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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Accelerating Multivariate Functional Approximation Computation with Domain Decomposition Techniques⋆

Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain -decomposed method for computing the MFA with B -spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees -of -freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high -order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C 0 or at best C 1 continuity for arbitrary B -spline degree expansions, or those that require post -processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real -world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest -neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.

additive Schwarz solvers↗
DOE OSTI2021

Static dipole polarizabilities of polyacenes using self-interaction-corrected density functional approximations

Density functional approximations are known to significantly overestimate the polarizabilities of long chain-like molecules. We study the static electric dipole polarizabilities and the vertical ionization potentials of polyacenes from benzene to pentacene using the Fermi-L\"owdin orbital based self-interaction corrected (FLOSIC) density functional method. The orbital-by-orbital self-interaction correction corrects for the overestimation tendency of density functional approximations. The polarizabilities calculated with FLOSIC-DFA are however overly corrected. We also tested the recently developed locally-scaled self-interaction correction (LSIC) method on the polyacenes. The local-scaling method applies full SIC in the one-electron regions and restores the proper behavior of the SIC exchange-correlation functionals in the uniform density limit. The results show that LSIC removes the overcorrection tendency of the FLOSIC-DFA and produces results that are in excellent agreement with reference CCSD values. The vertical ionization potentials with LSIC also show good agreement with available experimental values.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗
DOE OSTI2018

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation

The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. Here, we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew for performing self-interaction free calculations in density functional theory based on Fermi-orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction corrected (FLOSIC) method for practical density functional calculations without SIE.

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

Fresnel zone plate point spread function approximation for zeroth order mitigation in millimetric field of view x-ray imaging

High spatial and temporal resolution x-ray radiography images are required at the National Ignition Facility (NIF) for high-energy density experiments. One technique that is in development to achieve the required resolution uses Fresnel zone plate (FZP) optics to image an object that is backlit by an x-ray source. The multiple FZP diffraction orders do not focus on the same plane, which increases the background and reduces the contrast. Understanding the point spread function of the different diffraction orders will allow the prediction of the expected background using simulations. We find that the two-dimensional point spread function of the FZP can be approximated by the addition of a sharp Gaussian with a disk. This allowed for the estimation of the background in NIF experimental images of Rayleigh–Taylor spikes and their interpretation. An alternative design of FZP is discussed to allow the inclusion of a zeroth order blocker to reduce the background.

Do, A. (ORCID:0000000174372147)↗
DOE OSTI2023

Finite-Time Analysis of Whittle Index based Q-Learning for Restless Multi-Armed Bandits with Neural Network Function Approximation

Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with convergence rate, where is the number of iterations.

reinforcement learning, structured learning, conve↗
DOE OSTI2023

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew–Burke–Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew–Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. Finally, the quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

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

Localization in the SCAN meta-generalized gradient approximation functional leading to broken symmetry ground states for graphene and benzene

Density functional theory calculations play a central role in understanding chemical and solid-state systems. Progress depends on density functionals that accurately reproduce both energies, for thermochemistry, and properly describe ground states and other properties that are of interest. The Cr dimer, benzene and graphene are especially important benchmark systems for quantum chemistry and condensed matter physics. The Strongly Constrained and Appropriately Normed (SCAN) functional, which is an advanced meta-generalized gradient approximation functional that significantly improves molecular energies is shown to perform poorly for the Cr dimer. This is connected with its poor performance for itinerant solid-state magnets and is a consequence of over localization of electrons, thus illustrating an analogy between the Cr dimer and itinerant magnets. The Cr dimer is a notoriously difficult system for density functionals. However, we additionally find that SCAN predicts an incorrect symmetry broken ground state for 2D graphene and for the benzene molecule, which is surprising considering that ground states of these are known to be well described even by the simplest local density approximation. We show that SCAN overly favors localized spin polarized states, which is a serious deficiency of this approach. Thus, the challenge of finding density functionals that accurately treat both localized and delocalized electronic systems remains.

