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Results for “algorithmic differentiation”

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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Convex relaxation for Fokker–Planck equation

We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics by solving the high-dimensional Fokker–Planck equation in terms of low-order cluster moments or marginals. With this approach, we bypass the exponential complexity of estimating the full high-dimensional distribution and directly solve the simplified partial differential equations for low-order moments/marginals. Moreover, the proposed moment/marginal relaxation is fully convex and can be solved via off-the-shelf solvers. We further propose a time-dependent version of the convex programs to study non-equilibrium dynamics. In a specific setting, we show the proposed method can recover a mean-field-type equilibrium density. Numerical results are provided to demonstrate the performance of the proposed algorithm for high-dimensional systems.

Chen, Yian↗
DOE OSTI2024

Momentum informed muon scattering tomography for monitoring spent nuclear fuels in dry storage cask

Development of an effective monitoring method for spent nuclear fuel (SNF) in a dry storage cask (DSC) is important to meet the increasing demand for dry storage investigations. The DSC investigation should provide information about the quantity of stored SNF, and quality assurance of materials should be possible without opening the cask. However, traditional nondestructive examination (NDE) methods such as x-rays are difficult to deploy for DSC investigation because a typical DSC is intentionally designed to shield against radiation. To address this challenge, cosmic ray muons (CRMs) are used as an alternative NDE radiation probe because they can easily penetrate an entire DSC system; however, a wide application of muons is often hindered due to the naturally low CRM flux (~10 4 muons/m 2 /min). This paper introduces a newly proposed imaging algorithm, momentum-informed muon scattering tomography (MMST) , and presents how a limitation of the current muon scattering tomography technique has been addressed by measuring muon momentum. To demonstrate its functionality, a commercial DSC with 24 pressurized light water reactor fuel assemblies (FAs) and the MMST system were designed in GEANT4. Three noticeable improvements were observed for MMST system as a DSC investigation tool: (1) a signal stabilization, (2) an enhanced capability to differentiate various materials, and (3) statistically increased precision to identify and locate missing FAs. The results show that MMST improves the investigation accuracy from 79 to 98% when one FA is missing and 51% to 88% when one-half FA is missing. The advancement of the NDE technique using CRM for DSC verification is expected to resolve long-standing problems in increasing demand for DSC inspections and nuclear security.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

MedNAS: Multiscale Training-Free Neural Architecture Search for Medical Image Analysis

Deep neural networks have demonstrated impressive results in medical image analysis, but designing suitable architectures for each specific task is expertise dependent and time consuming. Neural architecture search (NAS) offers an effective means of discovering architectures. It has been highly successful in numerous applications, particularly in natural image classification. Yet, medical images possess unique characteristics, such as small regions and a wide variety of lesion sizes, that differentiate them from natural images. Furthermore, most current NAS methods struggle with high computational costs, especially when dealing with high-resolution image datasets. In this article, we present a novel evolutionary NAS method called multiscale training-free neural architecture search (MSTF-NAS) to address these challenges. Specifically, to accommodate the broad range of lesion region sizes in disease diagnosis, we develop a new reduction cell search space that enables the search algorithm to explicitly identify the optimal scale combination for multiscale feature extraction. Further, to overcome the issue of high computational costs, we utilize training-free indicators as performance measures for candidate architectures, which allows us to search for the optimal architecture more efficiently. More specifically, by considering the capability and simplicity of various networks, we formulate a multiobjective optimization problem that involves two training-free indicators and model complexity for candidate architectures. Extensive experiments on a large medical image benchmark and a publicly available breast cancer detection dataset are conducted. The empirical results demonstrate that our MSTF-NAS outperforms both human-designed architectures and current state-of-the-art NAS algorithms on both datasets, indicating the effectiveness of our proposed method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Application-driven Privacy-preserving Data Publishing with Correlated Attributes

Recent advances in computing have allowed for the possibility to collect large amounts of data on personal activities and private living spaces. To address the privacy concerns of users in this environment, we propose a novel framework called PR-GAN that offers privacy-preserving mechanism using generative adversarial networks. Given a target application, PR-GAN automatically modifies the data to hide sensitive attributes - which may be hidden and can be inferred by machine learning algorithms - while preserving the data utility in the target application. Unlike prior works, the public's possible knowledge of the correlation between the target application and sensitive attributes is built into our modeling. We formulate our problem as an optimization problem, show that an optimal solution exists and use generative adversarial networks (GAN) to create perturbations. We further show that our method provides privacy guarantees under the Pufferfish framework, an elegant generalization of the differential privacy that allows for the modeling of prior knowledge on data and correlations. Through experiments, we show that our method outperforms conventional methods in effectively hiding the sensitive attributes while guaranteeing high performance in the target application, for both property inference and training purposes. Finally, we demonstrate through further experiments that once our model learns a privacy-preserving task, such as hiding subjects' identity, on a group of individuals, it can perform the same task on a separate group with minimal performance drops.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2024

Characterizing 4-string contact interaction using machine learning

Abstract The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry ofn-string contact interaction is feasible.

