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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗
NASA NTRS1988

Approximation of the dielectric properties of Maxwellian plasmas - Dispersion functions and physical constraints

The dielectric properties of Maxwellian plasmas are approximated using high Pade approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytical work and in accelerating large-scale numerical computations.

Robinson, P. A.↗
DOE OSTI2023

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r 2 SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r 2 SCAN-D3. Our results show that r 2 SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Thermally-assisted-occupation density functional theory with generalized-gradient approximations

We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computational efficiency for systems with strong static correlation effects, TAO-LDA and TAO-GGAs are applied to study the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy) of acenes with different number of linearly fused benzene rings (up to 100), which is very challenging for conventional electronic structure methods. The ground states of acenes are shown to be singlets for all the chain lengths studied here. With the increase of acene length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy (i.e., a measure of polyradical character) increase monotonically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Why is MP2-Water "Cooler" and "Denser" than DFT-Water?

To maintain water in the liquid phase at the correct (1 g/cm3) density during first-principles simulations, density-functional theory (DFT) with a dispersionless generalized-gradient-approximation (GGA) functional requires a much higher temperature and pressure than the ambient conditions. Conversely, ab initio second-order many-body perturbation (MP2) calculations of liquid water performed by Del Ben et al. [J. Chem. Phys. Lett. 4, 3753 (2013); J. Chem. Phys. 143, 054506 (2015)] and by us [Willow et al., Sci. Rep. 5, 14358 (2015)] required a lower temperature and a negative pressure than DFT to keep water liquid. Here, we present a unifying explanation of these trends derived from classical water simulations using a polarizable force field with different sets of parameters. We show that the calculated temperature and pressure of the liquid phase are strongly correlated with the polarizability of water and the dispersion interaction, respectively. In DFT/GGA, the polarizability and thus the induced dipole moments and the hydrogen-bond strength are all overestimated. This hinders the rotational motion of molecules and requires a higher temperature for water to be liquid. In MP2 and DFT/GGA, the dispersion interaction is stronger and weaker (or lacking), respectively. This explains why liquid water contracts uniformly and becomes too dense in MP2, whereas the opposite is the case for dispersionless DFT/GGA.

Willow, Soohaeng Y.↗
DOE OSTI2019

The role of decomposition reactions in assessing first-principles predictions of solid stability

Abstract The performance of density functional theory approximations for predicting materials thermodynamics is typically assessed by comparing calculated and experimentally determined enthalpies of formation from elemental phases, Δ H f . However, a compound competes thermodynamically with both other compounds and their constituent elemental forms, and thus, the enthalpies of the decomposition reactions to these competing phases, Δ H d , determine thermodynamic stability. We evaluated the phase diagrams for 56,791 compounds to classify decomposition reactions into three types: 1. those that produce elemental phases, 2. those that produce compounds, and 3. those that produce both. This analysis shows that the decomposition into elemental forms is rarely the competing reaction that determines compound stability and that approximately two-thirds of decomposition reactions involve no elemental phases. Using experimentally reported formation enthalpies for 1012 solid compounds, we assess the accuracy of the generalized gradient approximation (GGA) (PBE) and meta-GGA (SCAN) density functionals for predicting compound stability. For 646 decomposition reactions that are not trivially the formation reaction, PBE (mean absolute difference between theory and experiment (MAD) = 70 meV/atom) and SCAN (MAD = 59 meV/atom) perform similarly, and commonly employed correction schemes using fitted elemental reference energies make only a negligible improvement (~2 meV/atom). Furthermore, for 231 reactions involving only compounds (Type 2), the agreement between SCAN, PBE, and experiment is within ~35 meV/atom and is thus comparable to the magnitude of experimental uncertainty.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A compendium of human gene functions derived from evolutionary modelling

A comprehensive, computable representation of the functional repertoire of all macromolecules encoded within the human genome is a foundational resource for biology and biomedical research. The Gene Ontology Consortium has been working towards this goal by generating a structured body of information about gene functions, which now includes experimental findings reported in more than 175,000 publications for human genes and genes in experimentally tractable model organisms 1,2 . Here, we describe the results of a large, international effort to integrate all of these findings to create a representation of human gene functions that is as complete and accurate as possible. Specifically, we apply an expert-curated, explicit evolutionary modelling approach to all human protein-coding genes. This approach integrates available experimental information across families of related genes into models that reconstruct the gain and loss of functional characteristics over evolutionary time. The models and the resulting set of 68,667 integrated gene functions cover approximately 82% of human protein-coding genes. The functional repertoire reveals a marked preponderance of molecular regulatory functions, and the models provide insights into the evolutionary origins of human gene functions. We show that our set of descriptions of functions can improve the widely used genomic technique of Gene Ontology enrichment analysis. The experimental evidence for each functional characteristic is recorded, thereby enabling the scientific community to help review and improve the resource, which we have made publicly available.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Development of Response Surface Models for Rapid Analysis & Multidisciplinary Optimization of Launch Vehicle Design Concepts

