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At least 1,153 records · Page 64
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Q-Law for Rapid Assessment of Low Thrust Cislunar Trajectories Via Automatic Differentiation

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

Nathan Steffen↗
DOE OSTI2016

Differentially pumped dual linear quadrupole ion trap mass spectrometer

The present disclosure provides a new tandem mass spectrometer and methods of using the same for analyzing charged particles. The differentially pumped dual linear quadrupole ion trap mass spectrometer of the present disclose includes a combination of two linear quadrupole (LQIT) mass spectrometers with differentially pumped vacuum chambers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Measurement of the Pole Mass of the Top Quark using Differential $t\bar{t}$ Cross Sections in $p\bar{p}$ Collisions at $\sqrt{s}$ = 1.96 TeV

The differential $t\bar{t}$ cross sections, measured as a function of the transverse momentum of the top quark and the invariant mass of the $t\bar{t}$ system, are employed to determine the pole mass of the top quark. The data corresponds to an integrated luminosity of 9.7 $fb^{-1}$, collected with the D0 detector of the Fermilab Tevatron. Precise calculations at next-to-next-to leading order in perturbative quantum chromodynamics provide the absolute differential cross sections that are employed to extract the pole mass of the top quark.We measure the pole mass of the top quark to be 169.1 ± 2.5 (tot.) GeV.

Czakon, M.↗
DOE OSTI2018

Gas stream analysis using voltage-current time differential operation of electrochemical sensors

A method for analysis of a gas stream. The method includes identifying an affected region of an affected waveform signal corresponding to at least one characteristic of the gas stream. The method also includes calculating a voltage-current time differential between the affected region of the affected waveform signal and a corresponding region of an original waveform signal. The affected region and the corresponding region of the waveform signals have a sensitivity specific to the at least one characteristic of the gas stream. The method also includes generating a value for the at least one characteristic of the gas stream based on the calculated voltage-current time differential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

CHEMNODE: CHEMICAL KINETICS SOLVER APPROACH BASED ON NEURAL ORDINARY DIFFERENTIAL EQUATIONS

This software contains an algorithm to model and predict the time evolution of chemical kinetics in reacting flow simulations using neural ordinary differential equations (NODEs). The approach works by using artificial neural networks to predict the chemical source terms. It achieves this by using forward-mode automatic differentiation and the Levenberg-Marquardt algorithm to adjust the neural network parameters, such that the discrepancies between the actual and predicted species profiles are minimized.

OWOYELE, OPEOLUWA↗
DOE OSTI2022

New directions for surrogate models and differentiable programming for High Energy Physics detector simulation

The computational cost for high energy physics detector simulation in future experimental facilities is going to exceed the current available resources. To overcome this challenge, new ideas on surrogate models using machine learning methods are being explored to replace computationally expensive components. Additionally, differentiable programming has been proposed as a complementary approach, providing controllable and scalable simulation routines. In this document, new and ongoing efforts for surrogate models and differential programming applied to detector simulation are discussed in the context of the 2021 Particle Physics Community Planning Exercise (`Snowmass').

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

First Measurement Of Charged-current 1 Muon 2 Proton 0 Pion Single Differential Cross-sections On Argon-40 At 0.8 Gev Average Neutrino Energy With The MicroBooNE Detector

Constraining systematic uncertainties that arise from neutrino-nucleon cross-section modeling is critical for upcoming neutrino oscillation experiments. Neutrino interactions that lead to the ejection of 2 particles from the target nucleus, leaving the nucleus with 2 holes, are one cross-section of interest. These instances, known as 2-particle 2-hole (2p2h) states, can be produced either by neutrino interaction modes or from the influence of nuclear physics on the neutrino interaction. While there are many theoretical models that attempt to describe the nature of 2p2h states, very few experimental measurements of this process exist, making it difficult to benchmark theoretical calculations. Furthermore, no high statistic cross-section measurements of 2p2h states exist on $^{40}$Ar, the target nucleus of many current and next generation neutrino oscillation experiments. This analysis aims to address this issue by providing the first high-statistic single differential cross-section me asurements of 2p2h states. Using data collected from the first 3 years of running of the MicroBooNE experiment, we select $\nu_\mu$ charged-current interaction events that produce a single muon, 2 protons, and no pions in the final state (CC1$\mu$2p0$\pi$). The single differential cross-section is then extracted as a function of a variety of physics variables and compared to theoretical predictions from several event generator model sets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Linear differential

