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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗
DOE OSTI2019

Semi-local Density Functional Approximations for Bulk, Surface, and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semi-local approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize the results of our research efforts within the LDRD 200202 titled "Making density functional theory work for all materials" in addressing this issue. Our efforts are grouped into two research thrusts. In the first thrust, we develop an exchange-correlation functional (BSC functional) within the subsystem functional formalism. It enables us to capture bulk, surface, and confinement physics with a single, semi-local exchange-correlation functional in density functional theory calculations. We present the analytical properties of the BSC functional and demonstrate that the BSC functional is able to capture confinement physics more accurately than standard semi-local exchange-correlation functionals. The second research thrust focusses on developing a database for transition metal binary compounds. The database consists of materials properties (formation energies, ground-state energies, lattice constants, and elastic constants) of 26 transition metal elements and 89 transition metal alloys. It serves as a reference for benchmarking computational models (such as lower-level modeling methods and exchange-correlation functionals). We expect that our database will significantly impact the materials science community. We conclude with a brief discussion on the future research directions and impact of our results.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Can Cooling and Heating Functions Be Modeled with Homogeneous Radiation Fields?

Abstract Cooling and heating functions describe how radiative processes impact the thermal state of a gas as a function of its temperature and other physical properties. In a most general case the functions depend on the detailed distributions of ionic species and on the radiation spectrum. Hence, these functions may vary on a very wide range of spatial and temporal scales. In this paper, we explore cooling and heating functions between 5 ≤ z ≤ 10 in simulated galaxies from the Cosmic Reionization On Computers project. We compare three functions: (1) the actual cooling and heating rates of hydrodynamic cells as a function of cell temperature, (2) the median cooling and heating functions computed using median interstellar medium (ISM) properties (median ISM), and (3) the median of the cooling and heating functions of all gas cells (instantaneous). We find that the median ISM and instantaneous approaches to finding a median cooling and heating function give identical results within the spread due to cell-to-cell variation. However, the actual cooling (heating) rates experienced by the gas at different temperatures in the simulations do not correspond to either summarized cooling (heating) functions. In other words, the thermodynamics of the gas in the simulations cannot be described by a single set of a cooling plus a heating function with a spatially constant radiation field that could be computed with common tools, such as CLOUDY.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2009

Defining the Physiological Factors that Contribute to Postflight Changes in Functional Performance

Astronauts experience alterations in multiple physiological systems due to exposure to the microgravity conditions of space flight. These physiological changes include sensorimotor disturbances, cardiovascular deconditioning and loss of muscle mass and strength. These changes might affect the ability of crewmembers to perform critical mission tasks immediately after landing on lunar and Martian surfaces. To date, changes in functional performance have not been systematically studied or correlated with physiological changes. To understand how changes in physiological function impact functional performance an interdisciplinary pre/postflight testing regimen (Functional Task Test, FTT) has been developed that systematically evaluates both astronaut postflight functional performance and related physiological changes. The overall objective of the FTT is to identify the key underlying physiological factors that contribute to performance of functional tests that are representative of critical mission tasks. This study will identify which physiological systems contribute the most to impaired performance on each functional test. This will allow us to identify the physiological systems that play the largest role in decrement in functional performance. Using this information we can then design and implement countermeasures that specifically target the physiological systems most responsible for the altered functional performance associated with space flight. The functional test battery was designed to address high priority tasks identified by the Constellation program as critical for mission success. The set of functional tests making up the FTT include the: 1) Seat Egress and Walk Test, 2) Ladder Climb Test, 3) Recovery from Fall/Stand Test, 4) Rock Translation Test, 5) Jump Down Test, 6) Torque Generation Test, and 7) Construction Activity Board Test. Corresponding physiological measures include assessments of postural and gait control, dynamic visual acuity, fine motor control, plasma volume, orthostatic intolerance, upper and lower body muscle strength, power, fatigue, control and neuromuscular drive. Crewmembers perform both functional and physiological tests before and after short (Shuttle) and long-duration (ISS) space flight. Data are collected on R+0 (Shuttle only), R+1, R+6 and R+30.