Physics↗
DOE OSTI2021

Integration of Dynamical System Scaling to RAVEN and Facility Application

As part of the design optimization and model validation effort within the hybrid energy systems program, the research to implement dynamical system scaling (DSS) code to RAVEN is funded under the Integrated Energy System program in collaboration with the Digital Reactor Technology & Development department. The DSS data processing algorithm has been coded within the RAVEN framework along with other metrics and postprocessing models. The implemented code was tested using a gravity-driven draining tank draining case modeled in RELAP5-3D and generated data was successfully postprocessed based on the scaling analyses defined by DSS. Postprocessed data concluded less agreement for the tank exit velocity and indicated that the modeled input deck for RELAP5-3D requires modification to enforce minimal pressure differential effects to the draining process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Dynamic calibration of differential equations using machine learning, with application to turbulence models

We present a methodology for calibration of parametric ordinary and partial differential equation models, using off-the-shelf software for back-propagation in Neural Networks (NN). As a prototypical example, we consider calibration of a Reynolds-averaged Navier-Stokes (RANS) turbulence closure model, against ground truth data from direct numerical simulations (DNS) of two different turbulent flows. Numerical time integration is represented as a custom NN, where only the RANS model parameters are trainable. A loss function is defined to quantify the mismatch between the NN prediction and the ground truth over a predefined, finite time integration window. This loss function is then minimized using a gradient descent method utilizing the back-propagation algorithm. Furthermore, this dynamic approach to training is to be contrasted with a static approach, wherein a least square regression estimate for parameters is obtained in the limit of an infinitesimal time integration window. In a first test of static and dynamic approaches against ground truth data generated by the model, the former proves to be significantly faster and more accurate than the latter at recovering the parameters. When both calibration approaches are tested against DNS data, for which it is known that the model cannot achieve a perfect fit, the static approach yields a good prediction only for short times, while the dynamic approach results in physical and stable predictions over the entire integration window. After optimization of the dynamic approach for time step, spatial resolution, stability, and physics-based constraints, we obtain a 50% improvement of outcomes over those obtained from the existing, manually calibrated set of parameters, demonstrating the merits of this systematic and automated procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reconstruction of beam parameters and betatron radiation spectra measured with a Compton spectrometer

The photon flux resulting from high-energy electron beam interactions with high-field systems, such as those found in the upcoming FACET-II experiments at the SLAC National Accelerator Laboratory, yields deep insight into the electron beam’s underlying dynamics during the interaction. However, extracting this information is an intricate process. To demonstrate how to approach this challenge using modern methods, this paper utilizes simulated data that models plasma wakefield acceleration-derived betatron radiation in experiments to determine reliable methods of reconstructing key beam and beam-plasma interaction properties. For betatron radiation measurements, translating the observed 200⁢ keV to 30⁢ MeV photon double-differential energy-angle spectra obtained from an advanced Compton spectrometer requires testing multiple methods to optimize the pipeline from its response to incident electron beam information. The paper compares maximum likelihood estimation and machine learning to refine the translation of photon spectra into precise electron beam metrics, such as spot size, energy, and emittance, enhancing the understanding of beam behavior within these dense, high-field environments. We also introduce machine learning and the expected maximization algorithm to reconstruct the primary photon spectrum, employing a multilayer neural network for regression analysis of the energy and angle spectra. With appropriate modifications, the advanced methods reproduce relevant incident beam parameters with high accuracy, even for beam sizes in the <10 μ⁢m range. This capacity is critical to understanding intense beam propagation and its optimization in plasma.

Beam code development & simulation techniques↗
DOE OSTI2023

Preliminary Development of Heat Transfer Model-Based Control Algorithms of Liquid Sodium Purification System: Advanced Sensors and Instrumentation Advanced Controls

Monitoring the operation of sodium purification system is essential for efficient operation of sodium fast reactors. In this work, a heat transfer model has been developed for monitoring the plugging meter and cold trap systems at the Mechanisms Engineering Test Loop (METL) liquid sodium facility at Argonne National Laboratory. The model of the purification system was developed by treating the respective aspects of the cold trap purification loop and plugging meter diagnostic loop as two separate control volumes using information from the METL piping and instrumentation diagram (P&ID). A model predictive controller was designed using first order differential equations with the specified boundary conditions. The system behavior was studied with a tuned optimized procedure using the internal cold trap temperature and plugging meter outlet temperature as control variables, and the air blower temperature as an independent variable respectively. Results of computer simulations obtained in this study compared favorably with experimental data showing very good reference tracking response with negligible overshoot as both plugging meter and cold trap physical models approach the setpoint.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Transformer Health Monitoring via Synchrophasors

