Search NASA⌕ Search

SEARCH · Search NASA

Results for “functional 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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods

The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

2D materials↗
DOE OSTI2024

Unsupervised Learning for Equitable DER Control: Preprint

In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.

asymptotic stability↗
DOE OSTI2026

Improved energies and local energies with weighted variational Monte Carlo

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Spatial Correlations of the Poisson Model for Radiation Transport

Characterizing the relationship between bulk physical properties and mixing in randomly heterogeneous media is a central challenge across many areas of science and engineering. A benchmark model for such studies is the Poisson model, a random tessellation of space by a Poisson process of hyperplanes. In radiation transport studies, the lack of exact expressions for the Poisson model’s spatial multipoint functions has led to approximate methods being used, introducing unquantified sources of error. Here, we recently introduced an exact solution for the Poisson model’s multipoint functions and closely related conditional probability functions (CPFs), providing a new opportunity to understand and reduce these sources of error. In this paper, we enable a more rigorous investigation of radiation transport in stochastic media by applying the recently introduced exact solution for the Poisson model’s CPFs. This paper consists of three main contributions. First, we introduce a unified framework for CPFs of the Poisson model, encompassing the recently introduced exact CPFs as well as the previously introduced atomic mix, nearest-neighbor, and combination CPFs. This framework also includes existing pruning techniques for the approximate CPFs, such as angular exclusion, as well as a novel form of angular exclusion suitable for the exact CPFs. Second, we use the exact CPFs to characterize the spatial regions where each approximate three-point CPF is most accurate, thereby explaining the observed hierarchy of accuracy among the approximate models. Finally, we evaluate material transmittance, reflectance, and flux in a three-dimensional test problem using conditional point sampling, demonstrating the relationship between CPF accuracy and transport simulation accuracy.

Poisson model↗
DOE OSTI2025

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Magnetic dipole γ-ray strength functions in the crossover from spherical to deformed neodymium isotopes

We calculate the magnetic dipole $\gamma$-ray strength functions in a chain of even-mass neodymium isotopes $^{144-152}$Nd in the framework of the configuration-interaction (CI) shell model. We infer the strength function by applying the maximum entropy method (MEM) to the exact imaginary-time response function calculated with the shell-model Monte Carlo (SMMC) method. The success of the MEM depends on the choice of a good strength function as a prior distribution. We investigate two choices for the prior strength function: the static path approximation (SPA) and the quasiparticle random-phase approximation (QRPA). We find that the QRPA is a better approximation at low temperatures (i.e., near the ground state), while the SPA is a better choice at finite temperatures. We identify a low-energy enhancement (LEE) in the MEM deexcitation $M1$ strength functions of the even-mass neodymium isotopes and compare with recent experimental results for the total deexcitation $\gamma$-ray strength functions. The LEE is already seen in the SPA strength function but not in the QRPA strength function, indicating the importance of large-amplitude static fluctuations around the mean field in reproducing the LEE. Our method is currently the only one which can reproduce LEE in heavy open-shell nuclei where conventional CI shell model calculations are prohibited. With the onset of deformation as number of neutrons increases along the chain of neodymium isotopes, we observe that some of the LEE strength transfers to a low-energy excitation, which we interpret as a finite-temperature ``scissors'' mode. Here, we also observe a finite-temperature spin-flip mode.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Investigation of Ethane Dehydrogenation and Hydrogenolysis on Pt(111), Pt(211), and Pt(100): Bayesian Quantification and Correction of DFT-Based Enthalpic and Entropic Uncertainties