Bloomberg, J. J.↗
NASA NTRS2013

Goal-Function Tree Modeling for Systems Engineering and Fault Management

The draft NASA Fault Management (FM) Handbook (2012) states that Fault Management (FM) is a "part of systems engineering", and that it "demands a system-level perspective" (NASAHDBK- 1002, 7). What, exactly, is the relationship between systems engineering and FM? To NASA, systems engineering (SE) is "the art and science of developing an operable system capable of meeting requirements within often opposed constraints" (NASA/SP-2007-6105, 3). Systems engineering starts with the elucidation and development of requirements, which set the goals that the system is to achieve. To achieve these goals, the systems engineer typically defines functions, and the functions in turn are the basis for design trades to determine the best means to perform the functions. System Health Management (SHM), by contrast, defines "the capabilities of a system that preserve the system's ability to function as intended" (Johnson et al., 2011, 3). Fault Management, in turn, is the operational subset of SHM, which detects current or future failures, and takes operational measures to prevent or respond to these failures. Failure, in turn, is the "unacceptable performance of intended function." (Johnson 2011, 605) Thus the relationship of SE to FM is that SE defines the functions and the design to perform those functions to meet system goals and requirements, while FM detects the inability to perform those functions and takes action. SHM and FM are in essence "the dark side" of SE. For every function to be performed (SE), there is the possibility that it is not successfully performed (SHM); FM defines the means to operationally detect and respond to this lack of success. We can also describe this in terms of goals: for every goal to be achieved, there is the possibility that it is not achieved; FM defines the means to operationally detect and respond to this inability to achieve the goal. This brief description of relationships between SE, SHM, and FM provide hints to a modeling approach to provide formal connectivity between the nominal (SE), and off-nominal (SHM and FM) aspects of functions and designs. This paper describes a formal modeling approach to the initial phases of the development process that integrates the nominal and off-nominal perspectives in a model that unites SE goals and functions of with the failure to achieve goals and functions (SHM/FM).

Johnson, Stephen B.↗
NASA NTRS2016

Exercise Effects on the Brain and Sensorimotor Function in Bed Rest

Long duration spaceflight microgravity results in cephalad fluid shifts and deficits in posture control and locomotion. Effects of microgravity on sensorimotor function have been investigated on Earth using head down tilt bed rest (HDBR). HDBR serves as a spaceflight analogue because it mimics microgravity in body unloading and bodily fluid shifts. Preliminary results from our prior 70 days HDBR studies showed that HDBR is associated with focal gray matter (GM) changes and gait and balance deficits, as well as changes in brain functional connectivity. In consideration of the health and performance of crewmembers we investigated whether exercise reduces the effects of HDBR on GM, functional connectivity, and motor performance. Numerous studies have shown beneficial effects of exercise on brain health. We therefore hypothesized that an exercise intervention during HDBR could potentially mitigate the effects of HDBR on the central nervous system. Eighteen subjects were assessed before (12 and 7 days), during (7, 30, and ~70 days) and after (8 and 12 days) 70 days of 6-degrees HDBR at the NASA HDBR facility in UTMB, Galveston, TX, US. Each subject was randomly assigned to a control group or one of two exercise groups. Exercise consisted of daily supine exercise which started 20 days before the start of HDBR. The exercise subjects participated either in regular aerobic and resistance exercise (e.g. squat, heel raise, leg press, cycling and treadmill running), or aerobic and resistance exercise using a flywheel apparatus (rowing). Aerobic and resistance exercise intensity in both groups was similar, which is why we collapsed the two exercise groups for the current experiment. During each time point T1-weighted MRI scans and resting state functional connectivity scans were obtained using a 3T Siemens scanner. Focal changes over time in GM density were assessed using voxel based morphometry (VBM8) under SPM. Changes in resting state functional connectivity was assessed using both a region of interest (ROI, or seed-to-voxel) approach as well as a whole brain intrinsic connectivity (i.e., voxel-to-voxel) analysis. For the ROI analysis we selected 11 ROIs of brain regions that are involved in sensorimotor function (i.e., L. Insular C., L. Putamen, R. Premotor C., L.+R. Primary Motor C., R. Vestibular C., L. Posterior Cingulate G., R. Cerebellum Lobule V + VIIIb + Crus I, and the R. Superior Parietal G.) and correlated their time course of brain activation during rest with all other voxels in the brain. The whole brain connectivity analysis tests changes in the strength of the global connectivity pattern between each voxel and the rest of the brain. Functional mobility was assessed using an obstacle course. Vestibular contribution to balance was measured using Neurocom Sensory Organization Test 5. Behavioral measures were assessed pre-HDBR, and 0, 8 and 12 days post-HDBR. Linear mixed models were used to test for effects of time, group, and group-by-time interactions. Family-wise error corrected VBM revealed significantly larger increases in GM volume in the right primary motor cortex in bed rest control subjects than in bed rest exercise subjects. No other significant group by time interactions in gray matter changes with bed rest were observed. Functional connectivity MRI revealed that the increase in connectivity during bed rest of the left putamen with the bilateral midsagittal precunes and the right cingulate gyrus was larger in bed rest control subjects than in bed rest exercise subjects. Furthermore, the increase in functional connectivity with bed rest of the right premotor cortex with the right inferior frontal gyrus and the right primary motor cortex with the bilateral premotor cortex was smaller in bed rest control subjects than in bed rest exercise subjects. Functional mobility performance was less affected by HDBR in exercise subjects than in control subjects and post HDBR exercise subjects recovered faster than control subjects. The group performance differences and GM changes were not related. Exercise in HDBR partially mitigates the adverse effect of HDBR on functional mobility, particularly during the post-bed rest recovery phase. In addition, exercise appears to result in differential brain structural and functional changes in motor regions such as the primary motor cortex, the premotor cortex and the putamen. Whether these central nervous system changes are related to motor behavioral changes including gait and balance warrants further research.