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

Sensitivity of the electronic and magnetic structures of cuprate superconductors to density functional approximations

Abstract We discuss the crystal, electronic, and magnetic structures of La 2− x Sr x CuO 4 (LSCO) for x = 0.0 and x = 0.25 employing 13 density functional approximations, representing the local, semi-local, and hybrid exchange-correlation approximations within the Perdew–Schmidt hierarchy. The meta-generalized gradient approximation (meta-GGA) class of functionals is found to perform well in capturing the key properties of LSCO, a prototypical high-temperature cuprate superconductor. In contrast, the localspin-density approximation, GGA, and the hybrid density functional fail to capture the metal-insulator transition under doping.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Learning nonlinear level sets for dimensionality reduction in function approximation

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.

Zhang, Guannan↗
DOE OSTI2023

Scalable Volume Visualization for Big Scientific Data Modeled by Functional Approximation

Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional approximation (MFA) is an innovative data model designed to tackle substantial challenges in scientific data analysis. It computes values and derivatives with high-order accuracy throughout the spatial domain, mitigating artifacts associated with zero- or first-order interpolation. However, the slow query time through MFA makes it less suitable for interactively visualizing a large MFA model. In this work, we develop the first scalable interactive volume visualization pipeline, MFA-DVV, for the MFA model encoded from large-scale datasets. Our method achieves low input latency through distributed architecture, and its performance can be further enhanced by utilizing a compressed MFA model while still maintaining a high-quality rendering result for scientific datasets. We conduct comprehensive experiments to show that MFA-DVV can decrease the input latency and achieve superior visualization results for big scientific data compared with existing approaches.

big scientific dataset↗
DOE OSTI2024

Self‐Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as “Jacob's ladder.” This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBEα framework with mathematical equation being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

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

Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations

The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For band gaps, semilocal density functionals up to the generalized gradient approximation (GGA) level cannot compete with the accuracy of hybrid-based approximations or GW. Meta-GGA density functionals with a strong dependence on the kinetic energy density ingredient can potentially give wider band gaps compared with GGAs. The recent TASK meta-GGA density functional from Aschebrock and Kümmel [ Phys. Rev. Research 1 , 033082 (2019) ], is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. Additionally, the reduced screening of these materials results in larger band gaps compared with their bulk counterparts, as an additional barrier to overcome. In this paper we demonstrate how the alteration of this functional affects the band gaps of monolayers and nanoribbons and present accurate band gaps competing with the revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper bound for one- or two-electron systems ( h X 0 ) from 1.174 to 1.29 and (b) by changing the limit of the interpolation function f X ( α → ∞ ) of the TASK functional that interpolates the exchange enhancement factor F X ( s , α ) from α = 0 to 1. The resulting modified TASK (mTASK) was tested for various materials from three dimensions to two dimensions to one dimension (nanoribbons) and was compared with the results of the higher-level hybrid functional HSE06 or with the G 0 W 0 approximation within many-body perturbation theory. We find that mTASK systematically improves the band gaps and band structures of two-dimensional (2D) and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared with the Perdew-Burke-Ernzerhof (PBE) GGA and the strongly constrained and appropriately normed (SCAN) meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of transition metal dichalcogenide nanoribbons with respect to various bending curvatures.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Semi-local Density Functional Approximations for Bulk, Surface, and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semi-local approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize the results of our research efforts within the LDRD 200202 titled "Making density functional theory work for all materials" in addressing this issue. Our efforts are grouped into two research thrusts. In the first thrust, we develop an exchange-correlation functional (BSC functional) within the subsystem functional formalism. It enables us to capture bulk, surface, and confinement physics with a single, semi-local exchange-correlation functional in density functional theory calculations. We present the analytical properties of the BSC functional and demonstrate that the BSC functional is able to capture confinement physics more accurately than standard semi-local exchange-correlation functionals. The second research thrust focusses on developing a database for transition metal binary compounds. The database consists of materials properties (formation energies, ground-state energies, lattice constants, and elastic constants) of 26 transition metal elements and 89 transition metal alloys. It serves as a reference for benchmarking computational models (such as lower-level modeling methods and exchange-correlation functionals). We expect that our database will significantly impact the materials science community. We conclude with a brief discussion on the future research directions and impact of our results.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. In this paper, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Presently the training of neural networks relies on data of comparable accuracy but in real applications only a very small set of high-fidelity data is available while inexpensive lower fidelity data may be plentiful. We propose a new composite neural network (NN) that can be trained based on multi-fidelity data. It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data. We first demonstrate the accuracy of the new multi-fidelity NN for approximating some standard benchmark functions but also a 20-dimensional function that is not easy to approximate with other methods, e.g. Gaussian process regression. Subsequently, we extend the recently developed physics-informed neural networks (PINNs) to be trained with multi-fidelity data sets (MPINNs). MPINNs contain four fully-connected neural networks, where the first one approximates the low-fidelity data, while the second and third construct the correlation between the low- and high-fidelity data and produce the multi-fidelity approximation, which is then used in the last NN that encodes the partial differential equations (PDEs). Specifically, by decomposing the correlation into a linear and nonlinear part, the present model is capable of learning both the linear and complex nonlinear correlations between the low- and high-fidelity data adaptively. By training the MPINNs, we can: (1) obtain the correlation between the low- and high-fidelity data, (2) infer the quantities of interest based on a few scattered data, and (3) identify the unknown parameters in the PDEs. In particular, we employ the MPINNs to learn the hydraulic conductivity field for unsaturated flows as well as the reactive models for reactive transport. The results demonstrate that MPINNs can achieve relatively high accuracy based on a very small set of high-fidelity data. Despite the relatively low dimension and limited number of fidelities (two-fidelity levels) for the benchmark problems in the present study, the proposed model can be readily extended to very high-dimensional regression and classification problems involving multi-fidelity data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

