In simulation-based models of the galaxy-halo connection, theoretical predictions for galaxy clustering and lensing are typically made based on Monte Carlo realizations of a mock universe. In this paper, we use Subhalo Abundance Matching (SHAM) as a toy model to introduce an alternative to stochastic predictions based on mock population, demonstrating how to make simulation-based predictions for clustering and lensing that are both exact and differentiable with respect to the parameters of the model. Conventional implementations of SHAM are based on iterative algorithms such as Richardson-Lucy deconvolution; here we use the JAX library for automatic differentiation to train SHAMNet, a neural network that accurately approximates the stellar-to-halo mass relation (SMHM) defined by abundance matching. In our approach to making differentiable predictions of large-scale structure, we map parameterized PDFs onto each simulated halo, and calculate gradients of summary statistics of the galaxy distribution by using autodiff to propagate the gradients of the SMHM through the statistical estimators used to measure one- and two-point functions. Our techniques are quite general, and we conclude with an overview of how they can be applied in tandem with more complex, higher-dimensional models, creating the capability to make differentiable predictions for the multi-wavelength universe of galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

An investigation of a mathematical model of an optically pumped Ti(3+):Al2O3 laser system

During the last several years, solid state lasers were developed that have the potential for meeting rigorous performance requirements for space-based remote sensing of the atmosphere. In order to design a stable and efficient laser and to understand the effect on laser output of changes in the physical and design parameters, an understanding of the development of the dynamical processes of the laser is necessary. Typically, the dynamical processes in a laser system are investigated via rate equations describing the evolution of the occupancy in the electronic levels and of the photon density in the laser cavity. There are two approaches to this type of study. Most often, for the sake of simplicity, the spatial variations of the dynamic variables in the laser system are disregarded and the mathematical model consists of a system of first order nonlinear ordinary differential equations (ODE). The second approach is to take into account both spatial and temporal variations in the dynamic variables in the laser cavity. The resulting model consists of a first order semilinear system of partial differential equations (PDE). The model which was studied was studied was generic in the sense that it was a four-level laser system, but the parameters used in the numerical study were specific to Titanium-doped sapphire. For simplicity, a constant, spatially uniform pumping scheme was considered. In addition, a simplification of the model was made so that it treats a single lasing wavelength with a narrow bandwidth. The purpose was to investigate both versions of the mathematical model and to determine whether the numerical solutions are similar both qualitatively and quantitatively. The systems of ordinary differential equations were solved numerically using a Runge-Kutta-Fehlberg algorithm which was very efficient for typical values of the physical parameters. A numerical scheme, based on the Modified Euler method, for computing solutions to the system of partial differential equations was developed and implemented. The PDE model was solved numerically at the expense of greatly increased computer time.

Roberts, Lila F.↗
DOE OSTI2014

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Measurement of photonuclear jet production in ultraperipheral Pb + Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV with the ATLAS detector

In ultrarelativistic heavy ion collisions at the LHC, each nucleus acts a sources of high-energy real photons that can scatter off the opposing nucleus in ultraperipheral photonuclear (𝛾 + 𝐴) collisions. Hard scattering processes initiated by the photons in such collisions provide a novel method for probing nuclear parton distributions in a kinematic region not easily accessible to other measurements. ATLAS has measured production of dijet and multijet final states in ultraperipheral Pb + Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV using a dataset recorded in 2018 with an integrated luminosity of 1.72 nb −1 . Photonuclear final states are selected by requiring a rapidity gap in the photon direction; this selects events where one of the outgoing nuclei remains intact. Jets are reconstructed using the anti-𝑘 t algorithm with radius parameter, 𝑅 = 0.4. Triple-differential cross sections, unfolded for detector response, are measured and presented using two sets of kinematic variables. The first set consists of the total transverse momentum (𝐻 T ), rapidity, and mass of the jet system. The second set uses 𝐻 T and particle-level nuclear and photon parton momentum fractions, 𝑥 A and 𝑧 𝛾 , respectively. The results are compared with leading-order perturbative QCD calculations of photonuclear jet production cross sections, where all leading order predictions using existing fits fall below the data in the shadowing region. More detailed theoretical comparisons will allow these results to strongly constrain nuclear parton distributions, and these data provide results from the LHC directly comparable to early physics results at the planned Electron-Ion Collider.

