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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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All sourcesNASA NTRSDOE OSTI
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 OSTI2025

ASDF: A Compiler for Qwerty, a Basis-Oriented Quantum Programming Language

Qwerty is a high-level quantum programming language built on bases and functions rather than circuits. This new paradigm introduces new challenges in compilation, namely synthesizing circuits from basis translations and automatically specializing adjoint or predicated forms of functions. This paper presents ASDF, an open-source compiler for Qwerty that answers these challenges in compiling basis-oriented languages. Enabled with a novel high-level quantum IR implemented in the MLIR framework, our compiler produces OpenQASM 3 or QIR for either simulation or execution on hardware. Our compiler is evaluated by comparing the fault-tolerant resource requirements of generated circuits with other compilers, finding that ASDF produces circuits with comparable cost to prior circuit-oriented compilers.

Adams, Austin J [Georgia Tech]↗
DOE OSTI2016

Integrated Design of Downwind Land-Based Wind Turbines using Analytic Gradients

Wind turbines are complex systems where component-level changes can have significant system-level effects. Effective wind turbine optimization generally requires an integrated analysis approach with a large number of design variables. Optimizing across large variable sets is orders of magnitude more efficient with gradient-based methods as compared with gradient-free method, particularly when using exact gradients. We have developed a wind turbine analysis set of over 100 components where 90% of the models provide numerically exact gradients through symbolic differentiation, automatic differentiation, and adjoint methods. This framework is applied to a specific design study focused on downwind land-based wind turbines. Downwind machines are of potential interest for large wind turbines where the blades are often constrained by the stiffness required to prevent a tower strike. The mass of these rotor blades may be reduced by utilizing a downwind configuration where the constraints on tower strike are less restrictive. The large turbines of this study range in power rating from 5-7MW and in diameter from 105m to 175m. The changes in blade mass and power production have important effects on the rest of the system, and thus the nacelle and tower systems are also optimized. For high-speed wind sites, downwind configurations do not appear advantageous. The decrease in blade mass (10%) is offset by increases in tower mass caused by the bending moment from the rotor-nacelle-assembly. For low-wind speed sites, the decrease in blade mass is more significant (25-30%) and shows potential for modest decreases in overall cost of energy (around 1-2%).

17 WIND ENERGY↗
DOE OSTI2024

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗
DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Tapsolver: A Python Package For The Simulation And Analysis Of Tap Reactor Experiments

TAPsolver is a python package, which automates TAP simulation and analysis routines. TAPsolver is built around the python packages FEniCS and Dolfin-Adjoint, which help take advantage of model adjoints to provide automatic derivatives. TAPsolver is flexible, with reaction mechanisms and rate constants that can be set through input files that allow users to take advantage of the different functionalities, which include sensitivity analyses, parameter optimization and uncertainty quantification.

Yonge, Adam↗
DOE OSTI2022

Scientific Computational Imaging Code (SCICO)

Scientific Computational Imaging Code (SCICO) is a Python package for solving the inverse problems that arise in scientific imaging applications. Its primary focus is providing methods for solving ill-posed inverse problems by using an appropriate prior model of the reconstruction space. SCICO includes a growing suite of operators, cost functionals, regularizers, and optimization routines that may be combined to solve a wide range of problems, and is designed so that it is easy to add new building blocks. SCICO is built on top of JAX rather than NumPy, enabling GPU/TPU acceleration, just-in-time compilation, and automatic gradient functionality, which is used to automatically compute the adjoints of linear operators. An example of how to solve a multi-channel tomography problem with SCICO is shown in Figure 1. The SCICO source code is available from GitHub, and pre-built packages are available from PyPI. It has extensive online documentation, including API documentation and usage examples, which can be run online at Google Colab and binder.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Tapsolver: A Python Package For The Simulation And Analysis Of Tap Reactor Experiments

TAPsolver is a python package, which automates TAP simulation and analysis routines. TAPsolver is built around the python packages FEniCS and Dolfin-Adjoint, which help take advantage of model adjoints to provide automatic derivatives. TAPsolver is flexible, with reaction mechanisms and rate constants that can be set through input files that allow users to take advantage of the different functionalities, which include sensitivity analyses, parameter optimization and uncertainty quantification.

Kunz, MatthewR.↗
DOE OSTI2021

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗
DOE OSTI2016

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Training material models using gradient descent algorithms

High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. Here, we demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Optimal Multistage Algorithm for Adjoint Computation

We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2020

Coupled Time-Lapse Full-Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation

We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion (FWI), subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) At the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in automatic differentiation operators from the TensorFlow backend; (3) at the flow physics level, we implemented customized partial differential equation (PDE) operators for the multiphase flow equations. The three-level coupled inversion strategy strikes a good balance between computational efficiency and programming efforts, and when the gradients are chained together, it constitutes a coupled inverse system. Our numerical experiments demonstrate that the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy. Additionally, our method is able to simultaneously invert for parameters in empirical relationships such as the rock physics models. Our proposed inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.

54 ENVIRONMENTAL SCIENCES↗
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

ReactionMechanismSimulator.jl: A modern approach to chemical kinetic mechanism simulation and analysis

Abstract We present ReactionMechanismSimulator.jl (RMS), a modern differentiable software for the simulation and analysis of chemical kinetic mechanisms, including multiphase systems. RMS has already been applied to problems in combustion, pyrolysis, polymers, pharmaceuticals, catalysis, and electrocatalysis. RMS is written in Julia, making it easy to develop and allowing it to take advantage of Julia's extensive numerical computing ecosystem. In addition to its extensive library of optimized analytic Jacobians, RMS can generate and use Jacobians computed using automatic differentiation and symbolically generated analytic Jacobians. RMS is demonstrated to be faster than Cantera and Chemkin in several benchmarks. RMS also implements an extensive set of features for analyzing chemical mechanisms, including a library of easy‐to‐call plotting functions, molecular structure resolved flux diagram generation, crash analysis, traditional sensitivity analysis, transitory sensitivity analysis, and an automatic mechanism analysis toolkit. RMS implements efficient adjoint and parallel forward sensitivity analyses. We also demonstrate the ease of adding new features to RMS.

Johnson, Matthew S.↗
DOE OSTI2015

A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Implications for jet noise reduction and turbulence control in general are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