On the Sensitivity to Density-Functional Approximations for CO Binding Energies of Single-Atom Catalysts in Nitrogen-Doped Graphene

Density functional theory (DFT) methods are the working horse in screening new catalytic materials. They are widely used to predict trends in binding energies, which are then used to compare the activity of different materials. Here, the binding strength of CO is an important descriptor to the CO 2 reduction catalytic activity of the single transition metal atoms embedded on nitrogen-doped graphene (TM/NG). In this work, however, we show that CO binding strengths in different TM/NG has very different sensitivity to DFT methods. Specifically, Fe/NG CO binding energy changes dramatically with the percentage of exact exchange in the functional; Co/NG does less so, while Ni/NG nearly has no change. Such varying behaviors is a direct result of different local spin configurations, similar to the performance of DFT methods for metal porphyrin complexes. Therefore, caution should be exercised when using DFT binding energies for quantitative predictions in TM/NG single atom catalysis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Interaction between water and carbon nanostructures: How good are current density functional approximations?

Due to their current and future technological applications, including realization of water filters and desalination membranes, water adsorption on graphitic sp2-bonded carbon is of overwhelming interest. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and noncovalent interactions, in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed WaC18), which includes a single water molecule interacting with a broad range of carbon structures and various bulk (3D) and two-dimensional (2D) ice polymorphs. The performance of 28 approaches, including semilocal exchange-correlation functionals, nonlocal (Fock) exchange contributions, and long-range van der Waals (vdW) treatments, is tested by computing the deviations from the reference interaction energies. The calculated mean absolute deviations on the WaC18 set depend crucially on the DFT approach, ranging from 135 meV for local density approximation (LDA) to 12 meV for PBE0-D4. We find that modern vdW corrections to DFT significantly improve over their precursors. Within the 28 tested approaches, we identify the best performing within the functional classes of generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, which are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, respectively.

Brandenburg, Jan Gerit (ORCID:0000000292192948)↗