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Results for “Adaptive moment estimation”

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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15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗
DOE OSTI2020

Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

This study proposes an automated calibration procedure for bond parameters in bonded discrete element modelling. By exploring the underlying physical correlations between microscopic parameters of bonds and macroscopic strength parameters of the continuum to be modelled, the microscopic shear strength and tensile strength are identified as independent variables for calibration purpose. Then a physics-informed iterative scheme is proposed to automatically approximate the bond parameters by viewing the micro-macro relation as an implicitly defined mathematical mapping function. As a result of highly non-convex features of this implicit mapping, the adaptive moment estimation (Adam), which is especially suitable for problems with noisy gradients, is adopted as the basic iterative scheme, in conjunction with other numerical techniques to approximately evaluate the partial derivatives involved. The whole procedure offers a simple and effective framework for bond parameter calibration. Finally, a numerical example of SiC ceramic is provided for validation. By compared with some existing calibration methods, the proposed method shows significant advantages in terms of calibration efficiency and accuracy.

42 ENGINEERING↗
DOE OSTI2025

Fast-RF-Shimming: Accelerate RF shimming in 7T MRI using deep learning

Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) offers an elevated signal-to-noise ratio (SNR), enabling exceptionally high spatial resolution that benefits both clinical diagnostics and advanced research. However, the jump to higher fields introduces complications, particularly transmit radiofrequency (RF) field ($B^{+}_{1}$) inhomogeneities, manifesting as uneven flip angles and image intensity irregularities. These artifacts can degrade image quality and impede broader clinical adoption. Traditional RF shimming methods, such as Magnitude Least Squares (MLS) optimization, effectively mitigate $B^{+}_{1}$ inhomogeneity, but remain time-consuming. Recent machine learning approaches, including RF Shim Prediction by Iteratively Projected Ridge Regression and other deep learning architectures, suggest alternative pathways. Although these approaches show promise, challenges such as extensive training periods, limited network complexity, and practical data requirements persist. In this paper, we introduce a holistic learning-based framework called Fast-RF-Shimming, which achieves a 5000 ​× ​speed-up compared to the traditional MLS method. In the initial phase, we employ random-initialized Adaptive Moment Estimation (Adam) to derive the desired reference shimming weights from multi-channel $B^{+}_{1}$ fields. Next, we train a Residual Network (ResNet) to map $B^{+}_{1}$ fields directly to the ultimate RF shimming outputs, incorporating the confidence parameter into its loss function. Finally, we design Non-uniformity Field Detector (NFD), an optional post-processing step, to ensure the extreme non-uniform outcomes are identified. Comparative evaluations with standard MLS optimization underscore notable gains in both processing speed and predictive accuracy, which indicates that our technique shows a promising solution for addressing persistent inhomogeneity challenges.

Deep learning↗
DOE OSTI2025

Optimizing transmit field inhomogeneity of parallel RF transmit design in 7T MRI using deep learning

Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) provides a higher signal-to-noise ratio and, thereby, higher spatial resolution. However, UHF MRI introduces challenges such as transmit radiofrequency (RF) field (B+1) inhomogeneities, leading to uneven flip angles and image intensity anomalies. These issues can significantly degrade imaging quality and its medical applications. This study addresses B+1 field homogeneity through a novel deep learning-based strategy. Traditional methods like Magnitude Least Squares (MLS) optimization have been effective but are time-consuming and dependent on the patient’s presence. Recent machine learning approaches, such as RF Shim Prediction by Iteratively Projected Ridge Regression and deep learning frameworks, have shown promise but face limitations like extensive training times and oversimplified architectures. We propose a two-step deep learning strategy. First, we obtain the desired reference RF shimming weights from multi-channel B+1 fields using random-initialized Adaptive Moment Estimation. Then, we employ Residual Networks (ResNets) to train a model that maps B+1 fields to target RF shimming outputs. Our approach does not rely on pre-calculated reference optimizations for the testing process and efficiently learns residual functions. Comparative studies with traditional MLS optimization demonstrate our method’s advantages in terms of speed and accuracy. The proposed strategy achieves a faster and more efficient RF shimming design, significantly improving imaging quality at UHF. This advancement holds potential for broader applications in medical imaging and diagnostics.

Lu, Zhengyi [Vanderbilt University]↗
DOE OSTI2022

A Method of Moments Wide Band Adaptive Rational Interpolation Method for High-Quality Factor Resonant Cavities

A new adaptive rational interpolation method is proposed to obtain the wideband frequency response of a resonant cavity simulated with the method of moments (MoM). This interpolation method uses both the Loewner matrix to construct a rational expression for the solution vector of MoM’s matrix system and an error estimator generated by the solution vectors and their derivatives. This error estimator is implemented in the adaptive procedure to gain a minimum set of frequencies and solution vectors required in the interpolation. The resulting set of frequencies and solution vectors is applied to interpolate other system variables, such as shielding effectiveness and input impedance. Here numerical results of a slotted cylindrical cavity supporting high-quality factor resonances are presented, showing that the new rational interpolation method is accurate and efficient in interpolating the complicated resonant response of the solution vector functions.