Koppelmans, V.↗
NASA NTRS2020

Evaluation of Fatigue Damage Accumulation Functions for Delamination Initiation and Propagation

The present report follows on the cohesive fatigue damage model methodology proposed in NASA-TP-2018-219838. In that report, an empirical function describing the incremental damage due to cyclic loading was used to calculate fatigue damage within a cohesive formulation. The form of the function was developed such that, when integrated at a constant stress amplitude from no damage to failure, it produces a life versus load response that is consistent with an S-N diagram. Therefore, the parameters of the damage model could be obtained by fitting the model predictions to an S-N diagram. The finite element analyses performed demonstrate that the cohesive fatigue accumulation function provides a link between the S-N diagram that describes crack initiation, and the Paris law that characterizes the rate of crack propagation. However, when the model was proposed, it was not known whether the form of the damage accumulation function associated with a desired S-N diagram is unique and, if not, if the link between S-N and the Paris law is unique and independent of the fatigue function selected. In the effort described herein, several alternative forms of the damage function that reproduce the desired features of S-N diagrams were found and evaluated. The effects of each of these functions on the predicted parameters of the Paris law and the propagation threshold are discussed. The results indicate that the predicted exponent m of the Paris law is indeed independent of the damage accumulation function. However, different functions predict different values for the pre-factor C of the Paris law. Therefore, the proper damage accumulation function must be selected by comparison with experiments. One of the new damage accumulation functions proposed herein was found to be particularly useful for analysis because of the ease with which the model parameters can be determined with a minimal amount of experimental information. The effectiveness of the proposed methodology and damage function was demonstrated by conducting analyses of a double cantilever beam test, a mixed-mode bending test, and a three-point bending test of a skin/doubler specimen. The results indicate that the same set of model parameters can provide accurate predictions of the rate of fatigue crack propagation for a variety of material interfaces, mode mixities, load levels, and stress ratios.

Cohesive elements↗
DOE OSTI2021

Scale dependence in functional equivalence and difference in the soil microbiome

Climatic history can shape the functioning of soil microbial communities and thus rates of ecosystem processes such as organic matter decomposition. For example, broad spatial scale differences in climatic history, such as contrasting precipitation regimes, have been shown to generate unique microbial functional responses to contemporary moisture conditions. Yet it is an open question as to whether local differences in soil microclimate similarly influence the functional potential of decomposer communities. Here, we use a multi-scale approach within and among two temperate forest field sites to investigate this question. Soils from fifty-four microsites, that vary in their soil moisture climate-regimes, were used as inocula for a common leaf litter (Quercus rubra L.) in a controlled, laboratory microcosm study. Microcosms were placed under dry, mesic and wet lab-moisture conditions and the rate of carbon (C) mineralization of the litter was measured over 202 days. Our results reveal differences in decomposition rates under controlled conditions that highlight broad-scale functional differences between the soil communities at each site. Specifically, we found that C mineralization differed by as much as two-fold for soil communities when compared between the sites. Our results also show that functional differences of soil communities are observable within one site but not the other. In the site where local-scale functional legacies were apparent, the historical soil moisture microclimate-regimes generated as much as an 89% change in C mineralization rates of the leaf litter under the same contemporary, lab-imposed moisture conditions. Here, a similar pattern was not observable in the other site; instead, laboratory moisture conditions explained almost all variation in C mineralization. Notably, for the site with pronounced local-scale functional legacies, there was much greater within-site variation in field-soil microsite moisture than at the site which did not exhibit functional legacies, suggesting that the extent of local-scale variation in microclimate may act as control on whether local-scale functional legacies are observed. Regardless of whether this mechanism does explain our findings, our observations do confirm those from prior studies where regional-scale moisture-regime differences shape microbial function, and extend this prior work by providing evidence that pronounced local-scale differences in soil moisture microclimate-regimes are associated with microbial functional legacies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

