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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Resilience Design Patterns: A Structured Approach to Resilience at Extreme Scale (V.2.0)

Reliability is a serious concern for future extreme-scale high-performance computing (HPC) systems. Projections based on the current generation of HPC systems and technology roadmaps suggest the prevalence of very high fault rates in future systems. The errors resulting from these faults will propagate and generate various kinds of failures, which may result in outcomes ranging from result corruptions to catastrophic application crashes. Therefore, the resilience challenge for extreme-scale HPC systems requires coordination between various hardware and software technologies that are capable of handling a broad set of fault models at accelerated fault rates. Also, due to practical limits on power consumption in future HPC systems, they are likely to embrace innovative architectures, increasing the levels of hardware and software complexities. Therefore, the techniques that seek to improve resilience must navigate the complex trade-off space between resilience and the overheads to power consumption and performance. While the HPC community has developed various resilience solutions, application-level techniques as well as system-based solutions, the solution space of HPC resilience techniques remains fragmented. There are no formal methods to integrate the various HPC resilience techniques into composite solutions, nor are there methods to holistically evaluate the adequacy and efficacy of such solutions in terms of their protection coverage, and their performance & power efficiency characteristics. Additionally, few implementations of current resilience solutions are portable to newer architectures and software environments that will be deployed on future systems. We developed a new structured approach to the management of HPC resilience using the concept of resilience-based design patterns. In general, a design pattern is a repeatable solution to a commonly occurring problem. We identified the well-known solutions that are commonly used to deal with faults, errors and failures in HPC systems. In the initial design patterns specification (version 1.0), we described the various solutions, which address specific problems in the design of resilient HPC environments, in the form of patterns. Each pattern describes a problem caused by a fault, error or failure event in an HPC environment, and then describes the core of the solution of the problem in such a way that this solution may be adapted to different systems and implemented at different layers of the system stack. The catalog of these resilience design patterns provides designers with a collection of design elements. To construct complete resilience solutions using combinations of various patterns, we defined a framework that enhances HPC designers' understanding of the important constraints and the opportunities for the design patterns to be implemented and deployed at various layers of the system stack. The design framework is also useful for establishing interfaces and mechanisms to coordinate flexible fault management across hardware and software components, as well as to consider the trade-off between performance, resilience, and power consumption when constructing a solution. The resilience design patterns specification version 1.1 included more detailed explanations of the pattern solutions, the context in which the patterns are applicable, and the implications for hardware or software design. It also provided several additional examples and detailed case studies to demonstrate the use of patterns to build realistic solutions. In version 1.2 of the specification document, we have improved the pattern descriptions, including graphical representations of the pattern components. These improvements are largely based on critical comments, feedback and suggestions received from pattern experts and readers of the previous versions of the specification. The pattern classification has been modified to further clarify the relationships between pattern categories. This version of the specification also introduces a pattern language for resilience design patterns. The pattern language presents the patterns in the catalog as a network, revealing the relations among the resilience patterns. The language provides designers with the means to explore alternative techniques for handling a specific fault model that may have different efficiency and complexity characteristics. Using the pattern language also enables the design and implementation of comprehensive resilience solutions as a set of interconnected resilience patterns that can be instantiated across layers of the system stack. The overall goal of this work is to provide hardware and software designers, as well as the users and operators of HPC systems, a systematic methodology for the design and evaluation of resilience technologies in HPC systems that keep scientific applications running to a correct solution in a timely and cost-efficient manner despite frequent faults, errors, and failures of various types. Version 2.0 expands the resilience design pattern classification and catalog to include self-stabilization patterns and reliability, availability and performance models for each structural pattern.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Resilience Design Patterns - A Structured Approach to Resilience at Extreme Scale (version 1.2)

