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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

The Memory Scaling of Reverse-Mode Differentiation in Particle Accelerator Simulations with Space Charge

The recent development of differentiable simulation codes for particle accelerators has enabled gradient-based workflows that promise finer control and more realistic modeling of accelerator facilities. However, when using reverse-mode automatic differentiation, the memory usage continuously increases during the simulation, and can potentially exceed the available hardware memory - especially when costly space charge computation is included. To study the memory requirements for differentiable simulations, we have implemented space charge in Cheetah, a PyTorch-based beam tracking code that supports reverse-mode differentiation. We find that the memory usage for reverse-mode differentiation grows linearly with the number of macroparticles and cells, and that it is proportional to the number of space charge kicks involved in the simulation. This general scaling can be used to evaluate whether a given differentiable simulation is feasible given hardware memory constraints.

Dhamrait, Arjun↗
DOE OSTI2019

Reverse-Mode Algorithmic Differentiation of an OpenMP-Parallel Compressible Flow Solver

y Reverse-mode algorithmic differentiation (AD) is an established method for obtaining adjoint derivatives of computer simulation applications. In computational fluid dynamics (CFD), adjoint derivatives of a cost function output such as drag or lift with respect to design parameters such as surface coordinates or geometry control points are a key ingredient for shape optimization, uncertainty quantification and flow control. The computational cost of CFD applications and their derivatives makes it essential to use high-performance computing hardware efficiently, including multi- and many-core architectures. Nevertheless, OpenMP is not supported in most AD tools, and previously shown methods achieve poor scalability of the derivative code. We present the AD of an OpenMP-parallelized finite volume compressible flow solver for unstructured meshes. Our approach enables us to reuse the parallelization of the original code in the computation of adjoint derivatives. The method works by identifying code segments that can be differentiated in reverse-mode without changing their memory access pattern. The OpenMP parallelization is integrated into the derivative code during the build process in a way that is robust to modifications of the original code and independent of the OpenMP support of the differentiation tool. We show the scalability of our adjoint CFD solver on test cases ranging from thousands to millions of finite volume mesh cells on CPUs with up to 16 threads as well as on an Intel XeonPhi card with 236 threads. We demonstrate that our approach is more practical to implement for production-sized CFD codes and produces more efficient adjoint derivative code than previously shown AD methods.

Huckelheim, Jan↗
DOE OSTI2026

Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications

We present a fast, spectrally (exponentially) accurate, automatically differentiable bounce-averaging algorithm that is used to simplify kinetic models. Using this algorithm, implemented in the DESC stellarator optimisation suite, we can perform efficient optimisation of many objectives to improve stellarator performance, such as the effective ripple 𝜖 eff metric for the neoclassical transport coefficient in the low collisionality regime and proxies for energetic particle confinement. For the first time, we optimise a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the computational cost of differentiation is independent of the number of controllable parameters.

fusion plasma↗
DOE OSTI2022

Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.

This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A general approach to seismic inversion with automatic differentiation

Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. Here, the mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.

58 GEOSCIENCES↗
DOE OSTI2024

Qualitative and quantitative enhancement of parameter estimation for model-based diagnostics using automatic differentiation with an application to inertial fusion

Parameter estimation using observables is a fundamental concept in the experimental sciences. Mathematical models that represent the physical processes can enable reconstructions of the experimental observables and greatly assist in parameter estimation by turning it into an optimization problem which can be solved by gradient-free or gradient-based methods. In this work, the recent rise in flexible frameworks for developing differentiable scientific computing programs is leveraged in order to dramatically accelerate data analysis of a common experimental diagnostic relevant to laser–plasma and inertial fusion experiments, Thomson scattering. A differentiable Thomson-scattering data analysis tool is developed that uses reverse-mode automatic differentiation (AD) to calculate gradients. By switching from finite differencing to reverse-mode AD, three distinct outcomes are achieved. First, gradient descent is accelerated dramatically to the extent that it enables near real-time usage in laser–plasma experiments. Second, qualitatively novel quantities which require $\mathcal{O}(10^3)$ parameters can now be included in the analysis of data which enables unprecedented measurements of small-scale laser–plasma phenomena. Third, uncertainty estimation approaches that leverage the value of the Hessian become accurate and efficient because reverse-mode AD can be used for calculating the Hessian.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Advanced Applications of Adifor 3.0 for Efficient Calculation of First-and Second-Order CFD Sensitivity Derivatives

This final report will document the accomplishments of the work of this project. 1) The incremental-iterative (II) form of the reverse-mode (adjoint) method for computing first-order (FO) aerodynamic sensitivity derivatives (SDs) has been successfully implemented and tested in a 2D CFD code (called ANSERS) using the reverse-mode capability of ADIFOR 3.0. These preceding results compared very well with similar SDS computed via a black-box (BB) application of the reverse-mode capability of ADIFOR 3.0, and also with similar SDs calculated via the method of finite differences. 2) Second-order (SO) SDs have been implemented in the 2D ASNWERS code using the very efficient strategy that was originally proposed (but not previously tested) of Reference 3, Appendix A. Furthermore, these SO SOs have been validated for accuracy and computational efficiency. 3) Studies were conducted in Quasi-1D and 2D concerning the smoothness (or lack of smoothness) of the FO and SO SD's for flows with shock waves. The phenomenon is documented in the publications of this study (listed subsequently), however, the specific numerical mechanism which is responsible for this unsmoothness phenomenon was not discovered. 4) The FO and SO derivatives for Quasi-1D and 2D flows were applied to predict aerodynamic design uncertainties, and were also applied in robust design optimization studies.