Computational investigations of heterogeneously catalyzed reactions using density functional theory (DFT) are often inaccurate, largely due to uncertainties in the choice of DFT functional (enthalpic uncertainty) and approximations for modeling adsorbate movement along the catalyst surface (entropic uncertainty). This work illustrates that both uncertainties are significant in the investigation of ethane dehydrogenation (EDH) and hydrogenolysis on Pt catalysts by considering the complete deconstruction of ethane on Pt(111), Pt(211), and Pt(100) using microkinetic modeling (MKM). Hence, this work uses both noncalibrated and Bayesian-calibrated MKMs to quantify and correct inaccuracies in macroscopic properties due to both uncertainties. A Bayesian approach to the correction of entropic errors was introduced using a “Modified Fermi Function (MFF)” to calibrate between the two bounds of entropy represented by the harmonic oscillator (HO) and free translator (FT) approximations. Regardless of enthalpic and entropic uncertainties, all three surfaces are capable of ethane activation; however, Pt(211) was found to be the most active and is largely responsible for methane production. Next, Pt(111) is largely responsible for acetylene production, and Pt(100) has the highest ethylene selectivity but is most susceptible to coking. By comparison of different calibrated models, the FT entropy approximation was found to better describe EDH under typical experimental conditions. Statistical evidence was found to support Pt(111) as the active site for EDH, assuming that one single site is responsible for the chemistry. On the three surfaces, competing second dehydrogenations to CH 2 CH 2 and CH 3 CH were observed as well as isomerization of CH 3 CH back to CH 2 CH 2 and deeper dehydrogenation of CH 3 CH. In conclusion, C–C cleavage was found to largely proceed via the CH 3 C intermediate on Pt(100) and Pt(111), while on Pt(211), it was via both CHC and CH 3 C.

Bayesian model selection↗
DOE OSTI2025

Electron capture of superheavy nuclei with realistic lepton wave functions

The superheavy nuclei push the periodic table of the elements and the chart of the nuclides to their limits, providing a unique laboratory for studies of the electron-nucleus interactions. The most important weak decay mode in known superheavy nuclei is electron capture (EC). In the standard calculations of EC, the lepton wave functions are usually considered in the lowest-order approximation. In this work, we investigate the sensitivity of EC rates on the choice of the electron wave functions by (i) assuming the single-particle approximation for the electron wave functions, and (ii) carrying out Dirac-Hartree-Fock (DHF) calculations. The nuclear response is generated based on the state-of-the-art quasiparticle random phase approximation employing relativistic nuclear energy density functional theory. Here, we show that using the improved lepton wave functions reduces the EC rates up to 40% in the superheavy nucleus oganesson (𝑍=118). Interestingly, because of screening effects, the difference between the EC rates obtained with the DHF and single-particle calculations is fairly small.

Atomic orbital↗
DOE OSTI2025

Evaluating the gradients of localized diabatic state energies and couplings at minimum cost

We calculate the gradients of Boys diabatic state energies and couplings when the electronic vector space is generated by configuration interaction singles. Our approach follows the Lagrangian approach of Paz and Glover (rather than direct differentiation of the adiabatic-to-diabatic approaches that have been published previously). The result is that we achieve a dramatic increase in savings over previous approaches, and the present approach should be immediately useful to scientists focused on electronic relaxation, especially chemists studying electron transfer who wish to go beyond the Condon approximation. Here, a future extension to time-dependent density functional theory in the Tamm–Dancoff approximation is clear.

Chemical physics↗
DOE OSTI2024

Revisiting Artifacts of Kohn–Sham Density Functionals for Biosimulation

We revisit the problem of unphysical charge density delocalization/fractionalization induced by the self-interaction error of common approximate Kohn–Sham (KS) density functional theory functionals on simulation of small to medium-sized proteins in a vacuum. Aside from producing unphysical electron densities and total energies, the vanishing of the HOMO–LUMO gap associated with the unphysical charge delocalization leads to an unphysical low-energy spectrum and catastrophic failure of most popular solvers for the KS self-consistent field (SCF) problem. We apply a robust quasi-Newton SCF solver to obtain solutions for some of these difficult cases. The anatomy of the charge delocalization is revealed by the natural deformation orbitals obtained from the density matrix difference between the Hartree–Fock and KS solutions; the charge delocalization not only can occur between charged fragments (such as in zwitterionic polypeptides) but also involves neutral fragments. The vanishing-gap phenomenon and troublesome SCF convergence are both attributed to the unphysical KS Fock operator eigenspectra of molecular fragments (e.g., amino acids or their side chains). Analysis of amino acid pairs suggests that the unphysical charge delocalization can be partially ameliorated by the use of some range-separated hybrid functionals but not by semilocal or standard hybrid functionals. Last, we demonstrate that solutions without the unphysical charge delocalization can be located even for semilocal KS functionals highly prone to such defects, but such solutions have non-Aufbau character and are unstable with respect to mixing of the non-overlapping “frontier” orbitals. Caution should be exercised when unexpectedly small (or vanishing) HOMO–LUMO gaps and atypical SCF convergence patterns (e.g., oscillatory) are observed in KS DFT simulations in any context (bio or otherwise).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Many-Body Benchmark of Electronic Charge and Spin Densities for Li 1–x NiO 2

