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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Field Work Proposal ERKJ358: Black-box training for scientific machine learning models (Final Report)

The overarching goal of this project is to develop a scalable black-box training capability for scientific machine learning (SciML) problems that are non-trainable with existing automatic differentiation (AD)-based algorithms. AD assumes that a loss function can be decomposed into a sequence of elementary operations whose derivatives are known. This assumption is violated when the loss function includes a black-box physical model (e.g., a legacy simulator). The current strategy, converting a black-box simulator to an AD-enabled code via differential programming, is inflexible and time-, labor-consuming. Thus, black-box optimization is a main workhorse for training SciML models, e.g., in scientific reinforcement learning, hyper-parameter fine tuning, designing SciML models with adversarial robustness, etc.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the numerical algorithms of parametrization method for solving a two-point boundary-value problem for impulsive systems of loaded differential equations

A linear two-point boundary value problem for a system of loaded differential equations with impulse effect is investigated. Values in the previous impulse points are taken into consideration in the conditions of impulse effect. The considered problem is reduced to an equivalent multi-point boundary value problem for the system of ordinary differential equations with parameters. A numerical implementation of parametrization method is offered using the Runge–Kutta method of 4th-order accuracy for solving the Cauchy problems for ordinary differential equations. The constructed numerical algorithms are illustrated by examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Drive-pressure optimization in ramp-wave compression experiments through differential evolution

Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying nonequilibrium material behavior, such as solidification kinetics. In ramp-wave compression experiments, the input drive pressure to the experimental setup may be exerted through one of a number of different mechanisms (e.g., magnetic fields, gas-gun-driven impactors, or high-energy lasers) and is generally required for simulating such experiments. Yet, regardless of the specific mechanism, this drive pressure cannot be measured directly (measurements are generally taken at a location near the back of the experimental setup through a transparent window), leading to an inverse problem where one must determine the drive pressure at the front of the experimental setup (i.e., the input) that corresponds to the particle velocity (the output) measured near the back of the experimental setup. Furthermore, we solve this inverse problem using a heuristic optimization algorithm, known as differential evolution, coupled with a multiphysics, hydrodynamics code that simulates the compression of the experimental setup. By running many rounds of forward simulations of the experimental setup, our optimization process iteratively searches for a drive pressure that is optimized to closely reproduce the experimentally measured particle velocity near the back of the experimental setup. While our optimization methodology requires a significant number of hydrodynamics simulations to be conducted, many of these can be performed in parallel, which greatly reduces the time cost of our methodology. One novel aspect of our method for determining the drive pressure is that it does not require physical modeling of the drive mechanism and can thus be broadly applied to many types of ramp-compression experiments, regardless of the drive mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Explicit time integration of the stiff chemical Langevin equations using computational singular perturbation

A stable explicit time-scale splitting algorithm for stiff chemical Langevin equations (CLEs) is developed, based on the concept of computational singular perturbation. The drift term of the CLE is projected onto basis vectors that span the fast and slow subdomains. The corresponding fast modes exhaust quickly, in the mean sense, and the system state then evolves, with a mean drift controlled by slow modes, on a random manifold. The drift-driven time evolution of the state due to fast exhausted modes is modeled algebraically as an exponential decay process, while that due to slow drift modes and diffusional processes is integrated explicitly. This enables time integration step sizes much larger than those required by typical explicit numerical methods for stiff stochastic differential equations. The algorithm is motivated and reported on, and extensive numerical experiments are conducted to illustrate its accuracy and stability with a number of model systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Optimized principal component analysis on coronagraphic images of the fomalhaut system

We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing angular differential imaging and locally optimized combination of images (LOCI) for increasing the contrast achievable next to a bright star. The stellar point spread function (PSF) is constructed by removing linear combinations of principal components, allowing the flux from an extrasolar planet to shine through. The number of principal components used determines how well the stellar PSF is globally modeled. Using more principal components may decrease the number of speckles in the final image, but also increases the background noise. We apply PCA to Fomalhaut Very Large Telescope NaCo images acquired at 4.05 μm with an apodized phase plate. We do not detect any companions, with a model dependent upper mass limit of 13-18 M {sub Jup} from 4-10 AU. PCA achieves greater sensitivity than the LOCI algorithm for the Fomalhaut coronagraphic data by up to 1 mag. We make several adaptations to the PCA code and determine which of these prove the most effective at maximizing the signal-to-noise from a planet very close to its parent star. We demonstrate that optimizing the number of principal components used in PCA proves most effective for pulling out a planet signal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Temporal coarse-graining method to simulate the movement of atoms

We propose a novel method to simulate the movement of atoms at finite temperature. The main idea of our method is to derive “renormalized,” or coarse-grained in time, dynamics from the Euler–Maruyama scheme, which is the standard method for solving the stochastic differential equations numerically. Based on this renormalization, we propose a new algorithm for solving overdamped Langevin equations. We test our renormalization scheme on two models and demonstrate that the results obtained by this method are consistent with those obtained by the standard method. Our algorithm performs better than the standard scheme, especially at low temperatures and with multiple processors.

