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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
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 OSTI2025

A multi-language auto differentiation package (mAD) v1.0

This is a multi-language auto differentiation package. It includes multiple language versions of the package. It can be included/used as a module/class in users' application program to enable differentiability of the program. It is simple, transparent, extensible, efficient compared with the other AD package such as Enzyme or Pytorch.

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↗
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↗
DOE OSTI2024

Towards reverse mode automatic differentiation of Kokkos-based codes

Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and the solving of nonlinear problems. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years, has been integrated into programming environments such as Jax, PyTorch, and TensorFlow to support derivative computations needed for training of machine learning models, facilitating wide-spread use of these technologies. The C++ language has become the de facto standard for scientific computing due to numerous factors, yet language complexity has made the wide-spread adoption of AD technologies for C++ difficult, hampering the incorporation of powerful differentiable programming approaches into C++ scientific simulations. This is exacerbated by the increasing emergence of architectures, such as GPUs, with limited memory capabilities and requiring massive thread-level concurrency. C++ AD tools must effectively use these environments to bring novel scientific simulations to next-generation DOE experimental and observational facilities. In this project, we investigated source transformation-based automatic differentiation using LLVM compiler infrastructure to automatically generate portable and efficient gradient computations of Kokkos-based code. We have demonstrated that our proposed strategy is feasible by investigating the usage of a prototype LLVM-based source transformation tool to generate gradients of simple functions made of sequences of simple Kokkos parallel regions. Speedups of up to 500x compared to Sacado were observed on NVIDIA V100 GPU.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

GenASiS Mathematics: Object-oriented manifolds, operations, and solvers for large-scale physics simulations (version 2)

We report GenASiS Mathematics provides modern Fortran classes furnishing extensible object-oriented functionality for the solution of fields governed by selected partial differential equations. The initial release included extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon. This revision - Version 2 of Mathematics - includes significant reorganization and streamlining of these classes, higher-order reconstruction by a different method, a Poisson solver, coarsening to avoid Courant time step limitations near coordinate singularities, and the offloading of computational kernels to GPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Cross Section Evaluation for Exclusive Channels of K+Λ and K+Σ0 Electroproduction off Protons Using CLAS Detector Data

In this work, a method for evaluating the cross sections of electroproduction of K+Λ0 and K+Σ0 off protons in the region of invariant masses of final hadrons MK + MY <W < 2.65 GeV (MK and MY being the masses of the kaon and hyperon, respectively) and squares of four-momentum transfers of virtual photons, i.e., photon virtualities 0 < Q2 < 5 GeV2, is developed based on experimental data of these exclusive channels’ cross sections measured by the CLAS detector in Hall B at Jefferson Lab. A set of algorithms has been implemented to evaluate the differential cross sections of these channels, along with their statistical and systematic uncertainties. A program was developed for the evaluation of differential cross sections and structure functions using C++ and Python libraries. An interactive website was created for working with the program, enabling the analysis of one-dimensional and two-dimensional dependences of structure functions and differential cross sections. The evaluation of differential cross sections for the K+Λ and K+Σ0 electroproduction channels is necessary for extracting the structure function σLT from the data on the polarization asymmetry of electroproduction reactions of these final states with longitudinally polarized electrons. The obtained results are also important for the development of realistic Monte Carlo event generators in planning future experiments and for evaluating the efficiency of detecting final particles when extracting reaction cross sections from experimental data.

Golda, A. V.↗
DOE OSTI2023

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Simple, efficient and open-source CRISPR/Cas9 strategy for multi-site genome editing in Populus tremula × alba