Accurate benchmarks are particularly important for highly correlated oxides as mean-field approximations often fail to describe the subtle balance of charge transfer and magnetism in these materials with an accuracy comparable to experimental needs. Here we present accurate diffusion Monte Carlo (DMC) results of the electronic charge and spin densities for the tunable highly correlated oxide Li 1–x NiO 2 for x = 0, 1/2, and 1. To enable quantitative comparisons, we introduce a robust density-partitioning scheme, extending Voronoi analysis to assign atomic charges from spatially noisy DMC densities. We then benchmark common approximations used in density functional theory (DFT). Comparison against DMC shows that r 2 SCAN delivers the most balanced performance across charge, spin, and radial density descriptors, nearly reproducing DMC results for LiNiO 2 and apical Ni sites in Li 0.5 NiO 2 . Hybrid functionals (PBE0, SCAN0) perform unexpectedly poorly, and PBE + U + V yields inconsistent trends between charge and spin densities. Therefore, the r 2 SCAN functional minimizes errors relative to DMC while capturing the variable valence of the Ni ion and also retaining the computational efficiency of DFT for large-scale simulations of the tunable structural and electronic phases of Li1−xNiO2. Our study highlights the importance of accurate benchmarking of the fundamental quantities involved in DFT to select appropriate DFT approximations in order to advance the predictive modeling of charge-transfer-driven phenomena in correlated electron systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences↗
DOE OSTI2026

Augmenting subspace optimization methods with linear bandits

In this work, we consider the framework of methods for unconstrained minimization that are, in each iteration, restricted to a model that is only a valid approximation to the objective function on some affine subspace containing an incumbent point. These methods are of practical interest in computational settings where derivative information is either expensive or impossible to obtain. Recent attention has been paid in the literature to employing randomized matrix sketching for generating the affine subspaces within this framework. We consider a relatively straightforward, deterministic augmentation of such a generic subspace optimization method. In particular, we consider a sequential optimization framework where actions consist of one-dimensional linear subspaces and rewards consist of (approximations to) the magnitudes of directional derivatives computed in the direction of the action subspace. Reward maximization in this context is consistent with maximizing lower bounds on descent guaranteed by first-order Taylor models. This sequential optimization problem can be analysed through the lens of dynamic regret. We modify an existing linear upper confidence bound (UCB) bandit method and prove sublinear dynamic regret in the subspace optimization setting. We demonstrate the efficacy of employing this linear UCB method in a setting where forward-mode algorithmic differentiation can provide directional derivatives in arbitrary directions and in a derivative-free setting. For the derivative-free setting, we propose SS-POUNDers, an extension of the derivative-free optimization method POUNDers that employs the linear UCB mechanism to identify promising subspaces. Our numerical experiments suggest a preference, in either computational setting, for employing a linear UCB mechanism within a subspace optimization method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Ensemble density functional theory (EDFT) is a generalization of ground-state DFT, which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional 'particle in a box' systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and local spin density approximation exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Comparison of Electronic Structure Methods for Predicting the Hydrogenation Energies of Candidate Molecules for Hydrogen Storage

The development of novel energy materials and fuels is required to expand current available energy sources. Aiming to reach this goal, there is growing interest in using molecular hydrogen as an energy carrier due to its abundance and high energy density. Liquid organic hydrogen carriers (LOHCs) are a promising route to the large-scale storage and transport of hydrogen for use in the energy economy. The search for thermodynamically viable LOHC molecules for real world use has led to a set of constraints on the dehydrogenation enthalpy and the minimum gravimetric hydrogen capacity. These constraints allow one to formulate the search for an ideal LOHC candidate molecule as an optimization problem well suited to the strengths of machine learning and artificial intelligence computational approaches. A critical barrier to a large-scale, high-throughput screening of LOHC candidate molecules is the lack of reliable training data. Computational electronic structure methods including density functional theory, coupled cluster approximations, and diffusion Monte Carlo can be used to provide training data where experimental data are either unreliable or do not exist. In this work, we use these methods to calculate the dehydrogenation energies and enthalpies of candidate LOHC molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