Search NASA⌕ Search

SEARCH · Search NASA

Results for “variational method”

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 343 records · Page 19

Fractal analysis for assessing the level of modulation of IMRT fields

Purpose: To investigate the potential of three fractal dimension (FD) analysis methods (i.e., the variation, power spectrum, and variogram methods) as metrics for quantifying the degree of modulation in planned intensity modulated radiation therapy (IMRT) treatment fields, and compare the most suitable FD method to the number of monitor units (MUs), the average leaf gap, and the 2D modulation index (2D MI) for assessing modulation. Methods: The authors implemented, validated, and compared the variation, power spectrum, and variogram methods for computing the FD. Validation of the methods was done using mathematical fractional Brownian surfaces of known FD that ranged in size from 128 x 128 to 512 x 512. The authors used a test set consisting of seven head and neck carcinoma plans (50 prescribed treatment fields) to choose an FD cut-point that ensures no false positives (100% specificity) in distinguishing between moderate and high degrees of field modulation. The degree of field modulation was controlled by adjusting the fluence smoothing parameters in the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA). The moderate modulation fields were representative of the degree of modulation used clinically at the authors' institution. The authors performed IMRT quality assurance (QA) on the 50 test fields using the MapCHECK device. The FD cut-point was applied to a validation set consisting of four head and neck plans (28 fields). The area under the curve (AUC) from receiver operating characteristic (ROC) analysis was used to compare the ability of FD, number of MUs, average leaf gap, and the 2D MI for distinguishing between the moderate and high modulation fields. Results: The authors found the variogram FD method to be the most suitable for assessing the modulation complexity of IMRT fields for head and neck carcinomas. Pass rates as measured by the gamma criterion for the MapCHECK IMRT field measurements were higher for the moderately modulated fields, and a gamma criterion with 1 mm distance-to-agreement and 1% dose difference showed a clear separation between the 94% pass rates of the moderate and high modulation groups. From the ROC analysis of the test set, the authors found the AUC of the variogram FD, number of MUs, average leaf gap, and 2D MI methods to be 0.99 (almost perfect), 0.91 (excellent), 0.91 (excellent), and 0.92 (excellent), respectively. A cut-point of FD > 2.25 correctly identified 92.8% of the high modulation fields and 100% of the moderately modulated fields in the validation set, satisfying the condition of no false positives. Conclusions: Of the three FD methods investigated, the variogram method is the most accurate and precise metric for identifying high modulation treatment fields. It is also more accurate and precise than the number of MUs, the average leaf gap, and the 2D MI. Although MapCHECK IMRT QA does a reasonable job at identifying high modulation fields, the variogram FD method provides one with the opportunity to quantitatively and accurately assess modulation and adjust overly modulated fields at the treatment planning stage before they are sent to the treatment machine for QA or patient treatment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Communication: Variation after response in quantum Monte Carlo

We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing coupled cluster’s accuracy for excitations with significant doubly excited character.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas

Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidences suggest that magnetized plasmas of this type are collisionless and can persist for long times (e.g., with respect to a distant observer, coordinate, time), while exhibiting geometrical structures characterized by the absence of well-defined spatial symmetries. In this paper, the problem is posed whether such configurations can correspond to some kind of kinetic equilibrium. The issue is addressed from a theoretical perspective in the framework of a covariant Vlasov statistical description, which relies on the method of invariants. For this purpose, a systematic covariant variational formulation of gyrokinetic theory is developed, which holds without requiring any symmetry condition on the background fields. As a result, an asymptotic representation of the relativistic particle magnetic moment is obtained from its formal exact solution, in terms of a suitably defined invariant series expansion parameter (perturbative representation). On such a basis, it is shown that spatially non-symmetric kinetic equilibria can actually be determined, an example being provided by Gaussian-like distributions. As an application, the physical mechanisms related to the occurrence of a non-vanishing equilibrium fluid 4-flow are investigated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Beam hardening correction using iterative total variation (ITV)-based algorithm in CBCT reconstruction

Recently, beam hardening reduction is required to produce high-quality reconstructions of X-ray cone-beam computed tomography (CBCT) system for medical applications. This paper introduces the iterative total variation (ITV) for filtered-backprojection suffering from the serious beam hardening problems. Feldkamp, Davis, and Kress (FDK) reconstruction algorithm for CBCT system is widely used reconstruction technique. FDK reconstruction algorithm could be realized by generating the weighted projection data, filtering the projection images, and back-projecting the filtered projection data into the volume. However, FDK algorithm suffers from the beam hardening artifacts by X-ray attenuation coefficients. Recently, total variation (TV) method for compressed sensing (CS) has been particularly useful in exploiting the prior knowledge of minimal variation in the X-ray attenuation characteristics across object or human body. But a practical implementation of this method still remains a challenge. The main problem is the iterative nature of solving the TV-based CS formulation, which generally requires multiple iterations of forward and backward projections of a large dataset in clinically or industrially feasible time frame. In this paper, we propose ITV method after FDK reconstruction for reducing the beam hardening artifacts. The beam hardening problems are reduced by the ITV method to promote sparsity inherent in the X-ray attenuation characteristics. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The 4DEnVar-based weakly coupled land data assimilation system for E3SM version 2

