Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “gradient methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Healing Gradient Degradation in Nb3Sn SRF Cavities Using a Recoating Method

Despite having advantageous superconducting properties, Nb3Sn superconducting radiofrequency (SRF) cavities still have practical challenges compared to Nb SRF cavities due to the brittle nature of Nb3Sn. Performance degradation can occur when a Nb3Sn SRF cavity experiences mechanical stresses such as during handling and tuning of the cavity. In this study, we present a potential treatment for SRF cavities that have experienced stress induced performance degradation that involves a recoating procedure. The degraded cavity is coated with a small amount of Sn using a single step vapor-diffusion methodology. Using this approach we can recover a significant portion of the lost performance of a Nb3Sn SRF cavity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms

We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a “powder-averaged” emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues. Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter. Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation. This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Density functional based methods for light harvesting molecules

The goal of the proposal was to computationally study the photoinduced charge transfer excited states of organic molecules. The systems of interest are the large organic supramolecules that have potential for photovoltaic applications. The simulation of the charge transfer excited states in large supramolecular assemblies require quantum mechanical methods that can be applied to systems with hundreds of atoms. Through this project we have implemented a perturbative delta-self-consistent field method that can easily describe the charge transfer excited states with regular density functionals without range separation. The cost of the calculations of an excited state is similar to that of the ground state. The method also allows for calculation of the energy gradients of the excited state. The developed method was applied to study a number of different supramolecular systems containing hundreds of atoms with excellent agreement with experiment. The absorption characteristics and the influence of density functional approximations were also examined. These led to several studies on the variety of organic electron donor and acceptor molecules. Apart from these developments through this project we also improved the code capabilities by implementing new meta-GGA functionals. This was a major step since the code is purely density functional and earlier the functional capabilities were limited only to generalized gradient approximations. A total of 23 peer-reviewed publications in top chemical physics journals resulted from this grant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance

The ability of neural networks to provide ‘best in class’ approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train (choose) the parameters defining the network. In general, neural networks are trained by gradient descent type optimization methods,a stochastic variant thereof. In practice, such methods result in the loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down. The loss may even appear to stagnate over the period of a large number of epochs, only to then suddenly start to decrease fast again for no apparent reason. This so-called plateau phenomenon manifests itself in many learning tasks. The present work aims to identify and quantify the root causes of plateau phenomenon.analysis is carried out in the setting of univariate ReLU networks. No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes. Here, the main findings are: plateaux correspond to periods during which activation patterns remain constant, where activation pattern refers to the number of data points that activate a given neuron; quantification of convergence of the gradient flow dynamics; and, characterization stationary points in terms solutions of local least squares regression lines over subsets of the training data. Based on these conclusions, we propose a new iterative training method, the Active Neuron Least Squares (ANLS), characterised by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau. Illustrative numerical examples are included throughout.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Deep probabilistic direction prediction in 3D with applications to directional dark matter detectors

Abstract We present the first method to probabilistically predict 3D direction in a deep neural network model. The probabilistic predictions are modeled as a heteroscedastic von Mises-Fisher distribution on the sphere S 2 , giving a simple way to quantify aleatoric uncertainty. This approach generalizes the cosine distance loss which is a special case of our loss function when the uncertainty is assumed to be uniform across samples. We develop approximations required to make the likelihood function and gradient calculations stable. The method is applied to the task of predicting the 3D directions of electrons, the most complex signal in a class of experimental particle physics detectors designed to demonstrate the particle nature of dark matter and study solar neutrinos. Using simulated Monte Carlo data, the initial direction of recoiling electrons is inferred from their tortuous trajectories, as captured by the 3D detectors. For 40 keV electrons in a 70% He 30% CO 2 gas mixture at STP, the new approach achieves a mean cosine distance of 0.104 (26 ∘ ) compared to 0.556 (64 ∘ ) achieved by a non-machine learning algorithm. We show that the model is well-calibrated and accuracy can be increased further by removing samples with high predicted uncertainty. This advancement in probabilistic 3D directional learning could increase the sensitivity of directional dark matter detectors.