Taylor, Arthur C., III↗
NASA NTRS1979

Transient shutdown analysis of low-temperature thermal diodes

The various thermal diodes available for use in cryogenic systems are described. Two diode types, liquid-trap and liquid-blockage diodes, were considered to be the most attractive, and thermal models were constructed to predict their behavior in the reverse mode. The diodes, which are of similar size and throughput, were also examined experimentally in a parallel test setup under nominally identical conditions. Their characteristics were ascertained in terms of forward-mode and reverse-mode conductances, shutdown times and energies, and recovery to forward-mode operation with ethane as the working fluid in the temperature range 170 K to 220 K. Results show that the liquid-blockage diode is the quicker of the two diodes to shut down from the forward mode (8 min as opposed to 10 min). However, the liquid-blockage diode has a larger reverse-mode conductance which results in a greater overall evaporator temperature rise. The importance of the relative size and heat inputs to the condenser/reservoir configuration of the liquid-blockage diode and the evaporator trap configuration for the liquid-trap diode are demonstrated. Also included are data which show the susceptibility of the diodes to recovery to forward-mode operation. Guidelines for the choice of a particular diode for an actual application are given.

Williams, R. J.↗
NASA NTRS2003

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Taylor, Arthur C., III↗
DOE OSTI2018

Parallelizable adjoint stencil computations using transposed forward-mode algorithmic differentiation

Algorithmic differentiation (AD) is a tool for generating discrete adjoint solvers, which efficiently compute gradients of functions with many inputs, for example for use in gradient-based optimization. AD is often applied to large computations such as stencil operators, which are an important part of most structured-mesh PDE solvers. Stencil computations are often parallelized, for example by using OpenMP, and optimized by using techniques such as cache-blocking and tiling to fully utilize multicore CPUs and many-core accelerators and GPUs. Differentiating these codes with conventional reverse-mode AD results in adjoint codes that cannot be expressed as stencil operations and may not be easily parallelizable. They thus leave most of the compute power of modern architectures unused. We present a method that combines forward-mode AD and loop transformation to generate adjoint solvers that use the same memory access pattern as the original computation that they are derived from and can benefit from the same optimization techniques. The effectiveness of this method is demonstrated by generating a scalable adjoint CFD solver for multicore CPUs and Xeon Phi accelerators.

algorithmic differentiation↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni 80 Fe 20 ) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.

Lorentz transmission electron microscopy↗
DOE OSTI2019

Automatic Differentiation for Adjoint Stencil Loops

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is aided by compilers, libraries, and domain-specific languages. Reverse-mode automatic differentiation, also known as algorithmic differentiation, autodiff, adjoint differentiation, or back-propagation, is sometimes used to obtain gradients of programs that contain stencil loops. Unfortunately, conventional automatic differentiation results in a memory access pattern that is not stencil-like and not easily parallelisable. In this paper we present a novel combination of automatic differentiation and loop transformations that preserves the structure and memory access pattern of stencil loops, while computing fully consistent derivatives. The generated loops can be parallelised and optimised for performance in the same way and using the same tools as the original computation. We have implemented this new technique in the Python tool PerforAD, which we release with this paper along with test cases derived from seismic imaging and computational fluid dynamics applications.

Automatic Differentiation↗
DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗
NASA NTRS1977

Parametric Performance of a Spiral-Artery, Liquid-Trap-Diode Heat Pipe

A series of parametric investigations are described which determine the effect of various fluid charges on the performance of a 0.635-cm-diam spiral-artery, liquid-trap diode in both the forward and reverse modes. Specific parameters such as forward- and reverse-mode conductances, shutdown times and energies, and recovery to forward-model operation, are evaluated for ethane as a working fluid in the temperature range 170 K to 220 K. Results indicate that the heat pipe will not reliably start up in the forward mode. However, startup can be initiated when preceded by a diode reversal. Also included are data which show the susceptibility of the diode to fluid charge and tilt. The optimum fluid charge was found to be 2.67 g and transport capability at this charge was in excess of 1200 W-cm at 200 K. The diode in the reverse mode exhibited a rapid shutdown (within 9 min) with a shutdown energy of 1150 J (0.32 Wh).

Williams, R. J.↗
NASA NTRS1978

Investigation of a cryogenic thermal diode

This paper describes a series of parametric investigations to determine the effect of various fluid charges on the performance of a 0.635-cm-diameter spiral-artery, liquid-trap diode in both the forward and reverse modes. Specific parameters such as forward- and reverse-mode conductances, shutdown times and energies, and recovery to forward-mode operation, are evaluated for ethane as a working fluid in the temperature range 170 K to 220 K. Results indicate that the heat pipe will not reliably start up in the forward mode. However, startup can be initiated when preceded by a diode reversal. Also concluded are data which show the susceptibility of the diode to fluid charge and tilt. The optimum fluid charge was found to be 2.67 g, and transport capability at this charge was in excess of 1200 W-cm at 200 K. The diode in the reverse mode exhibited a rapid shutdown (within 9 min) with a shutdown energy of 1150 J (0.32 Wh).

Williams, R. J.↗
NASA NTRS1982

Orifice Blocks Heat Pipe in Reverse Mode

High forward-mode conductance is combined with rapid reverse-mode shutoff in a heat pipe originally developed to cool spacecraft payloads. A narrow orifice within the pipe "chokes off" the evaporator if heat sink becomes warmer than source. During normal operation, with source warmer than sink, orifice has little effect. Design is simpler and more compact than other thermal-diode heat pipes and requires no special materials, forgings, or unusual construction techniques.

Alario, J. P.↗
NASA NTRS1999

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Green, Lawrence↗