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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 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

High-throughput predictions of metal–organic framework electronic properties: theoretical challenges, graph neural networks, and data exploration

Abstract With the goal of accelerating the design and discovery of metal–organic frameworks (MOFs) for electronic, optoelectronic, and energy storage applications, we present a dataset of predicted electronic structure properties for thousands of MOFs carried out using multiple density functional approximations. Compared to more accurate hybrid functionals, we find that the widely used PBE generalized gradient approximation (GGA) functional severely underpredicts MOF band gaps in a largely systematic manner for semi-conductors and insulators without magnetic character. However, an even larger and less predictable disparity in the band gap prediction is present for MOFs with open-shell 3 d transition metal cations. With regards to partial atomic charges, we find that different density functional approximations predict similar charges overall, although hybrid functionals tend to shift electron density away from the metal centers and onto the ligand environments compared to the GGA point of reference. Much more significant differences in partial atomic charges are observed when comparing different charge partitioning schemes. We conclude by using the dataset of computed MOF properties to train machine-learning models that can rapidly predict MOF band gaps for all four density functional approximations considered in this work, paving the way for future high-throughput screening studies. To encourage exploration and reuse of the theoretical calculations presented in this work, the curated data is made publicly available via an interactive and user-friendly web application on the Materials Project.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A modified cosmic brane proposal for holographic Renyi entropy

We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi index n ≥ 1, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. For n < 1, however, our proposal predicts a new phase with leading order (in Newton’s constant G) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: for n < 1, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to the n < 1 Renyi entropies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2021

Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics

The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive “full-wave” simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. Furthermore, the numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves on previously derived analytical approximations of the MGO integral.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Digitization and subduction of S U ( N ) gauge theories

The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still need to be clarified. To gain insights, we investigate the subduction of S U ( 2 ) and S U ( 3 ) to discrete crystal-like subgroups. Using classical lattice calculations, we show that subduction offers valuable information based on subduced direct sums, helping us identify additional terms to incorporate into the lattice action that can mitigate the effects of digitization. Furthermore, we compute the static potentials of all irreducible representations of Σ ( 360 × 3 ) at a fixed lattice spacing. Our results reveal a percent-level agreement with the Casimir scaling of S U ( 3 ) for irreducible representations that subduce to a single Σ ( 360 × 3 ) irreducible representation. This provides a diagnostic measure of approximation quality, as some irreducible representations closely match the expected results while others exhibit significant deviations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Computed Tomography Scans of Naturally Mineralized Fractures in Upper Wolfcamp Shale

Computed tomography scans of fractures in small samples of Wolfcamp Shale from the Permian Basin and a depth of approximately 10,400 feet that have been cemented through natural processes. These samples were CT scanned at NETL. The data sets compliment the manuscript by Hajirezaie et al entitled "Mineral characterization of a sealed fracture: A multiscale multimodal imaging study of a syntaxial vein"

Computed Tomography↗
DOE OSTI2023

Two-point correlator of twist-2 light-ray operators in N=4 SYM in BFKL approximation

We generalize local operators of the leading twist-2 of N = 4 SYM theory to the case of complex Lorentz spin j using principal series representation of sl(2,R). We give the direct computation of correlation function of two such non-local operators in the BFKL regime when j → 1. The correlator appears to have the expected conformal coordinate dependence governed by the anomalous dimension of twist-2 operator in NLO BFKL approximation predicted by Kotikov and Lipatov.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

First-Principles-Based Machine Learning Models for Phase Behavior and Transport Properties of CO 2

In this work, we construct distinct first-principles-based machine-learning models of CO 2 , reproducing the potential energy surface of the PBE-D3, BLYP-D3, SCAN and SCAN-rvv10 approximations of density functional theory. Here we employ the Deep Potential methodology to develop the models and consequently achieve a significant computational efficiency over ab initio molecular dynamics (AIMD) that allows for larger system sizes and time scales to be explored. Although our models are trained only with liquid phase configurations, they are able to simulate a stable interfacial system and predict vapor-liquid equilibrium properties, in good agreement with results from the literature. Because of the computational efficiency of the models, we are also able to obtain transport properties, such as viscosity and diffusion coefficients. We find that the SCAN-based model presents a temperature shift in the position of the critical point, while the SCAN-rvv10-based model shows improvement but still exhibits a temperature shift that remains approximately constant for all properties investigated in this work. We find that the BLYP-D3-based model generally performs better for liquid phase and vapor-liquid equilibrium properties, but the PBE-D3-based model is better suited for predicting transport properties.