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 OSTI2025

Harnessing the power of gradient-based simulations for multi-objective optimization in particle accelerators

Abstract Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraints on energy requirements of the beam. Using historical accelerator data, we develop a physics-based surrogate model which is differentiable and allows for back-propagation of gradients. The results are evaluated in the form of a Pareto-front with two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Glass-like energy and property landscape of Pt nanoclusters

Pt nanoclusters play an important role in catalysis-related applications. Essential to their activities are their geometries and energy landscapes. In this work, we studied the energy landscapes of Pt clusters using a parallel differential evolution optimization algorithm and an accelerated ab initio atomic relaxation method, which allowed us to explore unprecedentedly large numbers of geometry local minima at ab initio level. We found many lower-energy isomers with low symmetry in their geometry. The energy landscapes were demonstrated to be glass-like with a large number of local minimum structures close to the global minimum. The electronic and magnetic properties of most glass-like local minima were dramatically different from the global minimum, and they should be observed in the experimental measurements. The connections between these local minima were further analyzed using data mining techniques.

Chen, Zhanghui↗
DOE OSTI2025

Differentiable lagrangian shock hydrodynamics with application to stable shock acceleration of density interfaces

We develop a gradient based optimization approach for the equations of compressible, Lagrangian hydrodynamics and demonstrate how it can be employed to automatically uncover strategies to control hydrodynamic instabilities arising from shock acceleration of density interfaces. Strategies for controlling the Richtmyer-Meshkov instability (RMI) are of great benefit for inertial confinement fusion (ICF) where shock interactions with many small imperfections in the density interface lead to instabilities which rapidly grow over time. These instabilities lead to mixing which, in the case of laser driven ICF, quenches the runaway fusion process ruining the potential for positive energy return. Here, we demonstrate that control of these instabilities can be achieved by optimization of initial conditions with ( > 100) parameters. Optimizing over a large parameter space like this is not possible with gradient-free optimization strategies. This requires computation of the gradient of the outputs of a numerical solution to the equations of Lagrangian hydrodynamics with respect to the inputs. We show that the efficient computation of these gradients is made possible via a judicious application of (i) adjoint methods, the exact formal representation of sensitivities involving partial differential equations, and (ii) automatic differentiation (AD), the algorithmic calculation of derivatives of functions. Careful regularization of multiple operators including artificial viscosity and timestep control is required. We perform design optimization of > 100 parameter energy field driving the Richtmyer Meshkov instability showing significant suppression while simultaneously enhancing the acceleration of the interface relative to a nominal baseline case.

Hydrophysics↗
DOE OSTI2025

Inferring fracture dilation and shear slip from surface deformation utilising trained surrogate models

An important task in energy and CO 2 storage (sequestration) in the subsurface is to verify that the surrounding fractures and faults are not activated, acting as leakage pathways. This is achievable through effective and efficient Measurement, Monitoring and Verification (MMV) plans. In this work, two surrogate models are trained to captures dilation (opening) and shear deformation of fractures, and the associated surface deformation. The trained surrogate model, based on conditional Generative-Adversarial Networks (cGAN) receives fracture apertures from dilational fractures together with fracture slips from shear fractures and predicts the combined surface deformation. An inversion algorithm based on Bayesian framework is proposed to identify the geometry of both types of fractures, as well as volume of dilational fractures and deformation moment induced by shear fractures, all from the measured surface deformation data. The inversion algorithm utilises the Differential Evolution (DE) optimisation technique that has the superior performance in finding the global minimum of cost function. The proposed surrogate-assisted inversion successfully inferred the unknown dip, dip direction and the volume of the dilational fractures as well as the induced deformation moment in shear fractures. The model was further tested for the inversion of a field hydraulic fracturing tilt dataset applying different scenarios with varying unknowns to show the model's performance, as well as incorporating shear deformation for better match with the observed data.