The effect of the exchange-correlation functional on H{sub 2} dissociation on Ru(0001)

The specific reaction parameter (SRP) approach to density functional theory (DFT) has enabled a chemically accurate description of reactive scattering experiments for activated H{sub 2}–metal systems (H{sub 2} + Cu(111) and Cu(100)), but its application has not yet resulted in a similarly accurate description of non-activated or weakly activated H{sub 2}-metal systems. In this study, the effect of the choice of the exchange-correlation functional in DFT on the potential energy surface and dynamics of H{sub 2} dissociation on Ru(0001), a weakly activated system, is investigated. In total, full potential energy surfaces were calculated for over 20 different functionals. The functionals investigated include functionals incorporating an approximate description of the van der Waals dispersion in the correlation functional (vdW-DF and vdW-DF2 functionals), as well as the revTPSS meta-GGA. With two of the functionals investigated here, which include vdW-DF and vdW-DF2 correlation, it has been possible to accurately reproduce molecular beam experiments on sticking of H{sub 2} and D{sub 2}, as these functionals yield a reaction probability curve with an appropriate energy width. Diffraction probabilities computed with these two functionals are however too high compared to experimental diffraction probabilities, which are extrapolated from surface temperatures (T{sub s}) ⩾ 500 K to 0 K using a Debye–Waller model. Further research is needed to establish whether this constitutes a failure of the two candidate SRP functionals or a failure of the Debye–Waller model, the use of which can perhaps in future be avoided by performing calculations that include the effect of surface atom displacement or motion, and thereby of the experimental T{sub s}.

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

Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Function-based Taxonomy Implementation

Function-based taxonomies are relational mapping tools used to clearly illustrate how an organization delivers Critical Functions by using various people, processes, technologies, information, and infrastructure (PPTII). Critical Functions are the actions or activities that make up the organization’s primary purpose. Enabling Functions are the combination of PPTII used by the organization to deliver their Critical Functions. A function-based taxonomy provides a framework to categorize information and related artifacts that document an organization’s unique implementation of PPTII for Critical Function delivery. The ideal state of a function-based taxonomy is to organize the existing knowledge the organization already has throughout their numerous systems, policies, people, procedures, and configurations. A well-organized taxonomy helps organizations to effectively leverage their knowledge by clearly identifying dependencies and connections. This document is the result of combined engineering and analytical experience and describes a repeatable method for producing function-based taxonomies.

42 ENGINEERING↗
DOE OSTI2012

LUMINOSITY FUNCTIONS OF SPITZER-IDENTIFIED PROTOSTARS IN NINE NEARBY MOLECULAR CLOUDS

We identify protostars in Spitzer surveys of nine star-forming (SF) molecular clouds within 1 kpc: Serpens, Perseus, Ophiuchus, Chamaeleon, Lupus, Taurus, Orion, Cep OB3, and Mon R2, which combined host over 700 protostar candidates. These clouds encompass a variety of SF environments, including both low-mass and high-mass SF regions, as well as dense clusters and regions of sparsely distributed star formation. Our diverse cloud sample allows us to compare protostar luminosity functions in these varied environments. We combine near- and mid-infrared photometry from the Two Micron All Sky Survey and Spitzer to create 1-24 {mu}m spectral energy distributions (SEDs). Using protostars from the c2d survey with well-determined bolometric luminosities, we derive a relationship between bolometric luminosity, mid-IR luminosity (integrated from 1-24 {mu}m), and SED slope. Estimations of the bolometric luminosities for protostar candidates are combined to create luminosity functions for each cloud. Contamination due to edge-on disks, reddened Class II sources, and galaxies is estimated and removed from the luminosity functions. We find that luminosity functions for high-mass SF clouds (Orion, Mon R2, and Cep OB3) peak near 1 L{sub Sun} and show a tail extending toward luminosities above 100 L{sub Sun }. The luminosity functions of the low-mass SF clouds (Serpens, Perseus, Ophiuchus, Taurus, Lupus, and Chamaeleon) do not exhibit a common peak, however the combined luminosity function of these regions peaks below 1 L{sub Sun }. Finally, we examine the luminosity functions as a function of the local surface density of young stellar objects. In the Orion molecular clouds, we find a significant difference between the luminosity functions of protostars in regions of high and low stellar density, the former of which is biased toward more luminous sources. This may be the result of primordial mass segregation, although this interpretation is not unique. We compare our luminosity functions to those predicted by models and find that our observed luminosity functions are best matched by models that invoke competitive accretion, although we do not find strong agreement between the high-mass SF clouds and any of the models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Correspondence between structure and function in the human brain at rest

