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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and applications

Here, the increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH 3 ) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Toward machine-learning-assisted PW-class high-repetition-rate experiments with solid targets

We present progress in utilizing a machine learning (ML) assisted optimization framework to study the trends in a parameter space defined by spectrally shaped, high-intensity, petawatt-class (8 J, 45 fs) laser pulses interacting with solid targets and give the first simulation-based overview of predicted trends. A neural network (NN) incorporating uncertainty quantification is trained to predict the number of hot electrons generated by the laser–target interaction as a function of pulse shaping parameters. The predictions of this NN serve as the basis function for a Bayesian optimization framework to navigate this space. For post-experimental evaluation, we compare two separate neural network (NN) models. One is based solely on data from experiments, and the other is trained only on ensemble particle-in-cell simulations. Reviewing the predicted and observed trends across the experiment-capable laser parameter search space, we find that both ML models predict a maximal increase in hot electron generation at a level of approximately 12%–18%; however, no statistically significant enhancement was observed in experiments. On direct comparison of the NN models, the average discrepancy is 8.5%, with a maximum of 30%. Since shot-to-shot fluctuations in experiments affect the observations, we evaluate the behavior of our optimization framework by performing virtual experiments that vary the number of repeated observations and the noise levels. Here, we discuss the implications of such a framework for future autonomous exploration platforms in high-repetition-rate experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

An Algorithm for Atom-Centered Lossy Compression of the Atomic Orbital Basis in Density Functional Theory Calculations

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn–Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. Here, in this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10 –ϵ , by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree–Fock functional and taking the converged density matrix as input suggest that a threshold of 10 –5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10 –7 , while the compression factor is typically between 2 and 2.5.

basis sets↗
DOE OSTI2024

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Chemistry↗
DOE OSTI2024

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

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

Resolving local structural motifs across the phase evolution of zinc titanates with computational x-ray absorption spectroscopy

Resolving the local structure motifs that characterize phase evolution as a function of composition is a key challenge in structure characterization of complex materials. Here, in this study, we combine first-principles simulations and x-ray absorption near-edge structures (XANES) analysis to gain insights into the structure evolution revealed by measurements across a combinatorial zinc titanate thin film, which was grown with smoothly varying composition over a wide range of the Ti:Zn ratio. Specifically, we propose a cluster blind-signal-separation (cBSS) method for XANES spectral analysis based on a library of the structures and spectra of representative local motifs. In addition to motifs from zinc titanate crystals, two types of Ti-defect models constructed in this study are key to the understanding of the structure characteristics in the Zn-rich region. The cBSS method makes use of both spectral clustering of the simulated site-XANES spectra library and the BSS procedure to construct high-fidelity spectral basis functions from an experimental spectral sequence. The method provides a rigorous measure of the spectral sensitivity and basis completeness. The results of the XANES analysis are corroborated with other experimental modalities, including x-ray diffraction and spectroscopic ellipsometry, to validate the cBSS method. The calculated motif weights resulting from fitting the XANES spectra with the cBSS basis probe the atomic structure characteristics of both crystalline and amorphous phases as a function of the Ti/Zn composition. The insights of the local structure motif evolution are pivotal to the understanding of the nonmonotonic trend in the optical gap, which may lead to potential applications through tuning the optical properties of zinc titanate. The workflow of the XANES spectral analysis developed in this work can be generalized to construct the structure-property relationship in a broad material space.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Superluminal matter waves

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2024

MolSym : A Python package for handling symmetry in molecular quantum chemistry

A consideration of the point group symmetry of molecules is often advantageous from a computational efficiency standpoint and sometimes necessary for the correct treatment of chemical physics problems. Many modern electronic structure software packages include a treatment of symmetry, but these are sometimes incomplete or unusable outside of that program’s environment. Therefore, we have developed the MolSym package for handling molecular symmetry and its associated functionalities to provide a platform for including symmetry in the implementation and development of other methods. Features include point group detection, molecule symmetrization, arbitrary generation of symmetry element sets and character tables, and symmetry adapted linear combinations of real spherical harmonic basis functions, Cartesian displacement coordinates, and internal coordinates. We present some of the advantages of using molecular symmetry as achieved by MolSym, particularly with respect to Hartree–Fock theory, and the reduction of finite difference displacements in gradient/Hessian computations. Furthermore, this package is designed to be easily integrated into other software development efforts and may be extended to further symmetry applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Efficient online quantum circuit learning with no upfront training

Optimization is a promising candidate for studying the utility of variational quantum algorithms (VQAs). However, evaluating cost functions using quantum hardware introduces runtime overheads that limit exploration. Surrogate-based methods can reduce calls to a quantum computer, yet existing approaches require hyperparameter pre-training and have been tested only on small problems. Here, we show that surrogate-based methods can enable successful optimization at scale, without pre-training, by using radial basis function interpolation (RBF) to construct an adaptive, hyperparameter-free surrogate. Using the surrogate as an acquisition function drives hardware queries to the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut instances with the Quantum Approximate Optimization Algorithm (QAOA), our method outperforms state-of-the-art approaches, without considering their upfront training costs. Furthermore, we successfully optimize QAOA circuits for 127-qubit random Ising models on an IBM processor using 10 4 −10 5 measurements. Strong empirical performance demonstrates the promise of automated surrogate-based learning for large-scale VQA applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗
DOE OSTI2024

Predicting responses to climate change using a joint species, spatially dependent physiologically guided abundance model

Abstract Predicting the effects of warming temperatures on the abundance and distribution of organisms under future climate scenarios often requires extrapolating species–environment correlations to climatic conditions not currently experienced by a species, which can result in unrealistic predictions. For poikilotherms, incorporating species' thermal physiology to inform extrapolations under novel thermal conditions can result in more realistic predictions. Furthermore, models that incorporate species and spatial dependencies may improve predictions by capturing correlations present in ecological data that are not accounted for by predictor variables. Here, we present a joint species, spatially dependent physiologically guided abundance (jsPGA) model for predicting multispecies responses to climate warming. The jsPGA model uses a basis function approach to capture both species and spatial dependencies. We apply the jsPGA model to predict the response of eight fish species to projected climate warming in thousands of lakes in Minnesota, USA. By the end of the century, the cold‐adapted species was predicted to have high probabilities of extirpation across its current range—with 10% of lakes currently inhabited by this species having an extirpation probability >0.90. The remaining species had varying levels of predicted changes in abundance, reflecting differences in their thermal physiology. Though the model did not identify many strong species dependencies, the variation in estimated spatial dependence across species suggested that accounting for both dependencies was important for predicting the abundance of these fishes. The jsPGA model provides a new tool for predicting changes in the abundance, distribution, and extirpation probability of poikilotherms under novel thermal conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Kinematic flow for cosmological loop integrands

Recently, an interesting pattern was found in the differential equations satisfied by the Feynman integrals describing tree-level correlators of conformally coupled scalars in a power-law FRW cosmology [1, 2]. It was proven that simple and universal graphical rules predict the equations for arbitrary graphs as a flow in kinematic space. In this note, we show that the same rules — with one small addition — also determine the differential equations for loop integrands. We explain that both the basis of master integrals and the singularities of the differential equations can be represented by tubings of marked graphs. An important novelty in the case of loops is that some basis functions can vanish, and we present a graphical rule to identify these vanishing functions. Taking this into account, we then demonstrate that the kinematic flow correctly predicts the differential equations for all loop integrands.

Cosmological models↗
DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