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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 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 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↗
DOE OSTI2024

Metric Learning to Accelerate Convergence of Operator Splitting Methods

Recent developments in machine learning have led to promising advances in accelerating the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of proposed strategies for learning to produce fast solutions to optimization problems. For example, recent works have shown that it is possible to accelerate the convergence of optimization algorithms by learning to select their parameters, such as gradient descent stepsizes. This work proposes a new approach, in which the underlying metric spaces of proximal operator splitting algorithms are learned to maximize convergence rate. While prior works in optimization theory have derived optimal metrics in simple cases, no such result exists for many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the predicted proximal metrics can be viewed as a form of active set prediction.

King, Ethan [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2025

JuTrack: A Julia package for auto-differentiable accelerator modeling and particle tracking

Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming language and enhanced with compiler-level automatic differentiation (AD). With the aid of AD, JuTrack enables rapid derivative calculations in accelerator modeling, facilitating sensitivity analyses and optimization tasks. Here we demonstrate the effectiveness of AD-derived derivatives through several practical applications, including sensitivity analysis of space-charge-induced emittance growth, nonlinear beam dynamics analysis for a synchrotron light source, and lattice parameter tuning of the future Electron-Ion Collider (EIC). Through the incorporation of automatic differentiation, this package opens up new possibilities for accelerator physicists in beam physics studies and accelerator design optimization.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Status of 1eNp0π Charged-Current Electron Neutrino Cross Section on Argon in the NuMI Beam at ICARUS

The Short-Baseline Neutrino (SBN) Program is designed to probe short-baseline neutrino anomalies, including the LSND electron neutrino excess and the MiniBooNE low-energy excess. Essential to interpreting these anomalies and to the success of future experiments like DUNE, is the precise measurement of neutrino-argon interaction cross sections. The program utilizes two liquid argon time projection chamber (LArTPC) detectors: the Short-Baseline Near Detector (SBND) located 110 meters downstream from the Booster Neutrino Beam (BNB) target, and the ICARUS detector positioned 600 meters downstream. Additionally, the ICARUS detector lies off-axis to the NuMI beamline, providing a unique, high-statistics flux of electron neutrinos and sensitivity to energies that overlap with the DUNE spectrum. To analyze the data from these detectors, we have begun employing a machine-learning-based reconstruction algorithm referred to as “Scalable Particle Imaging with Neural Embeddings” (SPINE). SPINE has shown improvement in the ability to reconstruct the properties of final state particles in the detector, like the particle ID and momentum, with the potential to enhance the quality of measurements achievable within the SBN Program e.g., the resolution on kinematics used in differential cross section extraction. This poster presents progress toward measuring the electron neutrino argon interaction cross section in the 1eNp0π topology using the NuMI beam, highlighting the impact of SPINE through the ability to select signal events across a wide kinematic range without sacrificing background rejection power.

Carber, Dan [Colorado State U.] (ORCID:00090006451↗
DOE OSTI2025

End-to-end differentiable digital twin for the IOTA/FAST facility

As the design complexity of modern accelerators grows, there is more interest in using controllable-fidelity simulations that have fast execution time or can yield additional 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 an end-to-end 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 for linac and ring simulation, the development of generic interfaces between surrogate and physics-based sections, and presenting the control interface as 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 implement larger proton accelerators like PIPII and Booster.

Kuklev, N. [Fermilab]↗
DOE OSTI2025

FSEN Reaction Rate Calculations in MCNP [Slides]

FSEN provides an opportunity to quickly calculate sensitivities to orthogonal measurements during integral experiments. Toy problem has been deployed to expand on verification of FSEN for reaction rate ratios. While there is decent agreement, further investigation must be done on multiplication’s impact on sensitivity vector.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

First Differential Measurement of the Single 𝜋 + Production Cross Section in Neutrino Neutral-Current Scattering

Since its first observation in the 1970s, neutrino-induced neutral-current single positive pion production (NC⁢1⁢𝜋 + ) has remained an elusive and poorly understood interaction channel. This process is a significant background in neutrino oscillation experiments and studying it further is critical for the physics program of next-generation accelerator-based neutrino oscillation experiments. In this Letter, we present the first double-differential cross-section measurement of NC⁢1⁢𝜋 + interactions using data from the ND280 detector of the T2K experiment collected in 𝜈-beam mode. The measured flux-averaged integrated cross section is 𝜎 = (6.07 ± 1.22) × 10 −41 cm 2 /nucleon. We compare the results on a hydrocarbon target to the predictions of several neutrino interaction generators and final-state-interaction models. While model predictions agree with the differential results, the data show a weak preference for a cross-section normalization approximately 30% higher than predicted by most models studied in this Letter.

