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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Rotationally invariant slave-boson and density matrix embedding theory: Unified framework and comparative study on the one-dimensional and two-dimensional Hubbard model [Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model]

We present detailed benchmark ground-state calculations of the one- and two-dimensional Hubbard model utilizing the cluster extensions of the rotationally invariant slave-boson mean-field theory and the density matrix embedding theory. Our analysis shows that the overall accuracy and the performance of these two methods are very similar. Furthermore, we propose a unified computational framework that allows us to implement both of these techniques on the same footing. In conclusion, this provides us with a different line of interpretation and paves the ways for developing systematically distinct generalizations of these complementary approaches.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Rotation-invariant-neural-networks

Rotational symmetries are a fundamental and inherent property of many sources of data. Ensuring NNs embody rotation invariance will enhance their accuracy and radically lower their data requirements across a transformatively wide spectrum of applications.

Lubbers, Nicholas [Los Alamos National Laboratory]↗
DOE OSTI2016

SymPix: A spherical grid for efficient sampling of rotationally invariant operators

We present SymPix, a special-purpose spherical grid optimized for efficiently sampling rotationally invariant linear operators. This grid is conceptually similar to the Gauss–Legendre (GL) grid, aligning sample points with iso-latitude rings located on Legendre polynomial zeros. Unlike the GL grid, however, the number of grid points per ring varies as a function of latitude, avoiding expensive oversampling near the poles and ensuring nearly equal sky area per grid point. The ratio between the number of grid points in two neighboring rings is required to be a low-order rational number (3, 2, 1, 4/3, 5/4, or 6/5) to maintain a high degree of symmetries. Our main motivation for this grid is to solve linear systems using multi-grid methods, and to construct efficient preconditioners through pixel-space sampling of the linear operator in question. As a benchmark and representative example, we compute a preconditioner for a linear system that involves the operator D-hat + B-hat {sup T}N{sup −1} B-hat , where B-hat and D-hat may be described as both local and rotationally invariant operators, and N is diagonal in the pixel domain. For a bandwidth limit of ℓ{sub max} = 3000, we find that our new SymPix implementation yields average speed-ups of 360 and 23 for B-hat {sup T}N{sup −1} B-hat and D-hat , respectively, compared with the previous state-of-the-art implementation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Disentangling Rotational Dynamics and Ordering Transitions in a System of Self-Organizing Protein Nanorods via Rotationally Invariant Latent Representations

The dynamics of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally invariant variational autoencoder-based analysis of orientation and shape evolution. The latter allows for disentanglement of the particle orientation from other degrees of freedom and compensates for lateral shifts. The disentangled representations in the latent space encode the rich spectrum of local transitions that can now be visualized and explored via continuous variables. The time dependence of ensemble averages allows insight into the time dynamics of the system and, in particular, illustrates the presence of the potential ordering transition. Finally, analysis of the latent variables along the single-particle trajectory allows tracing these parameters on a single-particle level. The proposed approach is expected to be universally applicable for the description of the imaging data in optical, scanning probe, and electron microscopy seeking to understand the dynamics of complex systems where rotations are a significant part of the process.

representation learning↗
DOE OSTI2022

A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems

Here, we introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of $20 \sim 50 \times $ in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F 2 demonstrates favorable agreements with standard quantum-chemical calculations Bytautas et al (2007 J. Chem. Phys. 127 164317).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors

Here, we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Anisotropic inflation reexamined: upper bound on broken rotational invariance during inflation

The presence of a light vector field coupled to a scalar field during inflation makes a distinct prediction: the observed correlation functions of the cosmic microwave background (CMB) become statistically anisotropic. We study the implications of the current bound on statistical anisotropy derived from the Planck 2013 CMB temperature data for such a model. The previous calculations based on the attractor solution indicate that the magnitude of anisotropy in the power spectrum is proportional to N{sup 2}, where N is the number of e-folds of inflation counted from the end of inflation. In this paper, we show that the attractor solution is not necessarily compatible with the current bound, and derive new predictions using another branch of anisotropic inflation. In addition, we improve upon the calculation of the mode function of perturbations by including the leading-order slow-roll corrections. We find that the anisotropy is roughly proportional to [2(ε{sub H}+4η{sub H})/3−4(c−1)]{sup −2}, where ε{sub H} and η{sub H} are the usual slow-roll parameters and c is the parameter in the model, regardless of the form of potential of an inflaton field. The bound from Planck implies that breaking of rotational invariance during inflation (characterized by the background homogeneous shear divided by the Hubble rate) is limited to be less than O(10{sup −9}). This bound is many orders of magnitude smaller than the amplitude of breaking of time translation invariance, which is observed to be O(10{sup −2})