We developed a new structured approach to the management of HPC resilience using the concept of resilience-based design patterns. In general, a design pattern is a repeatable solution to a commonly occurring problem. We identified the well-known solutions that are commonly used to deal with faults, errors and failures in HPC systems. In the initial design patterns specification (version 1.0), we described the various solutions, which address specific problems in the design of resilient HPC environments, in the form of patterns. Each pattern describes a problem caused by a fault, error or failure event in an HPC environment, and then describes the core of the solution of the problem in such a way that this solution may be adapted to different systems and implemented at different layers of the system stack. The catalog of these resilience design patterns provides designers with a collection of design elements. To construct complete resilience solutions using combinations of various patterns, we defined a framework that enhances HPC designers’ understanding of the important constraints and the opportunities for the design patterns to be implemented and deployed at various layers of the system stack. The design framework is also useful for establishing interfaces and mechanisms to coordinate flexible fault management across hardware and software components, as well as to consider the trade-off between performance, resilience, and power consumption when constructing a solution. The resilience design patterns specification version 1.1 included more detailed explanations of the pattern solutions, the context in which the patterns are applicable, and the implications for hardware or software design. It also provided several additional examples and detailed case studies to demonstrate the use of patterns to build realistic solutions. In this version 1.2 of the specification document, we have improved the pattern descriptions, including graphical representations of the pattern components. These improvements are largely based on critical comments, feedback and suggestions received from pattern experts and readers of the previous versions of the specification. The pattern classification has been modified to further clarify the relationships between pattern categories. This version of the specification also introduces a pattern language for resilience design patterns. The pattern language presents the patterns in the catalog as a network, revealing the relations among the resilience patterns. The language provides designers with the means to explore alternative techniques for handling a specific fault model that may have different effciency and complexity characteristics. Using the pattern language also enables the design and implementation of comprehensive resilience solutions as a set of interconnected resilience patterns that can be instantiated across layers of the system stack. The overall goal of this work is to provide hardware and software designers, as well as the users and operators of HPC systems, a systematic methodology for the design and evaluation of resilience technologies in HPC systems that keep scientific applications running to a correct solution in a timely and cost-effcient manner despite frequent faults, errors, and failures of various types.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Run 16, eIPM Summary

Three problems with the eIPMs were corrected during the 2015 summer shutdown. These involved ac coupling and 'negative profiles', detector 'dead zone' created by biasing, and gain control on ramp. With respect to Run 16, problems dealt with included gain depletion on horizontal MCP and rf pickup on profile signals; it was found that the MCP was severely damaged over part of the aperture. Various corrective measures were applied. Some results of these measured obtained during Run 16 are shown. At the end of Run 16 there was a three-­day beam run to study polarized proton beams in the AGS. Attempts to minimize beam injection errors which increase emittance by using the eIPMs to measure the contribution of injection mismatch to the AGS output beam emittance are recounted. .

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Fast neutron leakage spectra of the EUCLID experiment

Special nuclear material in sub-critical and critical configurations measured in integral experiments are important for validation and adjustment of nuclear data. Many different evaluations of nuclear data exist, and these different evaluations can provide different values for individual cross sections that vary due to the uncertainties in differential experiments or lack of such data. For integral experiments, differences in these individual cross sections can have compensating errors, which lead to the same answer. One example of this is the Jezebel critical assembly, where k eff of the system is correctly computed by both ENDF/B-VIII.0 and JEFF-3.3, despite having substantially different underlying evaluated values for specific reactions (such as elastic and inelastic cross sections). To reduce compensating errors in nuclear data, the Experiments Underpinned by Computational Learning for Improvements in Nuclear Data (EUCLID) project has utilized machine learning to design a set of sub-critical and critical experiments. These experiments include slab- and cube-like configurations of 239 Pu in the form of the ZPPR plates. Six different responses were measured on a total of thirteen different configurations. One of these responses, the neutron leakage spectrum, was measured using an EJ301D detector. Finally, the results of the neutron leakage spectra show good agreement (within 1–2 σ ) with the expected spectrum from simulations and will be used in the subsequent nuclear data adjustment done by the EUCLID team.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Harmonic analysis for the characterization and correction of geometric distortion in MRI

Purpose: Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. Methods: The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace’s equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. Results: The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45–0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. Conclusions: A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations?