Although the CRISPR/Cas9 system has been successfully used for crop breeding, its application remains limited in forest trees. Here, we describe an efficient gene editing strategy for hybrid poplar, (Populus tremula × alba INRA clone 717-1B4) based on the Golden Gate MoClo cloning. To test the system efficiency for generating single gene mutants, two single guide RNAs (sgRNAs) were designed and incorporated into the MoClo Tool Kit level 2 binary vector with the Cas9 expression cassette to mutate the SHORT ROOT (SHR) gene. Moreover, we also tested its efficiency for introducing mutations in two genes simultaneously by expressing one sgRNA targeting a single site of the YUC4 gene and the other sgRNA targeting the PLT1 gene. For a robust evaluation of the approach, we repeated the strategy to target the LBD12 and LBD4 genes simultaneously, using an independent construct. We generated hairy roots by Agrobacterium rhizogenes-mediated leaf transformation. Sequencing results confirmed the CRISPR/Cas9-mediated mutation in the targeted sites of PtaSHR. Biallelic and homozygous knockout mutations were detected. A deletion spanning both target sites and small insertions/deletions were the most common mutations. Out of the 22 SHR alleles sequenced, 21 were mutated. The phenotype’s characterization showed that transgenic roots with biallelic mutations for the SHR gene lacked a defined endodermal single cell layer, suggesting a conserved gene function similar to its homolog in Arabidopsis Arabidopsis thaliana (L.) Heynh. Sequencing results also revealed the high efficiency of the system for generating double mutants. Biallelic mutations for both genes in the yuc4/plt1 and lbd12/lbd4 roots were detected in three (yuc4/plt1) and two (lbd12/lbd4) out of four transgenic roots evaluated. A small deletion or a single nucleotide insertion at the single target site was the most common mutations. This CRISPR/Cas9 strategy arises as a rapid, simple and standardized gene-editing tool to evaluate the gene role in essential developmental programs such as radial cell differentiation of poplar roots.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Unified differentiable digital twin for the IOTA/FAST facility

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or produce insights about accelerator state. One notable example of additional information are gradients of physical observables with respect to design parameters produced by differentiable simulations. The IOTA/FAST facility has recently begun a program to implement and experimentally validate a unified start-to-end differentiable digital twin to serve as a virtual accelerator test stand, allowing for rapid prototyping of new software and experiments with minimal beam time costs. In this contribution we will discuss our plans and progress. Specifically, we will cover the selection and benchmarking of both physics and ML codes, the development of generic interfaces between device models and surrogate or physics-based sections, and the export of the parameters through either a deterministic event loop or a fully asynchronous EPICS soft input/output controller. We will also discuss challenges in model calibration and uncertainty quantification, as well as future plans to support larger proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]↗
DOE OSTI2021

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Scrutinizing Variables for Checkpoint Using Automatic Differentiation

Checkpoint/Restart (C/R) saves the running state of the programs periodically, which consumes considerable time and system resources. We observe that not every piece of data is involved in the computation in typical HPC applications; such unused data should be excluded from checkpointing for better storage and compute efficiency. We propose a systematic approach that leverages automatic differentiation (AD) to scrutinize every element within variables (e.g., arrays) necessary for checkpointing. This allows us to identify critical and uncritical elements and eliminate uncritical elements from checkpointing. Specifically, we inspect every single element within a variable necessary for checkpointing with an AD tool to determine whether the element has an impact on the application output or not. We validate our approach with all benchmarks from the NPB suite. We visualize the distribution of critical and uncritical elements within a variable with respect to its binary impact (yes or no) on the application output.

Huang, Xin [Kobe University]↗
DOE OSTI2022

Source-to-Source Automatic Differentiation of OpenMP Parallel Loops

This article presents our work toward correct and efficient automatic differentiation of OpenMP parallel worksharing loops in forward and reverse mode. Automatic differentiation is a method to obtain gradients of numerical programs, which are crucial in optimization, uncertainty quantification, and machine learning. The computational cost to compute gradients is a common bottleneck in practice. For applications that are parallelized for multicore CPUs or GPUs using OpenMP, one also wishes to compute the gradients in parallel. Here, we propose a framework to reason about the correctness of the generated derivative code, from which we justify our OpenMP extension to the differentiation model. We implement this model in the automatic differentiation tool Tapenade and present test cases that are differentiated following our extended differentiation procedure. Performance of the generated derivative programs in forward and reverse mode is better than sequential, although our reverse mode often scales worse than the input programs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