Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “function approximation”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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)↗
DOE OSTI2022

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

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

A sparse Gaussian sigmoid basis function approximation of hyperspectral data for detection of solids

We define a new characterization of emissivity and reflectance curves for compositional exploitation of hyperspectral data. Here, our method decomposes each spectrum into a sparse set of Gaussian sigmoid components using penalized regression. Detection is based on the combination of Gaussian sigmoid components unique to a target material. Focusing on the presence of spectral upslopes and downslopes rather than spectral correlations makes detection more robust to both target variation and spectral variability from atmosphere and background encountered during the collection process. We present simulation studies that demonstrate the potential to reduce false positive rates without compromising sensitivity. Characterization of long–wave infrared (LWIR) experimental data validates our method using minerals of different particle sizes, measurement angles, and collection conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

How Accurate Are Approximate Density Functionals for Noncovalent Interaction of Very Large Molecular Systems?

Noncovalent intermolecular interactions are very important in many research areas. Therefore, it is vital to understand the extent to which approximate density functionals give a proper description of noncovalent interactions. Previous research has demonstrated that some approximate density functionals can predict usefully accurate interaction energies for many noncovalent systems; however, most of that work is limited to small and moderate-sized molecules. Very recently though, accurate benchmarks have become available for some very large molecules. Here, the present work applies 21 approximate density functionals to compute the binding energies of seven large molecular systems that have a number of atoms ranging from 200 to 910. The results are judged by comparison to the recently published CIM-DLPNO-CCSD(T) results, which are assumed to provide a reliable benchmark. The five most accurate methods among those tested are found to be PW6B95-D4, PW6B95-D3(BJ), revM11, M06-L, and MN15.

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

The Impulse Approximation Scattering Function and Its Use in Monte Carlo Photon Transport Simulations

The viability of using the impulse approximation scattering function in Monte Carlo photon transport simulations is explored. This scattering function can be constructed from the double differential incoherent scattering cross section developed by Ribberfors and Berggren. A commonly used method for modeling photon Doppler broadening, which is referred to as the hybrid Doppler broadening method, can also be derived from this cross section. A new photon Doppler broadening method, called the consistent Doppler broadening method, is derived and discussed. This method eliminates some of the commonly employed approximations in the hybrid Doppler broadening method, in part, by using the impulse approximation scattering function. Integrated incoherent cross sections generated using the impulse approximation scattering function and the widely used Waller-Hartree scattering function are in good agreement above 20 keV. Below 20 keV, differences as high as 70% are observed, which differs from the roughly 5% differences observed by Ribberfors for some of the materials. Integral and spectral quantities for two problems are also generated using the Monte Carlo photon transport capabilities of the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). Due to the small, relative result differences observed when using the impulse approximation scattering function, it is considered a viable alternative to the Waller-Hartree scattering function. In addition, some small, but expected, differences in spectral fluxes at low energies can be avoided by adopting the consistent Doppler broadening method.

42 ENGINEERING↗