Apparatuses and methods of operating a linear differential (100, 600) are described herein. The linear differential (100, 600) contains a slide portion (102) with parallel right-hand and left-hand threaded rods (112, 114). Threaded onto the right-hand and left-hand threaded rods (112, 114) and attached to the slide portion (102) are right-hand and left-hand gears (116, 118). Meshed between the right-hand and left-hand gears (116, 118) and also attached to the slide portion (102) is a driven gear (200). An end effector (104) is attached to the driven gear (200) and is configured to translate along a translation axis (110) and rotate around a rotation axis (120).

Crawford, Anthony↗
DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗
DOE OSTI2023

Cycloidal wave energy converter using fixed differential buoyancy to control operating torques

A floating mooring system for a single CycWEC applies counter forces and torques to keep a generator suitably stationary for power generation without requiring fixed attachments to the ocean floor or requiring a large frame interconnecting multiple CycWECs. The mooring system uses floats or floatation structure with differential ballasting to counter operating torque and drag plates to counter reactive forces. The floatation structures may be used to float the CycWEC for transport to a deployment location, where changing the overall ballasting of the floatation structures submerges the CycWEC to a desired depth and differential ballasting in the floatation structures counts expected operating torques.

Siegel, Stefan G.↗
DOE OSTI2017

Determining Physical Parameters of Shielded Uranium using Gamma Spectroscopy and the Differential Evolution Adaptive Metropolis (DREAM) Method

Inverse radiation transport is a well-established method for determining unknown parameters within a system that exhibits particle leakage. Two significant challenges of solving inverse transport problems are (1) to determine multiple unknowns without false convergence on local minima and (2) to be able to quantify uncertainty. It was recently demonstrated that the Differential Evolution Adaptive Metropolis (DREAM) method effectively meets both of these challenges. In Bledsoe's 2014 article, the DREAM method was only applied to numerical test cases in which measured data were simulated using MCNP. This paper provides results of research conducted at Oak Ridge National Laboratory (ORNL) in which DREAM was applied to two-dimensional inverse transport problems using real-world measurements. The DREAM method uses a Markov chain Monte Carlo (MCMC) method to obtain a posterior distribution of unknown parameters. In this application, the posterior distribution is determined by using a uniform prior distribution and a likelihood function. The goal of the inverse problem is to find the regions in which the likelihood function is at or near its maximum. In the traditional MCMC approach, a single Markov chain is employed. In practice, MCMC approaches have a high acceptance rate to solutions that are near the current point of sampling, but they exhibit slow convergence to solutions far from the sampling point. The DREAM algorithm was designed to alleviate this issue by initiating multiple Markov chains and using the differential evolution algorithm to generate trial points for each chain. Solving for the mass of radioactive material within a voluminous source is a challenging problem for gamma-ray spectroscopy. Inverse gamma-ray transport can supply a range of possible material compositions, but reducing the differences between predicted and actual measurements can lead to false results. DREAM is a rapid technique for determining the most likely solution for several unknown parameters in an inverse transport problem. This work applies DREAM to a series of gamma spectroscopy experiments performed at ORNL.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Measurement of the double-differential cross section of muon-neutrino charged-current interactions with low hadronic energy in the NOvA Near Detector