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

Lower bounds on circuit depth of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which classes of problems are best suited for it. One factor in demonstrating quantum advantage is the relationship between a problem instance and the circuit depth required to implement the QAOA method. As errors in noisy intermediate-scale quantum (NISQ) devices increase exponentially with circuit depth, identifying lower bounds on circuit depth can provide insights into when quantum advantage could be feasible. In this work, we identify how the structure of problem instances can be used to identify lower bounds for circuit depth for each iteration of QAOA and examine the relationship between problem structure and the circuit depth for a variety of combinatorial optimization problems including MaxCut and MaxIndSet. Specifically, we show how to derive a graph, G, that describes a general combinatorial optimization problem and show that the depth of circuit is at least the chromatic index of G. By looking at the scaling of circuit depth, we argue that MaxCut, MaxIndSet, and some instances of vertex covering and Boolean satisfiability problems are suitable for QAOA approaches while knapsack and traveling salesperson problems are not.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Real-space formulation of the stress tensor for O (N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O (N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O (N) methods. We then describe its evaluation within the O (N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 10 6 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations

The Raviart–Thomas mixed finite-element method of the lowest order (Raviart and Thomas in mixed finite-element methods for second-order elliptic problems, Lecture Notes in mathematics, Springer, New York, 1977) commonly known as the RT{sub 0} method, is a well-established and popular numerical tool to solve diffusion-like problems providing flux continuity across inter-element boundaries. Douglas and Roberts extended the method to the case of more general second-order boundary-value problems including the convection–diffusion equations (cf. this journal Douglas in Comput Appl Math 1:91–103; 1982). The main drawback of these methods, however, is the poor representation of the primal variable by piecewise constant functions. The Hermite analog of the RT{sub 0} method for treating pure diffusion phenomena proposed in Ruas (J Comput Appl Math, 246:234–242; 2013) proved to be a valid alternative to attain higher order approximation of the primal variable while keeping intact the matrix structure and the quality of the discrete flux variable of the original RT{sub 0} method. Non-trivial extensions of this method are studied here that can be viewed as Hermite analogs of the two Douglas and Roberts’ versions of the RT{sub 0} method, to solve convection–diffusion equations. A detailed convergence study is carried out for one of the Hermite methods, and numerical results illustrate the performance of both of them, as compared to each other and to the corresponding mixed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

The effect of self-interaction error on electrostatic dipoles calculated using density functional theory

Spurious electron self-interaction in density functional approximations (DFAs) can lead to inaccurate predictions of charge transfer in heteronuclear molecules that manifest as errors in calculated electrostatic dipoles. Here we show the magnitude of these errors on dipoles computed for a diverse set of 47 molecules taken from the recent benchmark study of Hait and Head-Gordon. We compare results of Perdew-Wang local spin density approximation (PW92), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriatedly normed (SCAN) meta-GGA dipole calculations, along with those of their respective self-interaction-corrected (SIC) counterparts, to reference values from accurate wave function-based methods. The SIC calculations were carried out using the Fermi-Löwdin orbital (FLO-SIC) approach. We find that correcting for self-interaction generally increases the degree of charge transfer, thereby increasing the size of calculated dipole moments. The FLO-SIC-PW92 and FLO-SIC-PBE dipoles are in better agreement with reference values than their uncorrected DFA counterparts, particularly for strongly ionic molecules where significant improvement is seen. Applying FLO-SIC to SCAN does not improve dipole values overall. In addition, we show that removing self-interaction improves the description of the dipole for stretched-bond geometries and recovers the physically correct separated atom limit of zero dipole. Finally, we find that the best agreement between the FLO-SIC-DFA and reference dipoles occurs when the molecular geometries are optimized using the FLO-SIC-DFA.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

A multi-center quadrature scheme for the molecular continuum

We report a common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Height Above Nearest Drainage (HAND) and Hydraulic Property Table for CONUS

