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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Study of fully coupled three-dimensional envelope instability using automatic differentiation

Automatic differentiation is a powerful tool for computing derivatives of simulation results with respect to given parameters. In this Letter, we have applied this tool to investigate the instability of a dynamical system governed by 21 ordinary differential equations. This second-order instability (named envelope instability) is driven by space-charge effects and has a significant impact on the operational regimes of particle accelerators. Our study delves into the three-dimensional envelope instability, incorporating both transverse and longitudinal coupling. Conventionally, analyzing this complex system would necessitate solving 441 ordinary differential equations, which is computationally intractable. However, by employing automatic differentiation, we were able to track only 21 equations. This approach allowed us to uncover an additional instability stopband, which arises from space-charge-induced coupling and has not been reported in previous studies. This research highlights the significant advantages of automatic differentiation in analyzing complicated dynamical systems involving a large number of ordinary differential equations.

Qiang, Ji [Lawrence Berkeley National Laboratory (↗
DOE OSTI2024

A taxonomy of automatic differentiation pitfalls

Automatic differentiation is a popular technique for computing derivatives of computer programs. While automatic differentiation has been successfully used in countless engineering, science, and machine learning applications, it can sometimes nevertheless produce surprising results. In this paper, we categorize problematic usages of automatic differentiation, and illustrate each category with examples such as chaos, time-averages, discretizations, fixed-point loops, lookup tables, linear solvers, and probabilistic programs, in the hope that readers may more easily avoid or detect such pitfalls. We also review debugging techniques and their effectiveness in these situations.

Autodiff↗
NASA NTRS1996

Development of an Automatic Differentiation Version of the FPX Rotor Code

The ADIFOR2.0 automatic differentiator is applied to the FPX rotor code along with the grid generator GRGN3. The FPX is an eXtended Full-Potential CFD code for rotor calculations. The automatic differentiation version of the code is obtained, which provides both non-geometry and geometry sensitivity derivatives. The sensitivity derivatives via automatic differentiation are presented and compared with divided difference generated derivatives. The study shows that automatic differentiation method gives accurate derivative values in an efficient manner.

Hu, Hong↗
NASA NTRS1994

Parallel Calculation of Sensitivity Derivatives for Aircraft Design using Automatic Differentiation

Sensitivity derivative (SD) calculation via automatic differentiation (AD) typical of that required for the aerodynamic design of a transport-type aircraft is considered. Two ways of computing SD via code generated by the ADIFOR automatic differentiation tool are compared for efficiency and applicability to problems involving large numbers of design variables. A vector implementation on a Cray Y-MP computer is compared with a coarse-grained parallel implementation on an IBM SP1 computer, employing a Fortran M wrapper. The SD are computed for a swept transport wing in turbulent, transonic flow; the number of geometric design variables varies from 1 to 60 with coupling between a wing grid generation program and a state-of-the-art, 3-D computational fluid dynamics program, both augmented for derivative computation via AD. For a small number of design variables, the Cray Y-MP implementation is much faster. As the number of design variables grows, however, the IBM SP1 becomes an attractive alternative in terms of compute speed, job turnaround time, and total memory available for solutions with large numbers of design variables. The coarse-grained parallel implementation also can be moved easily to a network of workstations.

Bischof, c. H.↗
NASA NTRS1993

Sensitivity derivatives for advanced CFD algorithm and viscous modelling parameters via automatic differentiation

The computational technique of automatic differentiation (AD) is applied to a three-dimensional thin-layer Navier-Stokes multigrid flow solver to assess the feasibility and computational impact of obtaining exact sensitivity derivatives typical of those needed for sensitivity analyses. Calculations are performed for an ONERA M6 wing in transonic flow with both the Baldwin-Lomax and Johnson-King turbulence models. The wing lift, drag, and pitching moment coefficients are differentiated with respect to two different groups of input parameters. The first group consists of the second- and fourth-order damping coefficients of the computational algorithm, whereas the second group consists of two parameters in the viscous turbulent flow physics modelling. Results obtained via AD are compared, for both accuracy and computational efficiency with the results obtained with divided differences (DD). The AD results are accurate, extremely simple to obtain, and show significant computational advantage over those obtained by DD for some cases.

