Search NASA⌕ Search

SEARCH · Search NASA

Results for “Polynomials”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Creation of an Fe 3 P Schreibersite Density Functional Tight Binding Model for Astrobiological Simulations

The mineral schreibersite, e.g., Fe 3 P, is commonly found in iron-rich meteorites and could have served as an abiotic phosphorus source for prebiotic chemistry. However, atomistic calculations of its degradation chemistry generally require quantum simulation approaches, which can be too computationally cumbersome to study sufficient time and length scales for this process. In this regard, we have created a computationally efficient semiempirical quantum density functional tight binding (DFTB) model for iron and phosphorus-containing materials by adopting an existing semiautomated workflow that represents many-body interactions by linear combinations of Chebyshev polynomials. Here, we have utilized a relatively small training set to optimize a DFTB model that is accurate for schreibersite physical and chemical properties, including its bulk properties, surface energies, and water absorption. We then show that our model shows strong transferability to several iron phosphide solids as well as multiple allotropes of iron metal. Our resulting DFTB parametrization will allow us to interrogate schreibersite aqueous decomposition at longer time and length scales than standard quantum approaches, providing for more detailed investigations of its role in prebiotic chemistry on early Earth.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗
DOE OSTI2022

Accurate Modeling of Bromide and Iodide Hydration with Data-Driven Many-Body Potentials

Ion–water interactions play a central role in determining the properties of aqueous systems in a wide range of environments. However, a quantitative understanding of how the hydration properties of ions evolve from small aqueous clusters to bulk solutions and interfaces remains elusive. Here, we introduce the second generation of data-driven many-body energy (MBnrg) potential energy functions (PEFs) representing bromide–water and iodide–water interactions. The MB-nrg PEFs use permutationally invariant polynomials to reproduce two-body and three-body energies calculated at the coupled cluster level of theory, and implicitly represent all higher-body energies using classical many-body polarization. Further, a systematic analysis of the hydration structure of small Br - (H 2 O) n and I - (H 2 O) n clusters demonstrates that the MBnrg PEFs predict interaction energies in quantitative agreement with “gold standard” coupled cluster reference values. Importantly, when used in molecular dynamics simulations carried out in the isothermal-isobaric ensemble for single bromide and iodide ions in liquid water, the MB-nrg PEFs predict extended X-ray absorption fine structure (EXAFS) spectra that accurately reproduce the experimental spectra, which thus allows for characterizing the hydration structure of the two ions with high level of confidence.

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

High-Accuracy Semiempirical Quantum Models Based on a Minimal Training Set

A great need exists for computationally efficient quantum simulation approaches that can achieve an accuracy similar to high-level theories at a fraction of the computational cost. In this regard, we have leveraged a machine-learned interaction potential based on Chebyshev polynomials to improve density functional tight binding (DFTB) models for organic materials. The benefit of our approach is two-fold: (1) many-body interactions can be corrected for in a systematic and rapidly tunable process, and (2) high-level quantum accuracy for a broad range of compounds can be achieved with ~0.3% of data required for one advanced deep learning potential. Our model exhibits both transferability and extensibility through comparison to quantum chemical results for organic clusters, solid carbon phases, and molecular crystal phase stability rankings. Overall, our efforts thus allow for high-throughput physical and chemical predictions with up to coupled-cluster accuracy for systems that are computationally intractable with standard approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Formation of Carbon–Carbon Interlinkage Bonds under High Pressure

The formation of carbon–carbon interlinkage bonds (CCIBs) via the chemical binding of interlayer carbon atoms of many sp 2 -bonded carbon precursors is an essential step for synthesizing various diamond and diamond-like materials. Although the existence of CCIBs may be reasonably assumed under high-pressure conditions, direct experimental evidence has been scarce. Micro-Raman spectroscopy is here employed to track in situ the evolution of C–C bonds in a pressure range from ambient to 54 GPa. A pressure-induced two-stage (polynomial and linear) shift of the G peak and new generation of the CCIB peak at about 1550 cm –1 are observed in multiple types of layer-structured carbon precursors, including glassy carbon, natural graphite, and carbon nanotubes. In conclusion, the experimental discovery of CCIBs holds significance in comprehending phase transitions of sp 2 -bonded carbon materials and has implications for the advancement of novel carbon structures.