The continental flood inundation mapping (CFIM) framework is a high-performance computing (HPC)-based computational framework for the Height Above Nearest Drainage (HAND)-based inundation mapping methodology. Using the 10m Digital Elevation Model (DEM) data produced by U.S. Geological Survey (USGS) 3DEP (the 3-D Elevation Program) and the NHDPlus hydrography dataset produced by USGS and the U.S. Environmental Protection Agency (EPA), a hydrological terrain raster called HAND is computed for HUC6 units in the conterminous U.S. (CONUS). The value of each raster cell in HAND is an approximation of the relative elevation between the cell and its nearest water stream. Derived from HAND, a hydraulic property table is established to calculate river geometry properties for each of the 2.7 million river reaches covered by NHDPlus (5.5 million kilometers in total length). This table is a lookup table for water depth given an input stream flow value. Such lookup is available between water depth 0m and 25m at 1-foot interval. The flood inundation map is then computed by using HAND and this lookup table based on the near real-time water forecast from the National Water Model (NWM) at the National Oceanic and Atmospheric Administration (NOAA). HAND and the Hydraulic Property Table version 0.2. is created to correspond to data updates in the USGS 1/3 arcsec DEM, the USGS National Hydrography Dataset, including its Water Boundary Dataset, and the NHDPlus medium resolution dataset. This dataset comprises 331 HUC6 units for CONUS (excluding the five great lakes units), each is a downloadable zip file. Version 0.1 was computed at the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urban-Champaign in 2016 and is currently hosted at the Texas Advanced Computing Center (TACC). Please cite this data DOI and the following publications and data DOIs when you use HAND and the hydraulic property table: Liu, Yan Y., David R. Maidment, David G. Tarboton, Xing Zheng, and Shaowen Wang. 'A CyberGIS integration and computation framework for high-resolution continental-scale flood inundation mapping.' JAWRA Journal of the American Water Resources Association 54, no. 4 (2018): 770-784. DOI: 10.1111/1752-1688.12660 Zheng, Xing, David G. Tarboton, David R. Maidment, Yan Y. Liu, and Paola Passalacqua. 'River channel geometry and rating curve estimation using height above the nearest drainage.' JAWRA Journal of the American Water Resources Association 54, no. 4 (2018): 785-806. DOI: 10.1111/1752-1688.12661 Liu, Y. (2018). Height Above Nearest Drainage (HAND) for CONUS - v0.1, HydroShare, https://doi.org/10.4211/hs.69f7d237675c4c73938481904358c789 LICENSE FOR USE -- MAPS AND DATA DISCLAIMER This resource is shared under the Creative Commons Attribution CC BY, http://creativecommons.org/licenses/by/4.0/ MAPS AND DATA DISCLAIMER The Oak Ridge National Laboratory (ORNL) shall not be held liable for improper or incorrect use of the data described or information contained on this map or associated series of maps. The data and related map graphics are not legal, land survey or engineering documents and are not intended to be used as such. ORNL gives no warranty, express or implied, as to the accuracy, reliability, utility or completeness of this information. The user of these maps and data assumes all responsibility and risk for the use of the maps and data. ORNL disclaims all warranties, representations or endorsements either express or implied, with regard to the information contained in this map product, including, but not limited to, all implied warranties of merchantability, fitness for a particular purpose or non-infringement. This preliminary map product is for research and review purposes only. It is not intended to be used for emergency management operational or life safety decisions at the local or regional governmental level or by the general public. Users requiring information regarding hazardous conditions or meteorological conditions for specific geographic areas should consult directly with their city or county emergency management office.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Height Above Nearest Drainage (HAND) and Hydraulic Property Table for CONUS - Version 0.21 (20200601)