Green, Lawrence L.↗
NASA NTRS1994

Applications of automatic differentiation in computational fluid dynamics

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Green, Lawrence L.↗
NASA NTRS1992

Automatic differentiation as a tool in engineering design

Automatic Differentiation (AD) is a tool that systematically implements the chain rule of differentiation to obtain the derivatives of functions calculated by computer programs. AD is assessed as a tool for engineering design. The forward and reverse modes of AD, their computing requirements, as well as approaches to implementing AD are discussed. The application of two different tools to two medium-size structural analysis problems to generate sensitivity information typically necessary in an optimization or design situation is also discussed. The observation is made that AD is to be preferred to finite differencing in most cases, as long as sufficient computer storage is available; in some instances, AD may be the alternative to consider in lieu of analytical sensitivity analysis.

Barthelemy, Jean-Francois↗
NASA NTRS1992

Automatic Differentiation as a tool in engineering design

Automatic Differentiation (AD) is a tool that systematically implements the chain rule of differentiation to obtain the derivatives of functions calculated by computer programs. In this paper, it is assessed as a tool for engineering design. The paper discusses the forward and reverse modes of AD, their computing requirements, and approaches to implementing AD. It continues with application to two different tools to two medium-size structural analysis problems to generate sensitivity information typically necessary in an optimization or design situation. The paper concludes with the observation that AD is to be preferred to finite differencing in most cases, as long as sufficient computer storage is available.

Barthelemy, Jean-Francois M.↗
NASA NTRS1998

First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation

Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.

Hou, Gene↗
DOE OSTI2025

Uncertainty Quantification Enabled by Automatic Differentiation for Hydrodynamic Simulation of Shock‐to‐Detonation Transition in High Explosives

Quantifying the effects of uncertainty in a reactive burn model on the run-to-detonation time in high explosives (HEs) provides a robust methodology for assessing the probability of an HE failing the IHE qualification standard. Moreover, uncertainty quantification helps evaluate whether the model calibration accurately represents data outside the calibration set. This study uses a specialized hydrodynamic simulation code for modeling detonation to determine the run-to-detonation time of the HE PBX 9502 for various impact velocities. To quickly approximate uncertainties in the model, a surrogate was constructed using a Taylor series expansion centered at the mean of the input parameters. To obtain the sensitivities required for constructing the Taylor series, HYP-percomplex Automatic Differentiation (HYPAD) was implemented. HYPAD is a methodology for infusing existing codes with automatic differentiation capabilities by augmenting variables with one or more imaginary units to compute step-size independent partial derivatives. These derivatives are accurate to machine precision with respect to the implemented numerical algorithm, meaning their accuracy reflects that of the underlying method (e.g., integration or discretization schemes). Using reduced order modeling techniques, the mean and standard deviation of the run-to-detonation time of a shock within PBX 9502 were computed for a number of initial impact velocities. A weighted least squares regression was then performed to obtain a best fit curve and prediction interval for the computed statistics. Historical data points from explosively driven wedge tests were utilized to validate the prediction interval, ensuring its reliability in predicting future outcomes. With this prediction interval and a known safety constraint curve, the most probable point of failure and the probability of failure for the HE PBX 9502 were determined.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Q-Law for Rapid Assessment of Low Thrust Cislunar Trajectories Via Automatic Differentiation

Q-Law is a Lyapunov-based control law used to determine optimal controls for a low thrust trajectory. One major issue with its use is the difficult derivatives re-quired for calculating optimal controls at a given time. In this paper, an implementation of Q-Law with automatic differentiation via a Python package called JAX is applied. With automatic differentiation, the difficult derivatives for Q-Law’s optimal controls are calculated with ease, and derivatives of final states with respect to Q-Law’s weights are found enabling gradient-based optimization of Q-Law for the first time. Different search and optimization methods for finding optimal weights are then compared using the LEO to GEO problem, and it was found that gradient-free methods like design of experiments and genetic algorithm produced the best results, but they took the longest time to get a solution, while the gradient-based method found a locally optimal result in a much faster time. Overall, the run time for a single propagation is manageable and well-suited for a mission designer to use as an initial guess generator for trajectory optimization, or for simple orbit transfer analysis.