42 ENGINEERING↗
DOE OSTI2025

Moment-based adaptive time integration for thermal radiation transport

Here, in this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Improving the accuracy and efficiency of quantum connected moments expansions

The still-maturing noisy intermediate-scale quantum technology faces strict limitations on the algorithms that can be implemented efficiently. In the realm of quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become ubiquitous, with many variations. Alternatively, a promising new avenue has been unraveled by the quantum variants of techniques grounded on expansions of the moments of the Hamiltonian, notably the connected moments expansion (CMX) and the Peeters–Devreese–Soldatov (PDS) energy functional. Common to those approaches is that, upon preparing an approximate ground state used to compute the necessary moments, the accuracy of the estimated ground state energy depends on the degree of overlap between the prepared state and the true ground state. Thus, we use the ADAPT-VQE algorithm to test shallow circuit construction strategies for the purpose of increasing the overlap with the exact ground state, validated by the sizable accuracy improvement herein reported in the PDS and CMX ground state energies. We also show that we can take advantage of the fact that the terms to be measured are highly recurring in different moments, incurring a substantial reduction in the number of necessary measurements. Finally, by coupling this measurement caching with a threshold that determines whether a given term is to be measured based on its associated scalar coefficient, we observe a further reduction in the number of circuit implementations while allowing for tunable accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks

The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums.

Moya, Christian↗
DOE OSTI2024

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6 Li and 12 C using the ab initio symmetry-adapted no-core–shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3%–6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

ab initio↗
DOE OSTI2024

Adapting CLUTCH methodology to multigroup TSUNAMI-3D for eigenvalue sensitivity calculations

The sensitivity of the eigenvalue to uncertainties in nuclear data and its evaluation are important for nuclear criticality safety. TSUNAMI-3D sequences within the SCALE code system offer several options to the user community for calculating eigenvalue sensitivity coefficients with multigroup (MG) and continuous energy (CE) 3D transport capabilities. TSUNAMI-3D sequences implement the adjoint-based perturbation theory with MG KENO code, the Contributon Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method with CE KENO code, and the Iterated Fission Probability (IFP) method with CE KENO and Shift codes. Each method has benefits and limitations depending on the problem that is run. The work presented here aims to adapt the CLUTCH method, which enables the Contributon method's mesh-free, memory-efficient approach for calculating adjoint-weighted tallies for sensitivity calculations, to the MG TSUNAMI-3D sequence. This application would eliminate the explicit adjoint KENO calculation, as well as the memory-consuming mesh flux moment tallies required by the conventional MG TSUNAMI-3D. Smaller memory footprints in the CLUTCH methodology and relatively shorter runtimes in MG KENO transport can make MG TSUNAMI-3D a viable method for some complex problems. Moreover, this adaptation allows MG sensitivity calculations with Shift, ORNL's next-generation high-performance Monte Carlo transport code, which currently does not offer any sensitivity capabilities with MG particle transport simulations. Initial implementation of the new MG TSUNAMI-3D sequence and its preliminary results with a selected critical benchmark experiment in the Verified, Archived Library of Inputs and Data (VALID) are presented in this study.

KENO↗
DOE OSTI2020

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

We use a conditional Karhunen-Lo` eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, Y (x). We assume that a small number of Y (x) measurements are available and model Y (x) with a KL expansion. We achieve reduction in uncertainty by conditioning the KL expansion coefficients on measurements. We consider two approaches for conditioning the KL expansion: In Approach 1, we condition the KL model first and then truncate it. In Approach 2, we first truncate the KL expansion and then condition it. We employ the conditional KL expansion together with Monte Carlo and sparse grid collocation methods to compute the moments of the solution of the SPDE problem. Uncertainty of the problem is further reduced by adaptively selecting additional observation locations using two active learning methods. Method 1 minimizes the variance of the PDE coefficient, while Method 2 minimizes the variance of the solution of the PDE. We demonstrate that conditioning leads to dimension reduction of the KL representation of Y (x). For a linear diffusion SPDE with uncertain log-normal coefficient, we show that Approach 1 provides a more accurate approximation of the conditional log-normal coefficient and solution of the SPDE than Approach 2 for the same number of random dimensions in a conditional KL expansion. Furthermore, Approach 2 provides a good estimate for the number of terms of the truncated KL expansion of the conditional field of Approach 1. Finally, we demonstrate that active learning based on Method 2 is more efficient for uncertainty reduction in the SPDE’s states (i.e., it leads to a larger reduction of the variance) than active learning using Method 2.