Multdisciplinary design optimization (MDO) is an important step in the design and evaluation of launch vehicles, since it has a significant impact on performance and lifecycle cost. The objective in MDO is to search the design space to determine the values of design parameters that optimize the performance characteristics subject to system constraints. Vehicle Analysis Branch (VAB) at NASA Langley Research Center has computerized analysis tools in many of the disciplines required for the design and analysis of launch vehicles. Vehicle performance characteristics can be determined by the use of these computerized analysis tools. The next step is to optimize the system performance characteristics subject to multidisciplinary constraints. However, most of the complex sizing and performance evaluation codes used for launch vehicle design are stand-alone tools, operated by disciplinary experts. They are, in general, difficult to integrate and use directly for MDO. An alternative has been to utilize response surface methodology (RSM) to obtain polynomial models that approximate the functional relationships between performance characteristics and design variables. These approximation models, called response surface models, are then used to integrate the disciplines using mathematical programming methods for efficient system level design analysis, MDO and fast sensitivity simulations. A second-order response surface model of the form given has been commonly used in RSM since in many cases it can provide an adequate approximation especially if the region of interest is sufficiently limited.

Unal, Resit↗
NASA NTRS1984

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Pratt, D. T.↗
NASA NTRS1993

Neural network-based control using Lyapunov functions

We have successfully demonstrated how the problem of stabilization of plants can be reduced to a problem of approximation of functions. Neural networks have been shown to have approximating and interpolating properties. This approach is good for linear and nonlinear plants. Software has been generated to demonstrate this approach.

Luxemburg, Leon A.↗
DOE OSTI2014

Hierarchy of model Kohn–Sham potentials for orbital-dependent functionals: A practical alternative to the optimized effective potential method

We describe a method for constructing a hierarchy of model potentials approximating the functional derivative of a given orbital-dependent exchange-correlation functional with respect to electron density. Each model is derived by assuming a particular relationship between the self-consistent solutions of Kohn–Sham (KS) and generalized Kohn–Sham (GKS) equations for the same functional. In the KS scheme, the functional is differentiated with respect to density, in the GKS scheme—with respect to orbitals. The lowest-level approximation is the orbital-averaged effective potential (OAEP) built with the GKS orbitals. The second-level approximation, termed the orbital-consistent effective potential (OCEP), is based on the assumption that the KS and GKS orbitals are the same. It has the form of the OAEP plus a correction term. The highest-level approximation is the density-consistent effective potential (DCEP), derived under the assumption that the KS and GKS electron densities are equal. The analytic expression for a DCEP is the OCEP formula augmented with kinetic-energy-density-dependent terms. In the case of exact-exchange functional, the OAEP is the Slater potential, the OCEP is roughly equivalent to the localized Hartree–Fock approximation and related models, and the DCEP is practically indistinguishable from the true optimized effective potential for exact exchange. All three levels of the proposed hierarchy require solutions of the GKS equations as input and have the same affordable computational cost.

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

Quantum simulation of molecules without fermionic encoding of the wave function

Abstract Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N -qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H 4 is presented.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks

Hyperbolic neural networks have recently gained significant attention due to their promising results on several graph problems including node classification and link prediction. The primary reason for this success is the effectiveness of hyperbolic space in capturing the inherent hierarchy of graph datasets. However, they are limited in terms of generalization, scalability, and have inferior performance when applied to non-hierarchical datasets. In this paper, we take a completely different perspective for modeling hyperbolic networks and answer the following question: is an Euclidean model able to approximate a function or behavior in the hyperbolic space? Extending the universal approximation theory developed for Euclidean models, We draw an analogy from the hyperbolic components to the Euclidean counterparts and conclude that, in order to capture hierarchical features, it is possible to generalize hyperbolic models to be a special case of Euclidean models with the proposed Pseudo-Poincaré technique. We applied our non-linear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks and demonstrate significant improvements in performance compared to both Euclidean and hyperbolic counterparts. The primary impact of this work lies in its ability to capture hierarchical features in the Euclidean space, and thus, can replace hyperbolic networks without any loss in performance metrics while simultaneously leveraging the power of Euclidean networks such as interpretability and efficient execution of various model components.

