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DOE OSTI2014

The Potosi Reservoir Model 2013c, Property Modeling Update

As part of a larger project co-funded by the United States Department of Energy (US DOE) to evaluate the potential of formations within the Cambro-Ordovician strata above the Mt. Simon as potential targets for carbon sequestration in the Illinois and Michigan Basins, the Illinois Clean Coal Institute (ICCI) requested Schlumberger to evaluate the potential injectivity and carbon dioxide (CO2) plume size of the Cambrian Potosi Formation. The evaluation of this formation was accomplished using wireline data, core data, pressure data, and seismic data from this project as well as two other separately funded projects: the US DOE-funded Illinois Basin–Decatur Project (IBDP) being conducted by the Midwest Geological Sequestration Consortium (MGSC) in Macon County, Illinois, and the Illinois Industrial Carbon Capture and Sequestration (ICCS) project funded through the American Recovery and Reinvestment Act. In 2010, technical performance evaluations on the Cambrian Potosi Formation were performed through reservoir modeling. The data included formation tops from mud logs, well logs from the Verification Well #1 (VW1) and the Injection Well (CCS1), structural and stratigraphic formation from three dimensional (3D) seismic data, and field data from several waste water injection wells for Potosi Formation. The intention was for 2.2 million tons per annum (2 million tonnes per annum [MTPA]) of CO2 to be injected for 20 years. In the Task Error! Reference source not found., the 2010 Potosi heterogeneous model (referred to as the "Potosi Dynamic Model 2010") was re-run using a new injection scenario of 3.5 million tons per annum (3.2 MTPA) for 30 years. The extent of the Potosi Dynamic Model 2010, however, appeared too small for the new injection target. The models size was insufficient to accommodate the evolution of the plume. The new model, Potosi Dynamic Model 2013a, was built by extending the Potosi Dynamic Model 2010 grid to 30 by 30 mi (48 by 48 km), while preserving all property modeling workflows and layering. This model was retained as the base case. In the preceding Task [1], the Potosi reservoir model was updated to take into account the new data from the Verification Well #2 (VW2) which was drilled in 2012. The porosity and permeability modeling was revised to take into account the log data from the new well. Revisions of the 2010 modeling assumptions were also done on relative permeability, capillary pressures, formation water salinity, and the maximum allowable well bottomhole pressure. Dynamic simulations were run using the injection target of 3.5 million tons per annum (3.2 MTPA) for 30 years. This dynamic model was named Potosi Dynamic Model 2013b. In this Task, a new property modeling workflow was applied, where seismic inversion data guided the porosity mapping and geobody extraction. The static reservoir model was fully guided by PorosityCube interpretations and derivations coupled with petrophysical logs from three wells. The two main assumptions are: porosity features in the PorosityCube that correlate with lost circulation zones represent vugular zones, and that these vugular zones are laterally continuous. Extrapolation was done carefully to populate the vugular facies and their corresponding properties outside the seismic footprint up to the boundary of the 30 by 30 mi (48 by 48 km) model. Dynamic simulations were also run using the injection target of 3.5 million tons per annum (3.2 MTPA) for 30 years. This new dynamic model was named Potosi Dynamic Model 2013c. Reservoir simulation with the latest model gives a cumulative injection of 43 million tons (39 MT) in 30 years with a single well, which corresponds to 40% of the injection target. The injection rate is approx. 3.2 MTPA in the first six months as the well is injecting into the surrounding vugs, and declines rapidly to 1.8 million tons per annum (1.6 MTPA) in year 3 once the surrounding vugs are full and the CO2 start to reach the matrix. After, the injection rate declines gradually to 1.2 million tons per annum (1.1 MTPA) in year 18 and stays constant. This implies that a minimum of three (3) wells could be required in the Potosi to reach the injection target. The injectivity evaluated in this Task was higher compared to the preceding Task, since the current facies modeling (guided by the porosity map from the seismic inversion) indicated a higher density of vugs within the vugular zones. 5 As the CO2 follows the paths where vugs interconnection exists, a reasonably large and irregular plume extent was created. After 30 years of injection, the plume extends 13.7 mi (22 km) in E-W and 9.7 mi (16 km) in N-S directions. After injection finishes, the plume continues to migrate laterally, mainly driven by the remaining pressure gradient. After 60 years post-injection, the plume extends 14.2 mi (22.8 km) in E-W and 10 mi (16 km) in N-S directions, and remains constant as the remaining pressure gradient has become very low. Should the targeted cumulative injection of 106 million tons (96 MT) be achieved; a much larger plume extent could be expected. The increase of reservoir pressure at the end of injection is approximately 1,200 psia (8,274 kPa) around the injector and gradually decreases away from the well. The reservoir pressure increase is less than 10 psia (69 kPa) beyond 14 mi (23 km) away from injector. Should the targeted cumulative injection of 106 million tons (96 MT) be achieved; a much larger areal pressure increase could be expected. The reservoir pressure declines rapidly during the first 30 years post injection and the initial reservoir pressure is nearly restored after 100 years post-injection. The present evaluation is mainly associated with uncertainty on the vugs permeability and interconnectivity. The use of porosity mapping from seismic inversion might have reduced the uncertainty on the lateral vugs body distributions. However, major uncertainties on the Potosi vugs permeability remains. Therefore, injection test and pressure interference test among the wells could be considered to evaluate the local vugs permeability, extent, and interconnectivity. Facies modeling within the Potosi has yet to be thoroughly addressed. The carbonates during the time of deposition are believed to be regionally extensive. However, it may be worth delineating the reservoir with other regional wells or modern day analogues to understand the extent of the Potosi. More specifically, the model could incorporate lateral changes or trends if deemed necessary to represent facies transition. Data acquisitions to characterize the fracture pressure gradient, the formation water properties, the relative permeability, and the capillary pressure could also be considered in order to allow a more rigorous evaluation of the Potosi storage performance. A simulation using several injectors could also be considered to determine the required number of wells and appropriate spacing to achieve the injection target while taking into account the pressure interference.