To further understanding of basic and complex cognitive functions, previous connectome research has identified functional and structural connections of the human brain. Functional connectivity is often measured by using resting-state functional magnetic resonance imaging (rs-fMRI) and is generally interpreted as an indirect measure of neuronal activity. Gray matter (GM) primarily consists of neuronal and glia cell bodies; therefore, it is surprising that the majority of connectome research has excluded GM measures. Therefore, we propose that by exploring where GM corresponds to function would aid in the understanding of both structural and functional connectivity and in turn the human connectome. A cohort of 603 healthy participants underwent structural and functional scanning on the same 3 T scanner at the Mind Research Network. To investigate the spatial correspondence between structure and function, spatial independent component analysis (ICA) was applied separately to both GM density (GMD) maps and to rs-fMRI data. ICA of GM delineates structural components based on the covariation of GMD regions among subjects. For the rs-fMRI data, ICA identified spatial patterns with common temporal features. These decomposed structural and functional components were then compared by spatial correlation. Basal ganglia components exhibited the highest structural to resting-state functional spatial correlation (r = 0.59). Cortical components generally show correspondence between a single structural component and several resting-state functional components. We also studied relationships between the weights of different structural components and identified the precuneus as a hub in GMD structural network correlations. In addition, we analyzed relationships between component weights, age, and gender; concluding that age has a significant effect on structural components.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Triplet Tuning: A Novel Family of Non-Empirical Exchange–Correlation Functionals

In the framework of density functional theory (DFT), the lowest triplet excited state (T1) can be evaluated using multiple formulations, the most straightforward of which are unrestricted density functional theory (UDFT) and time-dependent density functional theory (TDDFT). Assuming the exact exchange-correlation (XC) functional is applied, UDFT and TDDFT provide identical energies for T1 ( ET), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T1 and the lowest singlet excited state (S1). Inspired by the optimal tuning strategy for frontier orbital energies [T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 2009, 131, 2818], we proposed a novel and nonempirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in ET is strictly enforced. Referred to as "triplet tuning", our procedure allows us to formulate the XC functional on a case-by-case basis, using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-ωPBEh, is formulated as a long-range-corrected (LRC) hybrid of Perdew-Burke-Ernzerhof (PBE) and Hartree-Fock (HF) functionals [M. A. Rohrdanz, K. M. Martins, and J. M. Herbert, J. Chem. Phys. 2009, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-ωPBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to ET, the optical band gap ( ES), the singlet-triplet gap (Δ EST), and the vertical ionization potential ( I⊥), as it adjusts the effective electron-hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging.

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

Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies

For a set of eight equilibrium intermolecular complexes, it is discovered in this paper that the basis set limit (BSL) cannot be reached by aug-cc-pV5Z for three of the Minnesota density functionals: M06-L, M06-HF, and M11-L. In addition, the M06 and M11 functionals exhibit substantial, but less severe, difficulties in reaching the BSL. By using successively finer grids, it is demonstrated that this issue is not related to the numerical integration of the exchange-correlation functional. In addition, it is shown that the difficulty in reaching the BSL is not a direct consequence of the structure of the augmented functions in Dunning’s basis sets, since modified augmentation yields similar results. By using a very large custom basis set, the BSL appears to be reached for the HF dimer for all of the functionals. As a result, it is concluded that the difficulties faced by several of the Minnesota density functionals are related to an interplay between the form of these functionals and the structure of standard basis sets. It is speculated that the difficulty in reaching the basis set limit is related to the magnitude of the inhomogeneity correction factor (ICF) of the exchange functional. A simple modification of the M06-L exchange functional that systematically reduces the basis set superposition error (BSSE) for the HF dimer in the aug-cc-pVQZ basis set is presented, further supporting the speculation that the difficulty in reaching the BSL is caused by the magnitude of the exchange functional ICF. In conclusion, the BSSE is plotted with respect to the internuclear distance of the neon dimer for two of the examined functionals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

mBEEF-vdW: Robust fitting of error estimation density functionals

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Traditional plant functional groups explain variation in economic but not size-related traits across the tundra biome