Khatir, Mehrdad↗
NASA NTRS2021

Characterizing the Aging of Alphasense NO2 Sensors in Long-term Field Deployments

Low-cost NO2 sensors have been widely deployed for atmospheric sampling. While their initial performance has been characterized, few studies have examined their long-term degradation. This study focused on the performance of Alphasense low-cost NO2 sensors (NO2-B42F and NO2-B43F) over 4 years (2016–2020). A total of 29 NO2 sensors from 10 batches were collocated 78 times at two sites with reference instruments. Raw signals from “functional” NO2 sensors correlated linearly with reference NO2 concentrations. After long-term deployment, sensor raw signals started to deviate from reference NO2 concentrations due to sensor aging, an accumulated effect after sensor unpacking. Several sensors eventually became “non-functional” as sensor raw signals showed no correlation with reference NO2 concentrations. Sensor aging and non-functionality may be primarily caused by expiration of the ozone (O3) scrubber built into these sensors so that sensors responded to both ambient NO2 and O3. The influence of O3 on sensor response is quantified through the permutation importance method. Most of the sensors are non-functional after approximately 200–400 days of deployment, and no sensor was functional after 400 days of deployment. This result agrees well with the estimated lifetime of the built-in ozone scrubbers considering the ambient ozone concentration in the Pittsburgh area where these sensors were deployed. To ensure reliable data quality in long-term field deployments, we recommend collocating NO2 sensors with reference instruments regularly after 200–400 days of deployment to identify and replace non-functional sensors in a timely manner.

NO2sensors↗
DOE OSTI2021

Time-dependent orbital-free density functional theory: Background and Pauli kernel approximations

Time-dependent orbital-free density functional theory (DFT) is an efficient method for calculating the dynamic properties of large-scale quantum systems due to the low computational cost compared to standard time-dependent DFT. In this work, we formalize this method by mapping the real system of interacting fermions onto a fictitious system of noninteracting bosons. The dynamic Pauli potential and associated kernel emerge as key ingredients of time-dependent orbital-free DFT. Using the uniform electron gas as a model system, we derive an approximate frequency-dependent Pauli kernel. Pilot calculations suggest that space nonlocality is a key feature for this kernel. Nonlocal terms arise already in the second-order expansion with respect to unitless frequency and reciprocal space variable ($\frac{ω}{qk_F}$ and $\frac{q}{2k_F}$, respectively). Given the encouraging performance of the proposed kernel, we expect it will lead to more accurate orbital-free DFT simulations of nanoscale systems out of equilibrium. Additionally, the proposed path to formulate nonadiabatic Pauli kernels presents several avenues for further improvements which can be exploited in future work to improve the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Automation of Active Space Selection for Multireference Methods via Machine Learning on Chemical Bond Dissociation

Predicting and understanding the chemical bond is one of the major challenges of computational quantum chemistry. Kohn–Sham density functional theory (KS-DFT) is the most common method, but approximate density functionals may not be able to describe systems where multiple electronic configurations are equally important. Multiconfigurational wave functions, on the other hand, can provide a detailed understanding of the electronic structures and chemical bonds of such systems. In the complete active space self-consistent field (CASSCF) method, one performs a full configuration interaction calculation in an active space consisting of active electrons and active orbitals. However, CASSCF and its variants require the selection of these active spaces. This choice is not black box; it requires significant experience and testing by the user, and thus active space methods are not considered particularly user-friendly and are employed only by a minority of quantum chemists. Our goal is to popularize these methods by making it easier to make good active space choices. Here, we present a machine learning protocol that performs an automated selection of active spaces for chemical bond dissociation calculations of main group diatomic molecules. The protocol shows high prediction performance for a given target system as long as a properly correlated system is chosen for training. Good active spaces are correctly predicted with a considerably better success rate than random guess (larger than 80% precision for most systems studied). Our automated machine learning protocol shows that a “black-box” mode is possible for facilitating and accelerating the large-scale calculations on multireference systems where single-reference methods such as KS-DFT cannot be applied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Structure and dynamics of aqueous solutions from PBE-based first-principles molecular dynamics simulations

Establishing an accurate and predictive computational framework for the description of complex aqueous solutions is an ongoing challenge for density functional theory based first-principles molecular dynamics (FPMD) simulations. In this context, important advances have been made in recent years, including the development of sophisticated exchange-correlation functionals. On the other hand, simulations based on simple generalized gradient approximation (GGA) functionals remain an active field, particularly in the study of complex aqueous solutions due to a good balance between the accuracy, computational expense, and the applicability to a wide range of systems. In such simulations we often perform them at elevated temperatures to artificially “correct” for GGA inaccuracies in the description of liquid water; however, a detailed understanding of how the choice of temperature affects the structure and dynamics of other components, such as solvated ions, is largely unknown. In order to address this question, we carried out a series of FPMD simulations at temperatures ranging from 300 to 460 K for liquid water and three representative aqueous solutions containing solvated Na + , K + , and Cl - ions. We show that simulations at 390–400 K with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional yield water structure and dynamics in good agreement with experiments at ambient conditions. Simultaneously, this computational setup provides ion solvation structures and ion effects on water dynamics consistent with experiments. These results suggest that an elevated temperature around 390–400 K with the PBE functional can be used for the description of structural and dynamical properties of liquid water and complex solutions with solvated ions at ambient conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