The NOvA collaboration reports cross-section measurements for $\nu_{\mu}$ charged-current interactions with low hadronic energy (maximum kinetic energy of 250 MeV for protons and 175 MeV for pions) in the NOvA Near Detector. The results are presented as a double-differential cross section as a function of the direct observables of the final-state muon kinematics. Results are also presented as a single-differential cross section as a function of the derived square of the four-momentum transfer, $Q^{2}$, and as a function of the derived neutrino energy. The data correspond to an accumulated 8.09$\times10^{20}$ protons-on-target (POT) in the neutrino mode of the NuMI beam, with a narrow band of neutrino energies peaked at 1.8 GeV. The analysis provides a sample of neutrino-nucleus interactions with an enhanced fraction of quasi-elastic and two-particle-two-hole (2p2h) interactions. This enhancement allows quantitative comparisons with various nuclear models. We find strong disagreement between data and theory-based models in various regions of the muon kinematic phase space, especially in the forward muon direction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗
DOE OSTI2026

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

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

Soos, Dominik [Old Dominion U.]↗
DOE OSTI2025

Measurements of differential charged-current cross sections on argon for electron neutrinos with final-state protons in MicroBooNE

This work presents single-differential electron-neutrino charged-current cross sections on argon measured using the MicroBooNE detector at the Fermi National Accelerator Laboratory. The analysis uses data recorded when the Neutrinos at the Main Injector beam was operating in both neutrino and antineutrino modes, with exposures of $2 \times 10^{20}$ and $5 \times 10^{20}$ protons on target, respectively. A selection algorithm targeting electron-neutrino charged-current interactions with at least one proton, one electron, and no pions in the final topology is used to measure differential cross sections as a function of outgoing electron energy, total visible energy, and opening angle between the electron and the most energetic proton. The interaction rate as a function of proton multiplicity is also reported. The total cross section is measured as [4.1 $\pm$ 0.4 (stat.) $\pm$ 1.2 (syst.)]$ $$\times 10^{-39} \mathrm{cm}^{2}/ \mathrm{nucleon}$. The unfolded cross-section measurements are compared to predictions from neutrino event generators commonly employed in the field. Good agreement is seen across all variables within uncertainties.

Abratenko, P. [Tufts U. (main)]↗
DOE OSTI2026

First inclusive triple-differential measurement of the muon-antineutrino charged-current cross section using the NOvA Near Detector

We present the first measurement of the triple-differential muon antineutrino charged-current inclusive cross section, using the NOvA Near Detector and $12.5 \times 10^{20}$ protons on target in the NuMI beam. This sample of muon antineutrino interactions is the largest ever published, with approximately 1 million selected muon antineutrino events. The triple-differential cross section is measured in the final-state kinetic energy, the scattering angle, and the available energy of the interaction. The measurement enables phase-space regions populated by differing neutrino reaction processes to be isolated and the transition regions between them to be defined. The results are compared with the predictions of the main event generators used in the neutrino community and we observe energy- and angle-dependent discrepancies across a broad range of energies and interaction types

Abubakar, S. [Erciyes U.]↗
DOE OSTI2022

Differentially Private Synthesis and Sharing of Network Data Via Bayesian Exponential Random Graph Models

Abstract Network data often contain sensitive relational information. One approach to protecting sensitive information while offering flexibility for network analysis is to share synthesized networks based on the information in originally observed networks. We employ differential privacy (DP) and exponential random graph models (ERGMs) and propose the DP-ERGM method to synthesize network data. We apply DP-ERGM to two real-world networks. We then compare the utility of synthesized networks generated by DP-ERGM, the DyadWise Randomized Response (DWRR) approach, and the Synthesis through Conditional distribution of Edge given nodal Attribute (SCEA) approach. In general, the results suggest that DP-ERGM preserves the original information significantly better than two other approaches in network structural statistics and inference for ERGMs and latent space models. Furthermore, DP-ERGM satisfies node DP through modeling the global network structure with ERGM, a stronger notion of privacy than the edge DP under which DWRR and SCEA operate.

graph synthesis↗
DOE OSTI2018

Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations

We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H{sup 2} spaces. It is shown that, under reasonable technical conditions, the convergence in L{sup 1} of the integral kernels implies the existence and convergence in H{sup 2} of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.

97 MATHEMATICS AND COMPUTING↗