Abstract. A new weakly coupled land data assimilation (WCLDA) system based on the four-dimensional ensemble variational (4DEnVar) method is developed and applied to the fully coupled Energy Exascale Earth System Model version 2 (E3SMv2). The dimension-reduced projection four-dimensional variational (DRP-4DVar) method is employed to implement 4DVar using the ensemble technique instead of the adjoint technique. With an interest in providing initial conditions for decadal climate predictions, monthly mean anomalies of soil moisture and temperature from the Global Land Data Assimilation System (GLDAS) reanalysis from 1980 to 2016 are assimilated into the land component of E3SMv2 within the coupled modeling framework with a 1-month assimilation window. The coupled assimilation experiment is evaluated using multiple metrics, including the cost function, assimilation efficiency index, correlation, root-mean-square error (RMSE), and bias, and compared with a control simulation without land data assimilation. The WCLDA system yields improved simulation of soil moisture and temperature compared with the control simulation, with improvements found throughout the soil layers and in many regions of the global land. In terms of both soil moisture and temperature, the assimilation experiment outperforms the control simulation with reduced RMSE and higher temporal correlation in many regions, especially in South America, central Africa, Australia, and large parts of Eurasia. Furthermore, significant improvements are also found in reproducing the time evolution of the 2012 US Midwest drought, highlighting the crucial role of land surface in drought lifecycle. The WCLDA system is intended to be a foundational resource for research to investigate land-derived climate predictability.

58 GEOSCIENCES↗

Excited states in variational Monte Carlo using a penalty method

Here, in this article, the authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. This technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states. This technique is applied to the well-characterized benzene molecule, in which ~10 000 parameters are optimized for the first 12 excited states. Agreement within ~0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.

36 MATERIALS SCIENCE↗

Wavelet and Deep-Learning-Based Approach for Generation System Problematic Parameters Identification and Calibration

Accurate models of generation systems are critical for maintaining reliable and secure grid operations. In this paper, a novel and systematic approach is proposed to identify and calibrate the generation system problematic parameters using continuous wavelet transform (CWT) and advanced deep-learning technology. The phasor measurement unit (PMU) data are used through “event playback” to check whether the parameter calibration is required, and if yes, a group of suspicious parameters will be identified as the primary problematic parameter candidates (PPCs). These primary PPCs are randomly perturbed to generate the event playback simulation data, which are used by the CWT and convolutional neural networks (CNNs) to further narrow down the primary PPCs into a smaller set of candidates. Then, the identified candidates are perturbed again to generate massive event playback simulation data for training a parameter calibration neural network. Here, we designed a multi-output neural network structure to find the mappings between the perturbed parameters and the simulation data using both CNN and long short-term memory (LSTM) models. Finally, the well-trained and tested CNN-LSTM model is used to estimate the accurate value of the suspicious parameters with actual PMU measurements. The proposed CNN-LSTM network can accurately and reliably estimate the generation-system problematic parameters, and has better performance when compared to other machine-learning methods, such as the multilayer perceptron network and the conditional variational autoencoder method. The accuracy and effectiveness of the proposed approach have been validated through simulation and real-world data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Development and evaluation of a new 4DEnVar-based weakly coupled ocean data assimilation system in E3SMv2

The development, implementation, and evaluation of a new weakly coupled ocean data assimilation (WCODA) system for the fully coupled Energy Exascale Earth System Model version 2 (E3SMv2) utilizing the four-dimensional ensemble variational (4DEnVar) method are presented in this study. The 4DEnVar method, based on the dimension-reduced projection four-dimensional variational (DRP-4DVar) approach, replaces the adjoint model with the ensemble technique, thereby reducing computational demands. Monthly mean ocean temperature and salinity data from the EN4.2.1 reanalysis are integrated into the ocean component of E3SMv2 from 1950 to 2021 with the goal of providing realistic initial conditions for decadal predictions and predictability studies. The performance of the WCODA system is assessed using various metrics, including the reduction rate of the cost function, root mean square error (RMSE) differences, correlation differences, and model biases. Results indicate that the WCODA system effectively assimilates the reanalysis data into the climate model, consistently achieving negative reduction rates of the cost function and notable improvements in RMSE and correlation across various ocean layers and regions. Significant enhancements are observed in the upper ocean layers across the majority of global ocean regions, particularly in the north Atlantic, north Pacific, and Indian Ocean. Model biases in sea surface temperature and salinity are also substantially reduced. For sea surface temperature, cold biases in the north Pacific and north Atlantic are diminished by about 1–2 °C, and warm biases in the Southern Ocean are corrected by approximately 1.5–2.5 °C. In terms of salinity, improvements are observed with bias reductions of about 0.5–1 psu in the north Atlantic and north Pacific and up to 1.5 psu in parts of the Southern Ocean. The ultimate goal of the WCODA system is to advance the predictive capabilities of E3SM for subseasonal to decadal climate predictions, thereby supporting research on strategic energy-sector policies and planning.