Adushita, Yasmin↗

DOE OSTI2020

Novel, Simplified Air Delivery System Design Gets Commercialized

Typical air delivery systems require contractors to design systems that are complex, difficult to integrate into the framing and structural components of a home, and often do not meet the optimization demands of newer energy-efficient homes. This complex process can be a burden to already strained construction labor costs. However, a new technology simplifies duct system design to improve comfort and eliminate sources of installation error for residential air delivery systems.

Building America↗

DOE OSTI2020

Novel, Simplified Air Delivery System Design Gets Commercialized

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2018

Conservative model reduction for finite-volume models

Here, this work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed reduced-order models associate with optimization problems characterized by a minimum-residual objective function and nonlinear equality constraints that explicitly enforce conservation over subdomains. Conservative Galerkin projection arises from formulating this optimization problem at the time-continuous level, while conservative least-squares Petrov–Galerkin (LSPG) projection associates with a time-discrete formulation. We equip these approaches with hyper-reduction techniques in the case of nonlinear flux and source terms, and also provide approaches for handling infeasibility. In addition, we perform analyses that include deriving conditions under which conservative Galerkin and conservative LSPG are equivalent, as well as deriving a posteriori error bounds. Numerical experiments performed on a parameterized quasi-1D Euler equation demonstrate the ability of the proposed method to ensure not only global conservation, but also significantly lower state-space errors than nonconservative reduced-order models such as standard Galerkin and LSPG projection.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Critical Assessment of Electronic Structure Descriptors for Predicting Perovskite Catalytic Properties

The discovery and design of materials which can efficiently catalyze the oxygen reduction and evolution reactions at reduced temperatures is important for facilitating the widespread adoption of fuel cell and electrolyzer technologies. Numerous studies have produced correlations between catalytic properties, such as oxygen surface exchange or electrode area specific resistance (ASR), and properties of the catalyst material. However, correlations have historically been limited in scope (e.g., using only a few materials or at a single temperature) and it has been difficult to provide detailed assessments of their robustness. Here, in this study, we assess the ability of the O p-band center electronic structure descriptor, obtained from density functional theory (DFT) calculations, to correlate with oxygen surface exchange rates, diffusivities, and area specific resistances for a large database of perovskite oxide catalytic properties. By data mining the literature, we obtain 747 catalytic property value data points spanning 299 unique perovskite compositions from 313 studies. We assess linear correlations of each property with the O p-band center and find generally modest correlations that are qualitatively useful (prediction mean absolute errors of about 0.5 log units are typical), where the correlations are improved at higher temperatures (e.g., 800 °C vs. 500 °C) and significantly improve when considering fits to the subset of materials which have multiple independent measurements. These findings suggest that the spread of property data is significantly influenced by experimental uncertainty, and subsequent measurements of additional materials will likely improve the O p-band center correlations.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2012