Herein, we examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys. , 2018, 20 , 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew–Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi–Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys. , 2019, 151 , 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

GPS Data Filtration Method for Drive Cycle Analysis Applications

When employing GPS data acquisition systems to capture vehicle drive-cycle information, a number of errors often appear in the raw data samples, such as sudden signal loss, extraneous or outlying data points, speed drifting, and signal white noise, all of which limit the quality of field data for use in downstream applications. Unaddressed, these errors significantly impact the reliability ofsource data and limit the effectiveness of traditional drive-cycle analysis approaches and vehicle simulation software. Without reliable speed and time information, the validity of derived metrics for drive cycles, such as acceleration, power, and distance, become questionable. This study explores some of the common sources of error present in raw onboard GPS data and presents a detailedfiltering process designed to correct for these issues. Test data from both light and medium/heavy duty applications are examined to illustrate the effectiveness of the proposed filtration process across the range of vehicle vocations. Graphical comparisons of raw and filtered cycles are presented, and statistical analyses are performed to determine the effects of the proposed filtration processon raw data. Finally, an evaluation of the overall benefits of data filtration on raw GPS data and present potential areas for continued research is presented.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Asymptotic errors in adiabatic evolution

The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved Hamiltonian. Understanding corrections to the adiabatic result that arise when the evolution of the Hamiltonian is slow—but not arbitrarily slow—has become increasingly important, especially since adiabatic evolution has been proposed as a method of state preparation in quantum computing. Here, this paper identifies two regimes, an adiabatic regime in which corrections are generically small and can depend on details of the evolution throughout the path, and a hyperadiabatic regime in which the error is given by a form similar to an asymptotic expansion in the inverse of the evolution time with the coefficients depending principally on the behavior at the endpoints. However, the error in this hyperadiabatic regime is neither given by a true asymptotic series nor solely dependent on the endpoints: the coefficients combine the contributions from both endpoints, with relative phase factors that depend on the average spectral gaps along the trajectory, multiplied by the evolution time. The central result of this paper is to identify a quantity, referred to as the typical error, which is obtained by appropriately averaging the error over evolution times that are small compared to the evolution time itself. This typical error is characterized by an asymptotic series and depends solely on the endpoints of the evolution, remaining independent of the details of the intermediate evolution.

adiabatic approximation↗
DOE OSTI2019

An Objective and Efficient Method for Assessing the Impact of Reduced-Precision Calculations On Solution Correctness

Recent studies have shown that reducing the precision of floating-point calculations in an atmospheric model can improve the models' computational performance without affecting model fidelity, but code changes are needed to accommodate lower precision, and a small number of calculations might need to retain higher precision to prevent undue round-off error. For complex and computationally expensive systems like the Energy Exascale Earth System Model (E3SM), a method is needed to objectively assess the quality of the lower-precision simulations and to quickly identify problematic code pieces This paper demonstrates that solution correctness can be evaluated through a simple and quantitative error metric based on time step convergence. The proposed test method can unambiguously detect the accumulation of precision error and objectively assess its impact on solution accuracy. Since fast physical processes are known to affect key features of the multi-year mean climate in an atmospheric model, we show that the convergence test applied to short simulations can provide useful information about the impact of reduced precision on a model’s long-term behavior. In contrast, the traditional way of climate model evaluation requires multi-year simulations and involves inspecting many physical quantities for statistical significance in the presence of natural variability. The simplicity, computational efficiency, and objectivity of the proposed method makes it very attractive for high-resolution model development. The method is also expected to be applicable to other models that numerically solve time evolution equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-C-207A-03: Development of Proton CT Imaging System Using Thick Scintillator and CCD Camera