Computer Science↗
DOE OSTI2026

Gradient Flow for Parton Distribution Functions: First Application to the Pion

Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides ⟨𝑥⟩, face severe challenges from reduced hypercubic symmetry, limiting results to the lowest moments. A recently proposed method resolves these issues using gradient flow. We demonstrate the efficacy of this method by computing ratios of flavor nonsinglet pion PDF moments up to ⟨𝑥 5 ⟩ on four lattice spacings at 𝑚 𝜋 ≃ 411 MeV. The moments and reconstructed PDF agree quantitatively with recent phenomenological extractions.

Francis, Anthony [National Yang Ming Chiao Tung Un↗
DOE OSTI2020

An adaptive discontinuous Petrov-Galerkin method for the Grad-Shafranov equation

In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov--Galerkin (DPG) method for the nonlinear Grad--Shafranov equation. An ultraweak formulation of the DPG scheme for the equation is given based on a minimal residual method. The DPG scheme has the advantage of providing more accurate gradients compared to conventional finite element methods, which is desired for numerical solutions to the Grad--Shafranov equation. The numerical scheme is augmented with an adaptive mesh refinement approach, and a criterion based on the residual norm in the minimal residual method is developed to achieve dynamic refinement. Nonlinear solvers for the resulting system are explored and a Picard iteration with Anderson acceleration is found to be efficient to solve the system. Finally, the proposed algorithm is implemented in parallel on MFEM using a domain-decomposition approach, and our implementation is general, supporting arbitrary order of accuracy and general meshes. Furthermore, numerical results are presented to demonstrate the efficiency and accuracy of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Enhancing Multi-Step Reservoir Inflow Forecasting: A Time-Variant Encoder–Decoder Approach

Accurate reservoir inflow forecasting is vital for effective water resource management. Reliable forecasts enable operators to optimize storage and release strategies to meet competing sectoral demands—such as water supply, irrigation, and hydropower scheduling—while also mitigating flood and drought risks. To address this need, in this study, we propose a novel time-variant encoder–decoder (ED) model designed specifically to improve multi-step reservoir inflow forecasting, enabling accurate predictions of reservoir inflows up to seven days ahead. Unlike conventional ED-LSTM and recursive ED-LSTM models, which use fixed encoder parameters or recursively propagate predictions, our model incorporates an adaptive encoder structure that dynamically adjusts to evolving conditions at each forecast horizon. Additionally, we introduce the Expected Baseline Integrated Gradients (EB-IGs) method for variable importance analysis, enhancing interpretability of inflow by incorporating multiple baselines to capture a broader range of hydrometeorological conditions. The proposed methods are demonstrated at several diverse reservoirs across the United States. Our results show that they outperform traditional methods, particularly at longer lead times, while also offering insights into the key drivers of inflow forecasting. These advancements contribute to enhanced reservoir management through improved forecasting accuracy and practical decision-making insights under complex hydroclimatic conditions.

58 GEOSCIENCES↗
DOE OSTI2026

Thermal Gradient Effects on Redox Evolution and Volatility-Driven Fractionation in Ternary U/Ce/Cs Condensates

Understanding how thermal history influences redox evolution and chemical fractionation is essential for characterizing high-temperature condensation in complex materials, including nuclear debris. Here, we tested the hypothesis that distinct thermal regimes in a plasma flow reactor influence redox pathways and elemental partitioning in ternary U/Ce/Cs systems. A configurable plasma flow reactor was modified with an external tube furnace to impose two distinct thermal gradients: continuous ambient cooling and a furnace-assisted thermal hold-up near 1400 K followed by rapid cooling. Transmission electron microscopy characterized phase identity, morphology, and nanoscale element distributions, while inductively coupled plasma-mass spectrometry quantified bulk elemental ratios. Across both thermal regimes, uranium and cerium condensed as UO 2 and CeO 2 as dominant refractory oxide products. Uranium partially oxidized to α-UO 3 during extended ambient cooling, while furnace-assisted hold-up preserved UO 2 and produced partial reduction of cerium to Ce 2 O 3 . Cesium remained volatile upstream and condensed later in the reactor, forming Cs 2 O and Cs-uranate phases with the highest incorporation after thermal hold-up. Bulk ICP-MS measurements supported these observations. U/Ce ratios remained comparatively stable and Cs displayed delayed and apparent transient enrichment that matched the nanoscale measurements. This integrated approach provides a quantitative method for linking thermal gradients to redox evolution and volatility-driven fractionation. These results show how the plasma flow reactor can identify where equilibrium descriptions remain adequate and where kinetic effects from residence time and temperature history must be considered when interpreting condensation behavior in multicomponent systems.