54 ENVIRONMENTAL SCIENCES↗

Dissipation-preserving spectral element method for damped seismic wave equations

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Application of Electromagnetic Methods for Reservoir Monitoring with Emphasis on Carbon Capture, Utilization, and Storage

The Controlled-Source ElectroMagnetic (CSEM) method provides crucial information about reservoir fluids and their spatial distribution. Carbon dioxide (CO2) storage, enhanced oil recovery (EOR), geothermal exploration, and lithium exploration are ideal applications for the CSEM method. The versatility of CSEM permits its customization to specific reservoir objectives by selecting the appropriate components of a multi-component system. To effectively tailor the CSEM approach, it is essential to determine whether the primary target reservoir is resistive or conductive. This task is relatively straightforward in CO2 monitoring, where the injected fluid is resistive. However, for scenarios involving brine-saturated (water-wet) or oil-wet (carbon capture, utilization, and storage—CCUS) reservoirs, consideration must also be given to conductive reservoir components. The optimization of data acquisition before the survey involves analyzing target parameters and the sensitivity of multi-component CSEM. This optimization process typically includes on-site noise measurements and 3D anisotropic modeling. Based on our experience, subsequent surveys tend to proceed smoothly, yielding robust measurements that align with scientific objectives. Other critical aspects to be considered are using magnetotelluric (MT) measurements to define the overall background resistivities and integrating real-time quality assurance during data acquisition with 3D modeling. This integration allows the fine tuning of acquisition parameters such as acquisition time and necessary repeats. As a result, data can be examined in real-time to assess subsurface information content while the acquisition is ongoing. Consequently, high-quality data sets are usually obtained for subsequent processing and initial interpretation with minimal user intervention. The implementation of sensitivity analysis during the inversion process plays a pivotal role in ensuring that the acquired data accurately respond to the target reservoirs’ expected depth range. To elucidate these concepts, we present an illustrative example from a CO2 storage site in North Dakota, USA, wherein the long-offset transient electromagnetic method (LOTEM), a variation of the CSEM method, and the MT method were utilized. This example showcases how surface measurements attain appropriately upscaled log-scale sensitivity. Furthermore, the sensitivity of the CSEM and MT methods was examined in other case histories, where the target reservoirs exhibited conductive properties, such as those encountered in enhanced oil recovery (EOR), geothermal, and lithium exploration applications. The same equipment specifications were utilized for CSEM and MT surveys across all case studies.

Barajas-Olalde, César↗

Variational Nodal 2D/1D Transport/Diffusion Solutions of the C5G7 Benchmark Problems

This work is the continuation of our effort to generalize the variational nodal method (VNM) for application to pin resolved whole-core PWR problems. To this end, a 2D/1D VNM method without spatial homogenization is formulated and implemented in the PANX code. We employ diffusion theory in the axial direction combined with two-dimensional transport in the x-y plane. In our initial work, we employed the standard spherical harmonics method. To increase accuracy and reduce computational effort, we present two refinements: First, the even-parity integral method within the nodes reduces the computational effort required to form the response matrices. Second, the use of quasi-reflected interface conditions reduces the dimension of the resulting response matrices and therefore the CPU time required to solve the equations. We apply the method to the three-dimensional, unrodded C5G7 benchmark problem.