Purpose: In the treatment planning of proton therapy, Water Equivalent Length (WEL), which is the parameter for the calculation of dose and the range of proton, is derived by X-ray CT (xCT) image and xCT-WEL conversion. However, about a few percent error in the accuracy of proton range calculation through this conversion has been reported. The purpose of this study is to construct a proton CT (pCT) imaging system for an evaluation of the error. Methods: The pCT imaging system was constructed with a thick scintillator and a cooled CCD camera, which acquires the two-dimensional image of integrated value of the scintillation light toward the beam direction. The pCT image is reconstructed by FBP method using a correction between the light intensity and residual range of proton beam. An experiment for the demonstration of this system was performed with 70-MeV proton beam provided by NIRS cyclotron. The pCT image of several objects reconstructed from the experimental data was evaluated quantitatively. Results: Three-dimensional pCT images of several objects were reconstructed experimentally. A finestructure of approximately 1 mm was clearly observed. The position resolution of pCT image was almost the same as that of xCT image. And the error of proton CT pixel value was up to 4%. The deterioration of image quality was caused mainly by the effect of multiple Coulomb scattering. Conclusion: We designed and constructed the pCT imaging system using a thick scintillator and a CCD camera. And the system was evaluated with the experiment by use of 70-MeV proton beam. Three-dimensional pCT images of several objects were acquired by the system. This work was supported by JST SENTAN Grant Number 13A1101 and JSPS KAKENHI Grant Number 15H04912.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys–Bernardi function counterpoise (CP) procedure “overcorrects” supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ~150 atoms and ligand–protein models with ~300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. Furthermore, this is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP “overcorrects” for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

FOCAL PLANE WAVEFRONT SENSING USING RESIDUAL ADAPTIVE OPTICS SPECKLES

Optical imperfections, misalignments, aberrations, and even dust can significantly limit sensitivity in high-contrast imaging systems such as coronagraphs. An upstream deformable mirror (DM) in the pupil can be used to correct or compensate for these flaws, either to enhance the Strehl ratio or suppress the residual coronagraphic halo. Measurement of the phase and amplitude of the starlight halo at the science camera is essential for determining the DM shape that compensates for any non-common-path (NCP) wavefront errors. Using DM displacement ripples to create a series of probe and anti-halo speckles in the focal plane has been proposed for space-based coronagraphs and successfully demonstrated in the lab. We present the theory and first on-sky demonstration of a technique to measure the complex halo using the rapidly changing residual atmospheric speckles at the 6.5 m MMT telescope using the Clio mid-IR camera. The AO system's wavefront sensor measurements are used to estimate the residual wavefront, allowing us to approximately compute the rapidly evolving phase and amplitude of speckle halo. When combined with relatively short, synchronized science camera images, the complex speckle estimates can be used to interferometrically analyze the images, leading to an estimate of the static diffraction halo with NCP effects included. In an operational system, this information could be collected continuously and used to iteratively correct quasi-static NCP errors or suppress imperfect coronagraphic halos.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

The calibration of the WISE W1 and W2 Tully-Fisher relation

In order to explore local large-scale structures and velocity fields, accurate galaxy distance measures are needed. We now extend the well-tested recipe for calibrating the correlation between galaxy rotation rates and luminosities—capable of providing such distance measures—to the all-sky, space-based imaging data from the Wide-field Infrared Survey Explorer (WISE) W1 (3.4 μm) and W2 (4.6 μm) filters. We find a correlation of line width to absolute magnitude (known as the Tully-Fisher relation, TFR) of M{sub W1}{sup b,i,k,a}=−20.35−9.56(log W{sub mx}{sup i}−2.5) (0.54 mag rms) and M{sub W2}{sup b,i,k,a}=−19.76−9.74(log W{sub mx}{sup i}−2.5) (0.56 mag rms) from 310 galaxies in 13 clusters. We update the I-band TFR using a sample 9% larger than in Tully and Courtois. We derive M{sub I}{sup b,i,k}=−21.34−8.95(log W{sub mx}{sup i}−2.5) (0.46 mag rms). The WISE TFRs show evidence of curvature. Quadratic fits give M{sub W1}{sup b,i,k,a}=−20.48−8.36(log W{sub mx}{sup i}−2.5)+3.60(log W{sub mx}{sup i}−2.5){sup 2} (0.52 mag rms) and M{sub W2}{sup b,i,k,a}=−19.91−8.40(log W{sub mx}{sup i}−2.5)+4.32(log W{sub mx}{sup i}−2.5){sup 2} (0.55 mag rms). We apply an I-band –WISE color correction to lower the scatter and derive M{sub C{sub W{sub 1}}}=−20.22−9.12(log W{sub mx}{sup i}−2.5) and M{sub C{sub W{sub 2}}}=−19.63−9.11(log W{sub mx}{sup i}−2.5) (both 0.46 mag rms). Using our three independent TFRs (W1 curved, W2 curved, and I band), we calibrate the UNION2 Type Ia supernova sample distance scale and derive H {sub 0} = 74.4 ± 1.4(stat) ± 2.4(sys) km s{sup –1} Mpc{sup –1} with 4% total error.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Direct discontinuous Galerkin method and its variations for second order elliptic equations