Conditioned Karhunen-Lo` eve expanion, machine lea↗
DOE OSTI2020

Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles

The molecular dipole moment ( μ ) is a central quantity in chemistry. It is essential in predicting infrared and sum-frequency generation spectra as well as induction and long-range electrostatic interactions. Furthermore, it can be extracted directly—via the ground state electron density—from high-level quantum mechanical calculations, making it an ideal target for machine learning (ML). Here, we choose to represent this quantity with a physically inspired ML model that captures two distinct physical effects: local atomic polarization is captured within the symmetry-adapted Gaussian process regression framework which assigns a (vector) dipole moment to each atom, while the movement of charge across the entire molecule is captured by assigning a partial (scalar) charge to each atom. The resulting “MuML” models are fitted together to reproduce molecular μ computed using high-level coupled-cluster theory and density functional theory (DFT) on the QM7b dataset, achieving more accurate results due to the physics-based combination of these complementary terms. The combined model shows excellent transferability when applied to a showcase dataset of larger and more complex molecules, approaching the accuracy of DFT at a small fraction of the computational cost. We also demonstrate that the uncertainty in the predictions can be estimated reliably using a calibrated committee model. The ultimate performance of the models—and the optimal weighting of their combination—depends, however, on the details of the system at hand, with the scalar model being clearly superior when describing large molecules whose dipole is almost entirely generated by charge separation. These observations point to the importance of simultaneously accounting for the local and non-local effects that contribute to μ ; furthermore, they define a challenging task to benchmark future models, particularly those aimed at the description of condensed phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. Finally, we propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Edgewise Structural Damping of a 2.8-MW Land-Based Wind Turbine Rotor Blade

Modern wind turbines push the predictive capabilities of state-of-the-art aero-servo-elastic tools. The existing limitations hide across the numerical tool chain and can result in serious issues, such as missing aeroelastic instabilities during the design phase. Structural damping is an input that is usually hard to estimate, but also has a major impact on the turbine behavior. In this paper, we discuss an experiment that aims to accurately quantify the structural damping characterizing the edgewise modes of modern wind turbine blades. The experiment is carried out on a 2.8-MW land-based wind turbine and features a fast yaw actuation that induces an edgewise motion on one of the three blades. The Covariant-subspace system identification (Cov-SSI) method is then used to post-process the blade root moment to estimate the short-term edgewise structural damping. Despite limitations of the Cov-SSI method, which consistently under-predicts the absolute values of damping, we observe that structural damping decreases across the first three blade edgewise modes, which is different from the stiffness-proportional damping model that assumes that structural damping increases with the modes. This paper argues that a stiffness-proportional damping model, which is implemented in most aeroelastic tools, is therefore not conservative and might hide aeroelastic instabilities that can instead appear in the field.

17 WIND ENERGY↗
DOE OSTI2020

Development of neural network force fields for corrosion studies

To fully understand the chemistry and physics of corrosion, novel methods of simulation must be developed. One approach is designing machine learning (ML) algorithms integrated with density functional theory to develop adaptive force fields to gain insight into corrosion behavior namely at the surface of metal oxides. Current methods of modeling corrosion are slow due to the computational cost of resolving both reaction mechanics and mass transport processes. Machine learning methods can be implemented to obtain structure-activity relationships at both the molecular and bulk scale while still retaining the accuracy of density functional theory (DFT) and significantly decreasing the time needed for simulations of complex chemical processes in the various environments of corrosion. Multiscale models are needed for corrosion studies to fully understand its processes not only at the atomic length scale (chemical bonding, energies, and forces), but also at the nano and meso length scales (solid-state physics and material science processes). Current methods of study include DFT, molecular dynamics, and Monte Carlo. The limitation of DFT is that only a small number of atoms or molecules can be simulated at that level of theory. Density functional theory is used to study the electronic structure of atoms and molecules, and calculate the force component of each atom. However, these calculations are limited to about 1000 atoms. Custom periodic boundary conditions (PBC) can be used to describe the various environments and defects that affect the atomic forces to produce a large data set from which a training set can be derived. Machine learning can be utilized to overcome the barrier of modeling macroscopic and multi-scale processes from ab initio calculations through the development of adaptive force fields. Local environments determine the atomic forces of a given system, therefore adaptive force fields must be created to produce reliable quantum mechanical calculations. This can be achieved by developing a learning algorithm that uses the mapped atomic forces or fingerprint as an input to produce energies and magnetic moments as output. A systematic approach was used to begin to build a data set in order to accurately describe the atomic forces in various environments. In Figure 4 below, a simple PBC cell of Fe{sub 2}O{sub 3} was first optimized. A surface optimization was performed next, followed by a hydroxylated surface optimization. Once this calculation has converged, the adsorption of halide species to the hydroxylated surface will be investigated. TensorFlow is an open source platform for machine learning developed by Google. Using a high level application program interface (API) such as Keras allows for building and training ML models easily in a number of different environments and languages. For this project, a neural network was developed within Anaconda in Python. Future Work: Further development of reference data set; Refining neural network and learning algorithm; Fingerprinting atomic environment to enable mapping of atomic force components; Choosing appropriate training set from reference data; Learning from training set and enabling non-linear mapping of training set fingerprints and the atomic forces; Estimation of uncertainty to identify ranges of outside applicability; Testing and analysis of molecular dynamic simulations.

36 MATERIALS SCIENCE↗