and nuclear chemistry↗
DOE OSTI2022

A simplified, efficient approach to hybrid wind and solar plant site optimization

Abstract. Wind plant layout optimization is a difficult, complex problem with a large number of variables and many local minima. Layout optimization only becomes more difficult with the addition of solar generation. In this paper, we propose a parameterized approach to wind and solar hybrid power plant layout optimization that greatly reduces problem dimensionality while guaranteeing that the generated layouts have a desirable regular structure. Thus far, hybrid power plant optimization research has focused on system sizing. We go beyond sizing and present a practical approach to optimizing the physical layout of a wind–solar hybrid power plant. We argue that the evolution strategy class of derivative-free optimization methods is well-suited to the parameterized hybrid layout problem, and we demonstrate how hard layout constraints (e.g., placement restrictions) can be transformed into soft constraints that are amenable to optimization using evolution strategies. Next, we present experimental results on four test sites, demonstrating the viability, reliability, and effectiveness of the parameterized evolution strategy approach for generating optimized hybrid plant layouts. Completing the tool kit for parameterized layout generation, we include a brief tutorial describing how the parameterized evolutionary approach can be inspected, understood, and debugged when applied to hybrid plant layouts.

14 SOLAR ENERGY↗
DOE OSTI2021

Navigator function for the conformal bootstrap

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Analytical gradients for molecular-orbital-based machine learning

We report molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

One‐Step Thermal Gradient‐ and Antisolvent‐Free Crystallization of All‐Inorganic Perovskites for Highly Efficient and Thermally Stable Solar Cells

Abstract All‐inorganic perovskites have emerged as promising photovoltaic materials due to their superior thermal stability compared to their heat‐sensitive hybrid organic–inorganic counterparts. In particular, CsPbI 2 Br shows the highest potential for developing thermally‐stable perovskite solar cells (PSCs) among all‐inorganic compositions. However, controlling the crystallinity and morphology of all‐inorganic compositions is a significant challenge. Here, a simple, thermal gradient‐ and antisolvent‐free method is reported to control the crystallization of CsPbI 2 Br films. Optical in situ characterization is used to investigate the dynamic film formation during spin‐coating and annealing to understand and optimize the evolving film properties. This leads to high‐quality perovskite films with micrometer‐scale grain sizes with a noteworthy performance of 17% (≈16% stabilized), fill factor (FF) of 80.5%, and open‐circuit voltage ( V OC ) of 1.27 V. Moreover, excellent phase and thermal stability are demonstrated even after extreme thermal stressing at 300 °C.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Analytically differentiable metrics for phase stability

Here, in this work, a long-established but sparsely documented method of obtaining semi-analytic derivatives of thermodynamic properties with respect to equilibrium conditions is briefly reviewed and rigorously derived. This procedure is then leveraged to construct general forms of derivatives of the residual driving force, a metric for measuring phase stability used in CALPHAD model optimization, with respect to overall system and individual phase compositions. Applied examples – calculating heat capacity in the Al-Fe system, thermodynamic factors in the Nb-V-W system, and residual driving force derivatives in the Ni-Ti system – demonstrate the versatility, accuracy, and extensibility of this method. Using the developed method, residual driving force gradients can be applied directly in CALPHAD model optimizers, as well as in materials design frameworks, to identify regions of phase stability with an efficient, gradient-based approach.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Visualizing electrode assembly movement and lithiation heterogeneity in lithium-metal batteries using operando energy dispersive X-ray diffraction

There is renewed interest in Li-metal anodes in order to increase the energy density of battery cells. Here, we demonstrate an operando X-ray crystallography method to visualize lithiation gradients and electrode assembly movement during electrochemical cycling of a Li-metal cell containing a Ni-Mn-Co layered oxide cathode (NMC811). During charge, deposition of Li + ions from the cathode increases the Li foil thickness; during discharge, the thickness decreases as Li + ions are stripped off the foil. Additionally, the resulting periodic movement is observed through tracking of Bragg peaks from the ordered phases of the cathode and separator. In addition to this 3.6 μm/mAh displacement, continuous mossy Li build-up on the anode causes an irreversible drift of the assembly, which is similar to 11.3 μm/cycle. Furthermore, our data indicate significant lithiation gradients in the NMC811 cathode during the oxide relithiation, which is not observed during the delithiation.

25 ENERGY STORAGE↗