Parton distribution functions↗
DOE OSTI2015

SU-E-T-183: Clinical Quality Assurance Workflow for Dynamic Tumor Tracking Radiation Dose Delivery

Purpose: One of the most important aspects of implementation of new treatment modalities is an ‘end-to-end’ verification of the treatment process. Radiation treatment based on dynamic tracking of a tumor is highly patient-specific, therefore, special attention should be paid to quality assurance of the treatment delivery. Our goal was to design the clinical workflow that ensures accurate delivery of the planned dose using the Dynamic Target Tracking option of VeroTM (BrainLab,MHI) linac. Methods: A patient simulation is designed to include a pre-treatment session to verify whether the system can reliably track the motion of the implanted marker and build the 4D model of the target motion. The external surrogate and target motion patterns are recorded in the ExactracTM log files. In this work, a spectrum of custom marker and external surrogate motion trajectories closely resembling the patient specific motion patterns was used. 1mm thick/11mm long VisicoilTM marker was placed 15 and 20mm from the center of the spherical tissue equivalent target (centroid to centroid distance) in the 4D motion phantom (CIRSTM). 3D conformal (3 mm block margin) SBRT plans were delivered to 2 moving targets in the phantom: 1) 20mm diameter target that allows ion chamber dose measurement and 2) 25mm target that allows using film to measure CAX dose (GafchromicTM EBT3 used). The measured dose was compared to the iPlanTM TPS results using MonteCarlo algorithm (1% variance, Dose-to-water). Results: On average, film shows 98.9% pass using gamma criterion for 2% and 2mm DTA, 94.3% match for 2% and 1 mm DTA, 98% pass for 1% and 2 mm DTA however only 88% points passing for 1% and 1 mm DTA. Ion chamber measurements agreed with the calculation within 1.5%. Conclusion: The clinical QA workflow was designed for SBRT delivery using real-time tumor tracking on VeroTM linac.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-P-39: End-To-End Validation of a 6 MV High Dose Rate Photon Beam, Configured for Eclipse AAA Algorithm Using Golden Beam Data, for SBRT Treatments Using RapidArc

Purpose: To use end-to-end testing to validate a 6 MV high dose rate photon beam, configured for Eclipse AAA algorithm using Golden Beam Data (GBD), for SBRT treatments using RapidArc. Methods: Beam data was configured for Varian Eclipse AAA algorithm using the GBD provided by the vendor. Transverse and diagonals dose profiles, PDDs and output factors down to a field size of 2×2 cm2 were measured on a Varian Trilogy Linac and compared with GBD library using 2% 2mm 1D gamma analysis. The MLC transmission factor and dosimetric leaf gap were determined to characterize the MLC in Eclipse. Mechanical and dosimetric tests were performed combining different gantry rotation speeds, dose rates and leaf speeds to evaluate the delivery system performance according to VMAT accuracy requirements. An end-to-end test was implemented planning several SBRT RapidArc treatments on a CIRS 002LFC IMRT Thorax Phantom. The CT scanner calibration curve was acquired and loaded in Eclipse. PTW 31013 ionization chamber was used with Keithley 35617EBS electrometer for absolute point dose measurements in water and lung equivalent inserts. TPS calculated planar dose distributions were compared to those measured using EPID and MapCheck, as an independent verification method. Results were evaluated with gamma criteria of 2% dose difference and 2mm DTA for 95% of points. Results: GBD set vs. measured data passed 2% 2mm 1D gamma analysis even for small fields. Machine performance tests show results are independent of machine delivery configuration, as expected. Absolute point dosimetry comparison resulted within 4% for the worst case scenario in lung. Over 97% of the points evaluated in dose distributions passed gamma index analysis. Conclusion: Eclipse AAA algorithm configuration of the 6 MV high dose rate photon beam using GBD proved efficient. End-to-end test dose calculation results indicate it can be used clinically for SBRT using RapidArc.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

A pencil beam dose calculation model for CyberKnife system

Purpose: CyberKnife system is initially equipped with fixed circular cones for stereotactic radiosurgery. Two dose calculation algorithms, Ray-Tracing and Monte Carlo, are available in the supplied treatment planning system. A multileaf collimator system was recently introduced in the latest generation of system, capable of arbitrarily shaped treatment field. The purpose of this study is to develop a model based dose calculation algorithm to better handle the lateral scatter in an irregularly shaped small field for the CyberKnife system. Methods: A pencil beam dose calculation algorithm widely used in linac based treatment planning system was modified. The kernel parameters and intensity profile were systematically determined by fitting to the commissioning data. The model was tuned using only a subset of measured data (4 out of 12 cones) and applied to all fixed circular cones for evaluation. The root mean square (RMS) of the difference between the measured and calculated tissue-phantom-ratios (TPRs) and off-center-ratio (OCR) was compared. Three cone size correction techniques were developed to better fit the OCRs at the penumbra region, which are further evaluated by the output factors (OFs). The pencil beam model was further validated against measurement data on the variable dodecagon-shaped Iris collimators and a half-beam blocked field. Comparison with Ray-Tracing and Monte Carlo methods was also performed on a lung SBRT case. Results: The RMS between the measured and calculated TPRs is 0.7% averaged for all cones, with the descending region at 0.5%. The RMSs of OCR at infield and outfield regions are both at 0.5%. The distance to agreement (DTA) at the OCR penumbra region is 0.2 mm. All three cone size correction models achieve the same improvement in OCR agreement, with the effective source shift model (SSM) preferred, due to their ability to predict more accurately the OF variations with the source to axis distance (SAD). In noncircular field validation, the pencil beam calculated results agreed well with the film measurement of both Iris collimators and the half-beam blocked field, fared much better than the Ray-Tracing calculation. Conclusions: The authors have developed a pencil beam dose calculation model for the CyberKnife system. The dose calculation accuracy is better than the standard linac based system because the model parameters were specifically tuned to the CyberKnife system and geometry correction factors. The model handles better the lateral scatter and has the potential to be used for the irregularly shaped fields. Comprehensive validations on MLC equipped system are necessary for its clinical implementation. It is reasonably fast enough to be used during plan optimization.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Machine-Learning-Based Multiscale Methods for 3D Modelling of Granular Materials by Incorporating History-Dependent State Variables

Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.

granular materials↗
DOE OSTI2012

Automated Thermal Image Processing for Detection and Classification of Birds and Bats (FY2012 Annual Report)

Surveying wildlife at risk from offshore wind energy development is difficult and expensive. Infrared video can be used to record birds and bats that pass through the camera view, but it is also time consuming and expensive to review video and determine what was recorded. We proposed to conduct algorithm and software development to identify and to differentiate thermally detected targets of interest that would allow automated processing of thermal image data to enumerate birds, bats, and insects. During FY2012 we developed computer code within MATLAB to identify objects recorded in video and extract attribute information that describes the objects recorded. We tested the efficiency of track identification using observer-based counts of tracks within segments of sample video. We examined object attributes, modeled the effects of random variability on attributes, and produced data smoothing techniques to limit random variation within attribute data. We also began drafting and testing methodology to identify objects recorded on video. We also recorded approximately 10 hours of infrared video of various marine birds, passerine birds, and bats near the Pacific Northwest National Laboratory (PNNL) Marine Sciences Laboratory (MSL) at Sequim, Washington. A total of 6 hours of bird video was captured overlooking Sequim Bay over a series of weeks. An additional 2 hours of video of birds was also captured during two weeks overlooking Dungeness Bay within the Strait of Juan de Fuca. Bats and passerine birds (swallows) were also recorded at dusk on the MSL campus during nine evenings. An observer noted the identity of objects viewed through the camera concurrently with recording. These video files will provide the information necessary to produce and test software developed during FY2013. The annotation will also form the basis for creation of a method to reliably identify recorded objects.

Bats↗
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 OSTI2022

Measurement of Piston Deposit Thickness Using Laser Profilometer

In this work, a novel method of measuring the thickness of deposits on engine pistons, including within ring grooves, is described. A laser profilometer is used in conjunction with a rotary stage to measure a continuous profile of the piston with deposits, and the measurement is repeated after cleaning the deposits from the piston. Algorithms for aligning the scans and determining the differential thickness are described, and results are compared to deposit thickness measurements using a contact-type magnetic induction coating thickness gauge. This method allows continuous measurement of deposit thickness across the entire surface including lands and ring grooves as well as quantification of the volume of the deposits.

42 ENGINEERING↗
NASA NTRS1973

Direct numerical solution of three-dimensional equations containing elliptic operators.

A direct three-dimensional elliptic solver is presented for application in a wide class of numerical methods for solving partial differential equations in physics and engineering. The derived algorithm and FORTRAN code implement Buzbee, Golub and Nielson's proposed extension of Buneman's Cyclic-Reduction Poisson solver to three dimensions. Both a 'most direct' cyclic reduction and a revised method (to eliminate roundoff error difficulties) are derived. Tests on an IBM 360/67 computer, using various optional combinations of subroutines, showed significant differences in accuracy and computing time, with the optimum subroutine combination depending on mesh size.

Martin, E. D.↗
NASA NTRS1978

NASA automatic subject analysis technique for extracting retrievable multi-terms (NASA TERM) system

Current methods for information processing and retrieval used at the NASA Scientific and Technical Information Facility are reviewed. A more cost effective computer aided indexing system is proposed which automatically generates print terms (phrases) from the natural text. Satisfactory print terms can be generated in a primarily automatic manner to produce a thesaurus (NASA TERMS) which extends all the mappings presently applied by indexers, specifies the worth of each posting term in the thesaurus, and indicates the areas of use of the thesaurus entry phrase. These print terms enable the computer to determine which of several terms in a hierarchy is desirable and to differentiate ambiguous terms. Steps in the NASA TERMS algorithm are discussed and the processing of surrogate entry phrases is demonstrated using four previously manually indexed STAR abstracts for comparison. The simulation shows phrase isolation, text phrase reduction, NASA terms selection, and RECON display.

Kirschbaum, J.↗
NASA NTRS1984

A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.

Radhakrishnan, K.↗