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Charge self-consistent density functional theory plus ghost rotationally invariant slave-boson theory for correlated materials

We present a charge self-consistent density functional theory combined with the ghost rotationally invariant slave-boson (DFT+gRISB) formalism for studying correlated materials. Here, this method is applied to SrVO 3 and NiO, representing prototypical correlated metals and charge-transfer insulators. For SrVO 3 , we demonstrate that DFT+gRISB yields an accurate equilibrium volume and effective mass close to experimentally observed values. Regarding NiO, DFT+gRISB enables the simultaneous description of charge-transfer and Mott-Hubbard bands, significantly enhancing the accuracy of the original DFT+RISB approach. Furthermore, the calculated equilibrium volume and spectral function reasonably agree with experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

Here, we compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

In this paper, we present a unified perspective on dynamical mean-field theory (DMFT), density-matrix embedding theory (DMET), and rotationally invariant slave bosons (RISB). We show that DMET can be regarded as a simplification of the RISB method where the quasiparticle weight is set to unity. Finally, this relation makes it easy to transpose extensions of a given method to another: For instance, a temperature-dependent version of RISB can be used to derive a temperature-dependent free-energy formula for DMET.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Probing atomic-scale symmetry breaking by rotationally invariant machine learning of multidimensional electron scattering

Abstract The 4D scanning transmission electron microscopy (STEM) method maps the structure and functionality of solids on the atomic scale, yielding information-rich data sets describing the interatomic electric and magnetic fields, structural and electronic order parameters, and other symmetry breaking distortions. A critical bottleneck is the dearth of analytical tools that can reduce complex 4D-STEM data to physically relevant descriptors. We propose an approach for the systematic exploration of 4D-STEM data using rotationally invariant variational autoencoders (rrVAE), which disentangle the general rotation of the object from other latent representations. The implementation of purely rotational rrVAE is discussed as are applications to simulated data for graphene and zincblende structures. The rrVAE analysis of experimental 4D-STEM data of defects in graphene is illustrated and compared to the classical center-of-mass analysis. This approach is universal for probing symmetry-breaking phenomena in complex systems and can be implemented for a broad range of diffraction methods.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Investigating Carboxysome Morphology Dynamics with a Rotationally Invariant Variational Autoencoder

Carboxysomes are a class of bacterial microcompartments that form proteinaceous organelles within the cytoplasm of cyanobacteria and play a central role in photosynthetic metabolism by defining a cellular microenvironment permissive to CO2 fixation. Critical aspects of the assembly of the carboxysomes remain relatively unknown, especially with regard to the dynamics of this microcompartment. Progress in understanding carboxysome dynamics is impeded in part because analysis of the subtle changes in carboxysome morphology with microscopy remains a low-throughput and subjective process. Here we use deep learning techniques, specifically a Rotationally Invariant Variational Autoencoder (rVAE), to analyze fluorescence microscopy images of cyanobacteria bearing a carboxysome reporter and quantitatively evaluate how carboxysome shell remodelling impacts subtle trends in the morphology of the microcompartment over time. Toward this goal, we use a recently developed tool to control endogenous protein levels, including carboxysomal components, in the model cyanobacterium Synechococcous elongatus PCC 7942. By utilization of this system, proteins that compose the carboxysome can be tuned in real time as a method to examine carboxysome dynamics. We find that rVAEs are able to assist in the quantitative evaluation of changes in carboxysome numbers, shape, and size over time. Further, we propose that rVAEs may be a useful tool to accelerate the analysis of carboxysome assembly and dynamics in response to genetic or environmental perturbation and may be more generally useful to probe regulatory processes involving a broader array of bacterial microcompartments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

On linear structure and phase rotation invariant properties of block M-PSK modulation codes

Two important structural properties of block M(=2')-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M-ary modulation code is first represented as a code with symbols from the integer group S(MPSK) = (0,1,2,...M-1) under modulo-M addition. Then the linear structure of block MPSK modulation codes over S(M-PSK) with respect to modulo-M vector addition is defined, and conditions are derived under which a block MPSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M-PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block MPSK modulation code that is linear as a binary code to be invariant under 2 h 180 deg/M phase rotation (for h = 1 to l) is derived. Finally, a list of short 8PSK and 16PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.

Kasami, Tadao↗