Traditional transformer protection schemes such as differential protection operate once the transformer is in a critical state. Proactive means of transformer health evaluation such as Sweep Frequency Response Analysis, can only be performed periodically with the transformer out-of-service. This work presents a framework where the health and structural integrity of transformers is monitored via synchrophasors in real-time. Synchrophasors and subspace estimation techniques are used to build reduced-order models which are then analyzed across multiple domains. A diagnostics algorithm is developed and tested via Matlab simulations. Test results are promising, opening up new prospects in transformer protection research.

cyber-physical security↗
DOE OSTI2024

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Parallel hybrid quantum-classical machine learning for kernelized time-series classification

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. Here, in this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a timeseries Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Production of Λ and $K^{0}_{S}$ in jets in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV and pp collisions at $\sqrt{s}$ =7 TeV

The production of Λ baryons and $K^{0}_{S}$ mesons (V 0 particles) was measured in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV and pp collisions at $\sqrt{s}$ = 7 TeV with ALICE at the LHC. The production of these strange particles is studied separately for particles associated with hard scatterings and the underlying event to shed light on the baryon-to-meson ratio enhancement observed at intermediate transverse momentum (p T ) in high multiplicity pp and p–Pb collisions. Hard scatterings are selected on an event-by-event basis with jets reconstructed with the anti-k T algorithm using charged particles. The production of strange particles associated with jets $p^{ch}_{T,}$ jet > 10 and $p^{ch}_{T,}$ jet > 20 GeV/c in p–Pb collisions, and with jet $p^{ch}_{T,}$ jet > 10 GeV/c in pp collisions is reported as a function of p T . Its dependence on angular distance from the jet axis, R(V 0 , jet), for jets with $p^{ch}_{T,}$ jet > 10 GeV/c in p–Pb collisions is reported as well. The p T -differential production spectra of strange particles associated with jets are found to be harder compared to that in the underlying event and both differ from the inclusive measurements. In events containing a jet, the density of the V 0 particles in the underlying event is found to be larger than the density in the minimum bias events. The Λ/$K^{0}_{S}$ ratio associated with jets in p–Pb collisions is consistent with the ratio in pp collisions and follows the expectation of jets fragmenting in vacuum. On the other hand, this ratio within jets is consistently lower than the one obtained in the underlying event and it does not show the characteristic enhancement of baryons at intermediate p T often referred to as “baryon anomaly” in the inclusive measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Entropic control of the free-energy landscape of an archetypal biomolecular machine

Biomolecular machines are complex macromolecular assemblies that utilize thermal and chemical energy to perform essential, multistep, cellular processes. Despite possessing different architectures and functions, an essential feature of the mechanisms of action of all such machines is that they require dynamic rearrangements of structural components. Surprisingly, biomolecular machines generally possess only a limited set of such motions, suggesting that these dynamics must be repurposed to drive different mechanistic steps. Although ligands that interact with these machines are known to drive such repurposing, the physical and structural mechanisms through which ligands achieve this remain unknown. Using temperature-dependent, single-molecule measurements analyzed with a time-resolution-enhancing algorithm, here, we dissect the free-energy landscape of an archetypal biomolecular machine, the bacterial ribosome, to reveal how its dynamics are repurposed to drive distinct steps during ribosome-catalyzed protein synthesis. Specifically, we show that the free-energy landscape of the ribosome encompasses a network of allosterically coupled structural elements that coordinates the motions of these elements. Moreover, we reveal that ribosomal ligands which participate in disparate steps of the protein synthesis pathway repurpose this network by differentially modulating the structural flexibility of the ribosomal complex (i.e., the entropic component of the free-energy landscape). Here, we propose that such ligand-dependent entropic control of free-energy landscapes has evolved as a general strategy through which ligands may regulate the functions of all biomolecular machines. Such entropic control is therefore an important driver in the evolution of naturally occurring biomolecular machines and a critical consideration for the design of synthetic molecular machines.

Science & Technology - Other Topics↗
DOE OSTI2021

Universality class for loopless invasion percolation models and a percolation avalanche burst model for hydraulic fracturing

Invasion percolation is a model that was originally proposed to describe growing networks of fractures. In this work, we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic b-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing (“fracking”). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths l. But since the networks are characterized by their large-scale behavior, l << L, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.

58 GEOSCIENCES↗
DOE OSTI2025

Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