97 MATHEMATICS AND COMPUTING↗

Multiparticle-multihole configuration mixing description of nuclear many-body systems

In this work we discuss the multiparticle-multihole configuration mixing method which aims to describe the structure of atomic nuclei. Based on a variational principle it is able to treat in a unified way all types of long-range correlations between nucleons, without introducing symmetry breaking. The formalism is presented along with some preliminary results obtained for a few sd-shell nuclei. In the presented applications, the D1S Gogny force has been used.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Spectroscopy of doubly charmed baryons from lattice QCD

This study presents the ground and excited state spectra of doubly charmed baryons from lattice QCD with dynamical quark fields. Calculations are performed on anisotropic lattices of size 16³ × 128, with inverse spacing in temporal direction a t ⁻¹=5.67(4) GeV and with a pion mass of about 390 MeV. A large set of baryonic operators that respect the symmetries of the lattice yet which retain a memory of their continuum analogues are used. These operators transform as irreducible representations of SU(3) F symmetry for flavor, SU(4) symmetry for Dirac spins of quarks and O(3) for spatial symmetry. The distillation method is utilized to generate baryon correlation functions which are analyzed using the variational fitting method to extract excited states. The lattice spectra obtained have baryonic states with well-defined total spins up to 7/2 and the pattern of low-lying states does not support the diquark picture for doubly charmed baryons. On the contrary the calculated spectra are remarkably similar to the expectations from models with an SU(6)×O(3) symmetry. Various spin-dependent energy splittings between the extracted states are also evaluated.

Padmanath, M.↗

Using a meshless kernel-based method to solve the Black–Scholes variational inequality of American options

Under the Black–Scholes model, the value of an American option solves a free boundary problem which is equivalent to a variational inequality problem. Using positive definite kernels, we discretize the variational inequality problem in spatial direction and derive a sequence of linear complementarity problems (LCPs) in a finite-dimensional euclidean space. We use special kind of kernels to impose homogeneous boundary conditions and to obtain LCPs with positive definite coefficient matrices to guarantee the existence and uniqueness of the solution. The LCPs are then successfully solved iteratively by the projected SOR algorithm.

97 MATHEMATICS AND COMPUTING↗

A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise

In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with additive noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with additive noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A rapid embodied carbon assessment tool for priority materials

Embodied carbon limits within building materials are a driving factor in global trade, generating new research and analysis tools in industry. These product assessments, which require utilizing life-cycle assessment (LCA) across broad supply chains, can be expensive, time and data-intensive, and subject to significant variations. Existing methods and tools, such as specific environmental product declarations, typically do not capture these variations and dynamics in supply and manufacturing. Moreover, models and tools must enable stakeholders to assess customized supply chains and future scenarios. In this study, we present the Rapid Embodied Carbon Assessment and Target-setting for Emissions-intensive Materials (REDuCE) tool for building materials. We developed a tool that allows users to select production technologies, transportation mode and distances, concrete carbonation, fuel sources, and regional electricity mixes to supply customization for cement and concrete produced and consumed in California. We generated and integrated a material demand model using residential building stock projections. We provide the user with a wide range of mitigation alternatives through low-carbon production pathways, material use efficiency, transportation modes, and projected electricity grid mixes. In a case study application through four mitigation scenarios, we find emission savings up to 80% by maximizing user mitigation alternatives, primarily driven by reductions in material use intensities. This work represents a foundation for expanding LCA and embodied carbon tools to better enable stakeholders to rapidly and accurately assess customized supply chains while meeting trade requirements.

building materials↗

A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo

We present a modification to variational Monte Carlo’s linear method optimization scheme that addresses a critical memory bottleneck while maintaining compatibility with both the traditional ground state variational principle and our recently-introduced variational principle for excited states. For wave function ansatzes with tens of thousands of variables, our modification reduces the required memory per parallel process from tens of gigabytes to hundreds of megabytes, making the methodology a much better fit for modern supercomputer architectures in which data communication and per-process memory consumption are primary concerns. We verify the efficacy of the new optimization scheme in small molecule tests involving both the Hilbert space Jastrow antisymmetric geminal power ansatz and real space multi-Slater Jastrow expansions. Satisfied with its performance, we have added the optimizer to the QMCPACK software package, with which we demonstrate on a hydrogen ring a prototype approach for making systematically convergent, non-perturbative predictions of Mott-insulators’ optical band gaps.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurements of the Differential Cross Sections for the Elastic n-{sup 3}H and n-{sup 2}H Scattering at 14.1 MeV by Using an Inertial Confinement Fusion Facility

For the first time the differential cross section for the elastic neutron-triton (n-{sup 3}H) and neutron-deuteron (n-{sup 2}H) scattering at 14.1 MeV has been measured by using an inertial confinement fusion facility. In these experiments, which were carried out by simultaneously measuring elastically scattered {sup 3}H and {sup 2}H ions from a deuterium-tritium gas-filled inertial confinement fusion capsule implosion, the differential cross section for the elastic n-{sup 3}H scattering was obtained with significantly higher accuracy than achieved in previous accelerator experiments. The results compare well with calculations that combine the resonating-group method with an ab initio no-core shell model, which demonstrate that recent advances in ab initio theory can provide an accurate description of light-ion reactions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