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Effect of Weld Consumable Conditioning on the Diffusible Hydrogen and Subsequent Residual Stress and Flexural Strength of Multipass Welded P91 Steels

P91 steel weld joint was prepared using the shielded metal arc welding process and four different conditions of weld consumable that provide the different levels of diffusible hydrogen in deposited metal. In the present research, the effects of diffusible hydrogen content on the flexural strength, lower critical stress, and tensile strength of P91 steel welds were also determined with respect to different electrode conditions. To investigate the effect of diffusible hydrogen on multipass welding, top and root side flexural tests were performed. The residual stresses (axial stress and transverse stress) were also measured using the blind hole drilling method for different conditions of welding consumable. The peak value of residual stresses was measured at the center of the weld fusion zone. The maximum value of transverse stress was measured to be 355 MPa for case II (6.21 mL/100 g of diffusible hydrogen), while the maximum axial stress was about 218 MPa for case IV (12.43 mL/100 g of diffusible hydrogen). A three-dimensional finite element simulation was also performed to predict the residual stress distribution and thermal profile along the welded joint. The experimentally determined residual stresses correlated well with the numerically estimated residual stresses. The diffusible hydrogen content was not observed to have any significant effect on the residual stresses. The corrected residual stress values were also predicted by considering the plasticity-induced error. However, the flexural performance of the welded joint was affected by the diffusible hydrogen content. The top and root flexural strength was measured to be optimum for the low level of diffusible hydrogen content, and the values decreased with an increase in diffusible hydrogen content.

36 MATERIALS SCIENCE↗
DOE OSTI2017

An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry

Here, the Fokker–Planck collision operator is an advection-diffusion operator which describe dynamical systems such as weakly coupled plasmas, photonics in high temperature environment biological, and even social systems. For plasmas in the continuum, the Fokker–Planck collision operator supports such important physical properties as conservation of number, momentum, and energy, as well as positivity. It also obeys the Boltzmann's H-theorem, i.e., the operator increases the system entropy while simultaneously driving the distribution function towards a Maxwellian. In the discrete, when these properties are not ensured, numerical simulations can either fail catastrophically or suffer from significant numerical pollution. There is strong emphasis in the literature on developing numerical techniques to solve the Fokker–Planck equation while preserving these properties. In this short note, we focus on the analytical equilibrium preserving property, meaning that the Fokker–Planck collision operator vanishes when acting on an analytical Maxwellian distribution function. The equilibrium preservation property is especially important, for example, when one is attempting to capture subtle transport physics. Since transport arises from small Ο(ϵ) corrections to the equilibrium (where ϵ is a small expansion parameter), numerical truncation error present in the equilibrium solution may dominate, overwhelming transport dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Regularized machine learning on molecular graph model explains systematic error in DFT enthalpies

Abstract A major goal of materials research is the discovery of novel and efficient heterogeneous catalysts for various chemical processes. In such studies, the candidate catalyst material is modeled using tens to thousands of chemical species and elementary reactions. Density Functional Theory (DFT) is widely used to calculate the thermochemistry of these species which might be surface species or gas-phase molecules. The use of an approximate exchange correlation functional in the DFT framework introduces an important source of error in such models. This is especially true in the calculation of gas phase molecules whose thermochemistry is calculated using the same planewave basis set as the rest of the surface mechanism. Unfortunately, the nature and magnitude of these errors is unknown for most practical molecules. Here, we investigate the error in the enthalpy of formation for 1676 gaseous species using two different DFT levels of theory and the ‘ground truth values’ obtained from the NIST database. We featurize molecules using graph theory. We use a regularized algorithm to discover a sparse model of the error and identify important molecular fragments that drive this error. The model is robust to rigorous statistical tests and is used to correct DFT thermochemistry, achieving more than an order of magnitude improvement.

36 MATERIALS SCIENCE↗