Nathan Steffen↗
DOE OSTI2025

Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

ZEUS: An Efficient GPU Optimization Method Integrating PSO, BFGS, and Automatic Differentiation

We introduce a novel, efficient computational method, ZEUS, for numerical optimization, and provide an open-source implementation. It has four key ingredients: (1) particle swarm optimization (PSO), (2) the use of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, (3) automatic differentiation (AD), and (4) GPUs. Our approach addresses the computational challenges inherent in high-dimensional, non-convex optimization problems. In the first phase of the algorithm, we get a potentially good set of starting points using PSO. Thereafter, we run BFGS independently in parallel from these starting points. BFGS is one of the best-performing algorithms for numerical optimization. However, it requires the gradient of the function being optimized. ZEUS integrates automatic differentiation into BFGS thus avoiding the need for the user to calculate derivatives explicitly. The use of GPUs allows ZEUS to speed up the calculations substantially. We carry out systematic studies to explore the trade-offs between the number of PSO iterations taken, starting points, and BFGS iteration depth. We show that a handful of iterations of PSO can improve global convergence when combined with BFGS. We also present performance studies using common test functions. The source code can be found at https://github.com/fnal-numerics/global-optimizer-gpu.

Soos, Dominik [Old Dominion U.]↗
NASA NTRS1996

Optimum Shape Design Using Automatic Differentiation in Reverse Mode

This paper shows how to use automatic differentiation in reverse mode as a powerful tool in optimization procedures. It is also shown that for aerodynamic applications the gradients have to be as accurate as possible. In particular, the effect of having the exact gradient of he first or second order spatial discretization schemes is presented. We show that the loss of precision in the gradient affects not only the convergence, but also the final shape. Both two and three dimensional configurations of transonic and supersonic flows have been investigated. These cases involve up to several thousand control parameters.

Hafez, M.↗
NASA NTRS1992

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗
NASA NTRS1994

Automatic differentiation for design sensitivity analysis of structural systems using multiple processors

An automatic differentiation tool (ADIFOR) is incorporated into a finite element based structural analysis program for shape and non-shape design sensitivity analysis of structural systems. The entire analysis and sensitivity procedures are parallelized and vectorized for high performance computation. Small scale examples to verify the accuracy of the proposed program and a medium scale example to demonstrate the parallel vector performance on multiple CRAY C90 processors are included.

Nguyen, Duc T.↗
NASA NTRS1995

Automatic differentiation evaluated as a tool for rotorcraft design and optimization

This paper investigates the use of automatic differentiation (AD) as a means for generating sensitivity analyses in rotorcraft design and optimization. This technique transforms an existing computer program into a new program that performs sensitivity analysis in addition to the original analysis. The original FORTRAN program calculates a set of dependent (output) variables from a set of independent (input) variables, the new FORTRAN program calculates the partial derivatives of the dependent variables with respect to the independent variables. The AD technique is a systematic implementation of the chain rule of differentiation, this method produces derivatives to machine accuracy at a cost that is comparable with that of finite-differencing methods. For this study, an analysis code that consists of the Langley-developed hover analysis HOVT, the comprehensive rotor analysis CAMRAD/JA, and associated preprocessors is processed through the AD preprocessor ADIFOR 2.0. The resulting derivatives are compared with derivatives obtained from finite-differencing techniques. The derivatives obtained with ADIFOR 2.0 are exact within machine accuracy and do not depend on the selection of step-size, as are the derivatives obtained with finite-differencing techniques.

Walsh, Joanne L.↗
DOE OSTI2026

MapsTorch : automatic differentiation for X-ray fluorescence data analysis

X-ray fluorescence (XRF) is a popular spectroscopy technique for elemental analysis. Spectrum fitting and parameter tuning are at the core of XRF analysis and are conventionally manually intensive, especially for synchrotron experiments involving large amounts of diverse samples. This work introduces the automatic differentiation (AD) technique to XRF and an open-source package called MapsTorch. By transforming an analytical model of the XRF spectrum into a differentiable computation graph with AD, MapsTorch enables robust optimization of parameters and elemental intensities. We evaluate MapsTorch by conducting computational experiments on a large number of historical synchrotron XRF datasets and compare its performance with the currently practiced fitting tool NLopt. The results show that MapsTorch consistently achieves high-quality fits and often leads to better fitting quality than NLopt, particularly in tasks such as initial spectrum fitting and elemental intensity refinement. The robust performance of MapsTorch paves the way for developing automated and high-throughput XRF data analysis workflows to handle the increasing data volumes expected from next-generation synchrotron facilities.

X-ray fluorescence↗