Anode materials↗
DOE OSTI2021

Topological Effects Near Order–Disorder Transitions in Symmetric Diblock Copolymer Melts

The effects of polymer chain topology on the order–disorder transition of symmetric AB diblock copolymer melts are studied using coarse-grained molecular dynamics simulations. Specifically, we compared chain conformations near the lamellar-disordered transition in melts of symmetric (i.e., 50–50) AB diblock copolymers of linear chains, rings, and trefoil knots at the same chain lengths. The order (lamellar)–disorder transition temperature and the domain sizes both shifted to lower values with the introduction of topological constraints, leading to the following sequence: linear chains > rings > trefoil knots. Furthermore, investigation of the polymer chain conformations in terms of their radii of gyration, their writhe values (a measure for the degree of intertwining of a chain around itself), and their Jones polynomials (a method to measure entanglement of curves) showed that linear chains and rings remained stretched, while knots were stretched and tightened in disordered melts close to the lamellar-disorder transition. This work highlights chain topology as an important factor in affecting microphase separation in block copolymers.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Statistical Multiobjective Optimization of Thiospinel CoNi 2 S 4 Nanocrystal Synthesis via Design of Experiments

Thiospinels, such as CoNi 2 S 4 , are showing promise for numerous applications, including as catalysts for the hydrogen evolution reaction, hydrodesulfurization, and oxygen evolution and reduction reactions; however, CoNi 2 S 4 has not been synthesized as small, colloidal nanocrystals with high surface-area-to-volume ratios. Traditional optimization methods to control nanocrystal attributes such as size typically rely upon one variable at a time (OVAT) methods that are not only time and labor intensive but also lack the ability to identify higher-order interactions between experimental variables that affect target outcomes. Herein, we demonstrate that a statistical design of experiments (DoE) approach can optimize the synthesis of CoNi 2 S 4 nanocrystals, allowing for control over the responses of nanocrystal size, size distribution, and isolated yield. After implementing a 2 5–2 fractional factorial design, the statistical screening of five different experimental variables identified temperature, Co:Ni precursor ratio, Co:thiol ratio, and their higher-order interactions as the most critical factors in influencing the aforementioned responses. Second-order design with a Doehlert matrix yielded polynomial functions used to predict the reaction parameters needed to individually optimize all three responses. A multiobjective optimization, allowing for the simultaneous optimization of size, size distribution, and isolated yield, predicted the synthetic conditions needed to achieve a minimum nanocrystal size of 6.1 nm, a minimum polydispersity (σ/$\bar{d}$) of 10%, and a maximum isolated yield of 99%, with a desirability of 96%. The resulting model was experimentally verified by performing reactions under the specified conditions. Furthermore, our work illustrates the advantage of multivariate experimental design as a powerful tool for accelerating control and optimization in nanocrystal syntheses.

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

High-Throughput Screening and Accurate Prediction of Ionic Liquid Viscosities Using Interpretable Machine Learning

Ionic liquids (ILs) are a novel group of green solvents with great promise for various industrial applications, including carbon capture and lignocellulosic biomass deconstruction. However, the use of ILs at the industrial scale remains challenging due to their high viscosities at ambient temperatures. To develop ILs with lower viscosities, a systematic study of their quantitative structure–property relationship (QSPR) is desirable. Here, we developed four machine learning (ML) models to predict viscosity at various temperature and pressure ranges, trained over a wide range of ILs consisting of various cationic and anionic families. ML methods including two-factor polynomial regression (two-factor PR), support vector regression (SVR), feed-forward neural networks (FFNN), and categorical boosting (CATBoost) were developed based on features that have proven useful in previous ML studies: COSMO-RS (conductor-like screening model for real solvents)-derived surface screening charge densities (sigma profiles). FFNN and CATBoost were the most accurate in predicting IL viscosities with lower average absolute relative deviation and higher R2 values on the test set. Tanimoto similarity scores were calculated to characterize the chemical space and structural similarity of the investigated ions. Furthermore, SHapley Additive exPlanation (SHAP) analysis was employed to interpret the ML results. Temperature, the polar area of ILs, and the nonpolar regions of ions are key features that influence the viscosity predictions. Importantly, the IL viscosity prediction here is the most accurate reported to date.

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

Statistical White-Line Analysis in High-Throughput TXM-XANES for Chemical State Quantification

The transmission X-ray microscopy (TXM) based X-ray absorption near-edge structure (XANES) technique provides three-dimensional mapping of element-specific chemical states at nanometer-scale spatial resolution and micrometer-scale fields of view. However, compared to conventional volume-averaged XANES (VA-XANES) measurements, the inherently small voxel size in TXM-XANES leads to a lower signal-to-noise ratio, making full-spectrum analysis computationally demanding and less robust. Here, we present the structural and compositional conditions for a statistical white-line analysis framework under which chemical state information can be directly extracted from the white-line peak position in voxel spectra without the need for voxel-wise background subtraction or normalization, under well-defined structural and compositional conditions. The method is validated on layered oxide cathode materials, where low-order polynomial fitting accurately reproduces white-line features, and the extracted energy distributions correlate strongly with VA-XANES results. This statistical approach enables high-throughput, dose-efficient, and noise-robust chemical state quantification in TXM-XANES, offering broad applicability to functional materials requiring nanoscale oxidation-state mapping.