The continental flood inundation mapping (CFIM) framework is a high-performance computing (HPC)-based computational framework for the Height Above Nearest Drainage (HAND)-based inundation mapping methodology. Using the 10m Digital Elevation Model (DEM) data produced by U.S. Geological Survey (USGS) 3DEP (the 3-D Elevation Program) and the NHDPlus hydrography dataset produced by USGS and the U.S. Environmental Protection Agency (EPA), a hydrological terrain raster called HAND is computed for HUC6 units in the conterminous U.S. (CONUS). The value of each raster cell in HAND is an approximation of the relative elevation between the cell and its nearest water stream. Derived from HAND, a hydraulic property table is established to calculate river geometry properties for each of the 2.7 million river reaches covered by NHDPlus (5.5 million kilometers in total length). This table is a lookup table for water depth given an input stream flow value. Such lookup is available between water depth 0m and 25m at 1-foot interval. The flood inundation map is then computed by using HAND and this lookup table based on the near real-time water forecast from the National Water Model (NWM) at the National Oceanic and Atmospheric Administration (NOAA). HAND and the Hydraulic Property Table version v0.21 is an upgrade to v0.2. Version 0.21 applies NHD HR etching to DEMs for all HUC6 units before running the HAND workflow. This new version also fixed the issue of void areas along HUC boundary. This dataset comprises 331 HUC6 units for CONUS (excluding the five great lakes units), each is a downloadable zip file. Version 0.1 was computed at the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urban-Champaign in 2016 and is currently hosted at the Texas Advanced Computing Center (TACC). Please cite this data DOI and the following publications and data DOIs when you use HAND and the hydraulic property table: Liu, Yan Y. Height Above Nearest Drainage (HAND) and Hydraulic Property Table for CONUS - Version 0.2. (20200301). Oak Ridge Leadership Computing Facility. (2020). DOI: 10.13139/ORNLNCCS/1608331 Liu, Yan Y., David R. Maidment, David G. Tarboton, Xing Zheng, and Shaowen Wang. 'A CyberGIS integration and computation framework for high-resolution continental-scale flood inundation mapping.' JAWRA Journal of the American Water Resources Association 54, no. 4 (2018): 770-784. DOI: 10.1111/1752-1688.12660 Zheng, Xing, David G. Tarboton, David R. Maidment, Yan Y. Liu, and Paola Passalacqua. 'River channel geometry and rating curve estimation using height above the nearest drainage.' JAWRA Journal of the American Water Resources Association 54, no. 4 (2018): 785-806. DOI: 10.1111/1752-1688.12661 Liu, Y. (2018). Height Above Nearest Drainage (HAND) for CONUS, HydroShare, https://doi.org/10.4211/hs.69f7d237675c4c73938481904358c789 LICENSE FOR USE -- MAPS AND DATA DISCLAIMER This resource is shared under the Creative Commons Attribution CC BY, http://creativecommons.org/licenses/by/4.0/ MAPS AND DATA DISCLAIMER The Oak Ridge National Laboratory (ORNL) shall not be held liable for improper or incorrect use of the data described or information contained on this map or associated series of maps. The data and related map graphics are not legal, land survey or engineering documents and are not intended to be used as such. ORNL gives no warranty, express or implied, as to the accuracy, reliability, utility or completeness of this information. The user of these maps and data assumes all responsibility and risk for the use of the maps and data. ORNL disclaims all warranties, representations or endorsements either express or implied, with regard to the information contained in this map product, including, but not limited to, all implied warranties of merchantability, fitness for a particular purpose or non-infringement. This preliminary map product is for research and review purposes only. It is not intended to be used for emergency management operational or life safety decisions at the local or regional governmental level or by the general public. Users requiring information regarding hazardous conditions or meteorological conditions for specific geographic areas should consult directly with their city or county emergency management office.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Bayesian Calibration of Stochastic Agent Based Model via Random Forest

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high-dimensional calibration can be computationally prohibitive. This paper presents a random forest-based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented, and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. Further, these results are compared with previous approximate Bayesian calibration (IMABC) results, and their predictive performance is analyzed, showing improved performance with a reduction in computation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fitting Matérn smoothness parameters using automatic differentiation

The Mat$\acute{e}$rn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities such as interpolants and forecasts. Unfortunately, derivatives of the Mat$\acute{e}$rn covariance function with respect to $\nu$ require derivatives of the modified second-kind Bessel function $K$ $\nu$ with respect to $\nu$. While closed form expressions of these derivatives do exist, they are prohibitively difficult and expensive to compute. For this reason, many software packages require fixing $\nu$ as opposed to estimating it, and all existing software packages that attempt to offer the functionality of estimating $\nu$ use finite difference estimates for $\partial$ $\nu$ $K$ $\nu$ . In this work, we introduce a new implementation of $K$$\nu$ that has been designed to provide derivatives via automatic differentiation (AD), and whose resulting derivatives are significantly faster and more accurate than those computed using finite differences. Here, we provide comprehensive testing for both speed and accuracy and show that our AD solution can be used to build accurate Hessian matrices for second-order maximum likelihood estimation in settings where Hessians built with finite difference approximations completely fail.

97 MATHEMATICS AND COMPUTING↗