Aim: Plant functional groups are widely used in community ecology and earth system modelling to describe trait variation within and across plant communities. However, this approach rests on the assumption that functional groups explain a large proportion of trait variation among species. We test whether four commonly used plant functional groups represent variation in six ecologically important plant traits. Location: Tundra biome. Time period: Data collected between 1964 and 2016. Major taxa studied: 295 tundra vascular plant species. Methods: We compiled a database of six plant traits (plant height, leaf area, specific leaf area, leaf dry matter content, leaf nitrogen, seed mass) for tundra species. We examined the variation in species-level trait expression explained by four traditional functional groups (evergreen shrubs, deciduous shrubs, graminoids, forbs), and whether variation explained was dependent upon the traits included in analysis. We further compared the explanatory power and species composition of functional groups to alternative classifications generated using post-hoc clustering of species-level traits. Results: Traditional functional groups explained significant differences in trait expression, particularly among traits associated with resource economics, which were consistent across sites and at the biome scale. However, functional groups explained 19% of overall trait variation and poorly represented differences in traits associated with plant size. Post-hoc classification of species did not correspond well with traditional functional groups, and explained twice as much variation in species-level trait expression. Main conclusion: Traditional functional groups only coarsely represent variation in well-measured traits within tundra plant communities, and better explain resource economic traits than size-related traits. We recommend caution when using functional group approaches to predict tundra ecosystem change, or ecosystem functions relating to plant size, such as albedo or carbon storage. We argue that alternative classifications or direct use of specific plant traits could provide new insight for ecological prediction and modelling.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

TU-F-12A-04: Differential Radiation Avoidance of Functional Liver Regions Defined by 99mTc-Sulfur Colloid SPECT/CT with Proton Therapy

Purpose: Radiotherapy for hepatocellular carcinoma patients is conventionally planned without consideration of spatial heterogeneity in hepatic function, which may increase risk of radiation-induced liver disease. Pencil beam scanning (PBS) proton radiotherapy (pRT) plans were generated to differentially decrease dose to functional liver volumes (FLV) defined on [{sup 99m}Tc]sulfur colloid (SC) SPECT/CT images (functional avoidance plans) and compared against conventional pRT plans. Methods: Three HCC patients underwent SC SPECT/CT scans for pRT planning acquired 15 min post injection over 24 min. Images were reconstructed with OSEM following scatter, collimator, and exhale CT attenuation correction. Functional liver volumes (FLV) were defined by liver:spleen uptake ratio thresholds (43% to 90% maximum). Planning objectives to FLV were based on mean SC SPECT uptake ratio relative to GTV-subtracted liver and inversely scaled to mean liver dose of 20 Gy. PTV target coverage (V{sub 95}) was matched between conventional and functional avoidance plans. PBS pRT plans were optimized in RayStation for single field uniform dose (SFUD) and systematically perturbed to verify robustness to uncertainty in range, setup, and motion. Relative differences in FLV DVH and target dose heterogeneity (D{sub 2}-D{sub 98})/D50 were assessed. Results: For similar liver dose between functional avoidance and conventional PBS pRT plans (D{sub mean}≤5% difference, V{sub 18Gy}≤1% difference), dose to functional liver volumes were lower in avoidance plans but varied in magnitude across patients (FLV{sub 70%max} D{sub mean}≤26% difference, V{sub 18Gy}≤8% difference). Higher PTV dose heterogeneity in avoidance plans was associated with lower functional liver dose, particularly for the largest lesion [(D{sub 2}-D{sub 98})/D{sub 50}=13%, FLV{sub 90%max}=50% difference]. Conclusion: Differential avoidance of functional liver regions defined on sulfur colloid SPECT/CT is feasible with proton therapy. The magnitude of benefit appears to be patient specific and dependent on tumor location, size, and proximity to functional volumes. Further investigation in a larger cohort of patients may validate the clinical utility of functional avoidance planning of HCC radiotherapy.

60 APPLIED LIFE SCIENCES↗