TXM↗
DOE OSTI2020

The Role of Subsurface Flow on Evapotranspiration: A Global Sensitivity Analysis

Abstract Water resources are impacted by water‐energy balance fluxes at the land surface, most notably evapotranspiration ( ET ), the largest component of surface energy balance. While integrated hydrologic models show promise in quantifying the nonlinear dynamics at this interface, the model results are plagued by parametric uncertainties. Given the high computational demand of running multiple parameter spaces of these models, little is known about how these uncertainties propagate into land surface processes. In this work, we perform a global sensitivity analysis by computing Sobol and AMAE indices using a surrogate model constructed with a polynomial chaos expansion to assess the impacts of the subsurface physical properties on ET . We do so by modeling a semisynthetic test case. Our results show that the effects of vertical hydraulic conductivity, porosity, and the water retention curve parameter Van Genuchten α mainly control ET . However, we note that while evaporation ( E ) shows behavior similar to the ET with high sensitivity to the parameters controlling the flow in the unsaturated zone, transpiration ( T ) is very sensitive to the saturated zone parameters and groundwater flow, especially during periods without rain. Our results also show that heterogeneities in land cover impact the flow in the saturated zone. Furthermore, our work demonstrates that reduced‐order models can be developed to make integrated models more accessible for rigorous sensitivity analyses and calibration purposes.

Maina, Fadji Zaouna↗
DOE OSTI2020

Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies

Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.

Rudi, Johann↗
DOE OSTI2023

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.

58 GEOSCIENCES↗
DOE OSTI2024

Autocalibration of the E3SM Version 2 Atmosphere Model Using a PCA-Based Surrogate for Spatial Fields

Global Climate Model tuning (calibration) is a tedious and time-consuming process, with high-dimensional input and output fields. Experts typically tune by iteratively running climate simulations with hand-picked values of tuning parameters. Many, in both the statistical and climate literature, have proposed alternative calibration methods, but most are impractical or difficult to implement. We present a practical, robust, and rigorous calibration approach on the atmosphere-only model of the Department of Energy's Energy Exascale Earth System Model (E3SM) version 2. Our approach can be summarized into two main parts: (a) the training of a surrogate that predicts E3SM output in a fraction of the time compared to running E3SM, and (b) gradient-based parameter optimization. To train the surrogate, we generate a set of designed ensemble runs that span our input parameter space and use polynomial chaos expansions on a reduced output space to fit the E3SM output. We use this surrogate in an optimization scheme to identify values of the input parameters for which our model best matches gridded spatial fields of climate observations. To validate our choice of parameters, we run E3SMv2 with the optimal parameter values and compare prediction results to expertly-tuned simulations across 45 different output fields. This flexible, robust, and automated approach is straightforward to implement, and we demonstrate that the resulting model output matches present day climate observations as well or better than the corresponding output from expert tuned parameter values, while considering high-dimensional output and operating in a fraction of the time.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is Ο(logn). Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Active learning of reactive Bayesian force fields applied to heterogeneous catalysis dynamics of H/Pt

Abstract Atomistic modeling of chemically reactive systems has so far relied on either expensive ab initio methods or bond-order force fields requiring arduous parametrization. Here, we describe a Bayesian active learning framework for autonomous “on-the-fly” training of fast and accurate reactive many-body force fields during molecular dynamics simulations. At each time-step, predictive uncertainties of a sparse Gaussian process are evaluated to automatically determine whether additional ab initio training data are needed. We introduce a general method for mapping trained kernel models onto equivalent polynomial models whose prediction cost is much lower and independent of the training set size. As a demonstration, we perform direct two-phase simulations of heterogeneous H 2 turnover on the Pt(111) catalyst surface at chemical accuracy. The model trains itself in three days and performs at twice the speed of a ReaxFF model, while maintaining much higher fidelity to DFT and excellent agreement with experiment.

42 ENGINEERING↗
DOE OSTI2022

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as $\sqrt{T/N}$. When only K$\ll$T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $\sqrt{K/N}$. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