Neutrino detection↗
DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗
DOE OSTI2026

qsp4pde v1.0

The software program is a collection of Python implementations of quantum circuits for solving linear partial differential equations using quantum signal processing. The circuits are implemented using the qiskit SDK.

Kim, Hyeongjin [Lawrence Berkeley National Laborat↗
DOE OSTI2025

A Tale from the Trenches: Applying Metamorphic and Differential Testing to Bioinformatics Software

Metamorphic and differential testing have been proposed as best practices for testing software that is difficult to test, such as for programs in scientific domains. An assumption is that these approaches can be easily customized and applied to almost any domain. However, scientific software is often data-driven, and metamorphic relations may require significant domain knowledge to develop. In addition, tools are often written for ad-hoc experimentation by the scientists and often embed many assumptions about the importance and representation of different natural phenomena. In this paper, we present our experience applying both metamorphic and differential testing to a set of four computational biology tools that predict the growth of an organism. While our original goal was to evaluate these techniques to improve our system-level testing, we encountered multiple roadblocks along the way. Although we did find faults (some confirmed by developers), we also uncovered a set of challenges, including the considerable manual effort required for (a) defining domain-specific tests, (b) validating correctness, and (c) distinguishing between issues stemming from poor data and those arising from incorrect software.

Marsh, Alexis L [Iowa State University/Ames Labora↗
DOE OSTI2025

On optimal control of hybrid dynamical systems using complementarity constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

First Temperature Profile of a Stellar Flare Using Differential Chromatic Refraction

We present the first derivation of a stellar flare temperature profile from single-band photometry. Stellar flare DWF 030225.574−545707.45129 was detected in 2015 by the Dark Energy Camera as part of the Deeper, Wider, Faster program. The brightness (Δm g = −6.12) of this flare, combined with the high air mass (1.45 ≲ X ≲ 1.75) and blue filter (DES g, 398–548 nm) in which it was observed, provided ideal conditions to measure the zenithward apparent motion of the source due to differential chromatic refraction (DCR) and, from that, infer the effective temperature of the event. We model the flare’s spectral energy distribution as a blackbody to produce the constraints on flare temperature and geometric properties derived from single-band photometry. We additionally demonstrate how simplistic assumptions on the flaring spectrum, as well as on the evolution of flare geometry, can result in solutions that overestimate the effective temperature. Exploiting DCR enables studying chromatic phenomena with ground-based astrophysical surveys, and stellar flares on M dwarfs are a particularly enticing target for such studies due to their ubiquity across the sky and the heightened color contrast between their red quiescent photospheres and the blue flare emission. Our novel method will enable similar temperature constraints for a large sample of objects in upcoming photometric surveys like the Vera C. Rubin Legacy Survey of Space and Time.

Clarke, Riley W. [University of Delaware, Newark, ↗
DOE OSTI2025

Boundary-Layer-Coupled and Decoupled Clouds in Global Storm-Resolving Models: Comparisons With the ARM Observations

The accurate representation of interactions between clouds and planetary boundary layer (PBL) is a persistent challenge in climate models, critical for simulating surface energy budget. The emergence of kilometer-grid-scale global storm resolving models (GSRMs) offers the potential for enhanced details of PBL processes in these complex interactions. This study evaluates the representation of PBL-coupled and decoupled clouds in nine GSRM simulations against extensive ground-based observations by the Department of Energy Atmospheric Radiation Measurement (ARM) program, across six sites encompassing diverse regimes such as marine and continental environments in tropics and midlatitude. By differentiating coupling based on the relative positions between cloud bases and PBL tops, our analysis focuses on the simulation of PBL height, cloud frequency, position and vertical extent. The GSRMs generally exhibit commendable agreements with observed cloud structures and PBL diurnal cycles across different ARM sites. In contrast to the relatively consistent representation of decoupled clouds, discrepancies exist between the simulated and the observed coupled clouds, particularly in areas of intense convection, for example, over tropical rainforests and mountainous regions. These biases are probably associated with the models' tendency to underestimate the boundary layer humidity and the frequency of coupled clouds within different ranges of PBL heights. This study underscores the importance for continuous improvements in the representation of boundary layer and convection within these global kilometer-grid-scale models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Generic Discretization Library

The GenDiL library is a collection of C++ software abstractions designed to discretize and solve partial differential equations (PDEs) for high-performance computing (HPC) applications. Its primary focus is on modern C++ generic programming, which helps ensure portability across various hardware architectures. The central idea behind the library is to provide building blocks for numerical algorithms-such as discretization methods and iteration patterns-so that domain experts can focus on the math, rather than the low-level details of hardware or implementation. By defining abstractions for data types, iteration over computational grids, and scheduling of operations, the library isolates the high-level PDE algorithms from the platform-specific optimizations needed to achieve efficient performance.

Dudouit, Yohann [Lawrence Livermore National Labor↗