Dilation and shear↗
DOE OSTI2014

Modeling self-subtraction in angular differential imaging: Application to the HD 32297 debris disk

We present a new technique for forward-modeling self-subtraction of spatially extended emission in observations processed with angular differential imaging (ADI) algorithms. High-contrast direct imaging of circumstellar disks is limited by quasi-static speckle noise, and ADI is commonly used to suppress those speckles. However, the application of ADI can result in self-subtraction of the disk signal due to the disk's finite spatial extent. This signal attenuation varies with radial separation and biases measurements of the disk's surface brightness, thereby compromising inferences regarding the physical processes responsible for the dust distribution. To compensate for this attenuation, we forward model the disk structure and compute the form of the self-subtraction function at each separation. As a proof of concept, we apply our method to 1.6 and 2.2 μm Keck adaptive optics NIRC2 scattered-light observations of the HD 32297 debris disk reduced using a variant of the 'locally optimized combination of images' algorithm. We are able to recover disk surface brightness that was otherwise lost to self-subtraction and produce simplified models of the brightness distribution as it appears with and without self-subtraction. From the latter models, we extract radial profiles for the disk's brightness, width, midplane position, and color that are unbiased by self-subtraction. Our analysis of these measurements indicates a break in the brightness profile power law at r ≈ 110 AU and a disk width that increases with separation from the star. We also verify disk curvature that displaces the midplane by up to 30 AU toward the northwest relative to a straight fiducial midplane.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Measurements of the suppression and correlations of dijets in Xe+Xe collisions at $\sqrt{s{NN}}$ = 5.44 TeV

Measurements of the suppression and correlations of dijets is performed using 3 µb –1 of Xe+Xe data at $\sqrt{s{NN}}$ = 5.44 TeV collected with the ATLAS detector at the CERN Large Hadron Collider. Dijets with jets reconstructed using the R = 0.4 anti- k t algorithm are measured differentially in jet p T over the range of 32 to 398 GeV and the centrality of the collisions. Significant dijet momentum imbalance is found in the most central Xe+Xe collisions, which decreases in more peripheral collisions. Results from the measurement of per-pair normalized and absolutely normalized dijet p T balance are compared with previous Pb + Pb measurements at $\sqrt{s{NN}}$ = 5.02 TeV. The differences between the dijet suppression in Xe+Xe and Pb + Pb are further quantified by the ratio of pair nuclear-modification factors. The results are found to be consistent with those measured in Pb + Pb data when compared in classes of the same event activity and when taking into account the difference between the center-of-mass energies of the initial parton scattering process in Xe+Xe and Pb + Pb collisions. These results should provide input for a better understanding of the role of energy density, system size, path length, and fluctuations in the parton energy loss.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Seasonal Reconfiguration of Electrical Distribution Systems to Mitigate the Impact of Electric Vehicle Charging

Power grids face challenges in their infrastructure related to the integration of electric vehicles (EV). In particular, EV charging stations may induce instability in key system parameters such as substantial voltage drops, active power losses, and transformer overload due to high demand during charging periods. This article presents a seasonal reconfiguration strategy based on the differential evolution (DE) algorithm, aimed at enhancing system performance under highly variable and stochastic load profiles, particularly those driven by EV charging. The DEA algorithm is hybridized with the find-union (FU) algorithm to efficiently ensure network radiality throughout the optimization process. The proposed methodology is validated on a hybrid distribution system composed of the IEEE 33-bus network, a modified IEEE 13-bus system, and a specific 13-bus microgrid. Results have demonstrated that seasonal reconfiguration significantly reduces active power losses and mitigates transformer loading during critical demand hours, thereby quantifiably increasing the system’s performance. As an integral component of the proposed approach, an analysis of CO2 emissions associated with energy losses is included, allowing a contextualized assessment of the environmental benefits of seasonal reconfiguration in various geographical areas.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system’s radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. Furthermore, the DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2020

Whole cell simulator

A whole cell model (WCM) is a comprehensive multi-scale computational model representing all the known biochemical processes in a cell. It relies on a variety of intracellular pathway models and omics data. This computational framework enables seamless integration of diverse simulation methods used in WCM such as stochastic simulation algorithm (SSA), ordinary differential equations (ODE), flux balance analysis (FBA), and logic-based approaches. These methods run simultaneously, not only for whole pathways but also for subsets of reactions. Furthermore, we aim to enable dynamic switching between the methods when beneficial. Is

GEORGAKOUDIS, GIORGIS↗
DOE OSTI2021

Multi-Energy Differential Evolution Reconstruction (MEnDER 1D) for Proton Deflectometry

This code is designed to reconstruct magnetic field deflections, and thus the path-integrated magnetic field, from sets of proton images at two distinct proton probe energies. A differential evolution (DE) algorithm is used to iteratively update a population of solution candidates of the magnetic deflections of the protons for reconstructing the input images, selecting improved candidates as they are discovered. This algorithm was written using MATLAB (R2019a) and makes use of the Image Processing and Parallel Processing Toolboxes.

Levesque, Joseph↗