Studies of the Electromagnetic Structure of Mesons at Jefferson Lab

The Jefferson Laboratory Hall B PrimEx Collaboration is using tagged photons to perform an absolute 1.4% level cross section measurement of the photoproduction of neutral pions in the Coulomb field of a nucleus. The absolute cross section for this process is directly proportional to the neutral pion radiative decay width and consequently the uncertainty in the luminosity is directly reflected in the final error bar of the measurement. The PI has taken primary responsibility for the photon flux determination and in this technical report, we outline the steps taken to limit the uncertainty in the tagged photon flux to the 1% level. These include the use of a total absorption counter for absolute flux calibration, a pair spectrometer for online relative flux monitoring, and updated procedures for postbremsstrahlung electron counting. The photon tagging technique has been used routinely in its various forms to provide quasimonochromatic photons for absolute photonuclear cross section measurements. The analysis of such experiments in the context of bremsstrahlung photon tagging was summarized by Owens in 1990. Since then, a number of developments have made possible significant improvements in the implementation of this technique. Here, we describe the steps taken by the PrimEx Collaboration in Hall B of Jefferson Laboratory to limit the systematic uncertainty in the absolute photon flux to 1%. They include an absolute flux calibration at low intensity with a total absorption counter, online relative flux monitoring with a pair spectrometer, and the use of multihit time to digital converters for post bremsstrahlung electron counting during production data runs. While this discussion focuses on the analysis techniques utilized by the PrimEx Collaboration which involves a bremsstrahlung based photon tagging system to measure the neutral pion lifetime, the methods described herein readily apply to other types of photon tagging systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

Methods, software and datasets to verify DVH calculations against analytical values: Twenty years late(r)

Purpose: The authors designed data, methods, and metrics that can serve as a standard, independent of any software package, to evaluate dose-volume histogram (DVH) calculation accuracy and detect limitations. The authors use simple geometrical objects at different orientations combined with dose grids of varying spatial resolution with linear 1D dose gradients; when combined, ground truth DVH curves can be calculated analytically in closed form to serve as the absolute standards. Methods: DICOM RT structure sets containing a small sphere, cylinder, and cone were created programmatically with axial plane spacing varying from 0.2 to 3 mm. Cylinders and cones were modeled in two different orientations with respect to the IEC 1217 Y axis. The contours were designed to stringently but methodically test voxelation methods required for DVH. Synthetic RT dose files were generated with 1D linear dose gradient and with grid resolution varying from 0.4 to 3 mm. Two commercial DVH algorithms—PINNACLE (Philips Radiation Oncology Systems) and PlanIQ (Sun Nuclear Corp.)—were tested against analytical values using custom, noncommercial analysis software. In Test 1, axial contour spacing was constant at 0.2 mm while dose grid resolution varied. In Tests 2 and 3, the dose grid resolution was matched to varying subsampled axial contours with spacing of 1, 2, and 3 mm, and difference analysis and metrics were employed: (1) histograms of the accuracy of various DVH parameters (total volume, D{sub max}, D{sub min}, and doses to % volume: D99, D95, D5, D1, D0.03 cm{sup 3}) and (2) volume errors extracted along the DVH curves were generated and summarized in tabular and graphical forms. Results: In Test 1, PINNACLE produced 52 deviations (15%) while PlanIQ produced 5 (1.5%). In Test 2, PINNACLE and PlanIQ differed from analytical by >3% in 93 (36%) and 18 (7%) times, respectively. Excluding D{sub min} and D{sub max} as least clinically relevant would result in 32 (15%) vs 5 (2%) scored deviations for PINNACLE vs PlanIQ in Test 1, while Test 2 would yield 53 (25%) vs 17 (8%). In Test 3, statistical analyses of volume errors extracted continuously along the curves show PINNACLE to have more errors and higher variability (relative to PlanIQ), primarily due to PINNACLE’s lack of sufficient 3D grid supersampling. Another major driver for PINNACLE errors is an inconsistency in implementation of the “end-capping”; the additional volume resulting from expanding superior and inferior contours halfway to the next slice is included in the total volume calculation, but dose voxels in this expanded volume are excluded from the DVH. PlanIQ had fewer deviations, and most were associated with a rotated cylinder modeled by rectangular axial contours; for coarser axial spacing, the limited number of cross-sectional rectangles hinders the ability to render the true structure volume. Conclusions: The method is applicable to any DVH-calculating software capable of importing DICOM RT structure set and dose objects (the authors’ examples are available for download). It includes a collection of tests that probe the design of the DVH algorithm, measure its accuracy, and identify failure modes. Merits and applicability of each test are discussed.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Performance of Laser-Based Electronic Devices for Structural Analysis of Amazonian Terra-Firme Forests

Tropical vegetation biomass represents a key component of the carbon stored in global forest ecosystems. Estimates of aboveground biomass commonly rely on measurements of tree size (diameter and height) and then indirectly relate, via allometric relationships and wood density, to biomass sampled from a relatively small number of harvested and weighed trees. Recently, however, novel in situ remote sensing techniques have been proposed, which may provide nondestructive alternative approaches to derive biomass estimates. Nonetheless, we still lack knowledge of the measurement uncertainties, as both the calibration and validation of estimates using different techniques and instruments requires consistent assessment of the underlying errors. To that end, we investigate different approaches estimating the tropical aboveground biomass in situ. We quantify the total and systematic errors among measurements obtained from terrestrial light detection and ranging (LiDAR), hypsometer-based trigonometry, and traditional forest inventory. We show that laser-based estimates of aboveground biomass are in good agreement (<10% measurement uncertainty) with traditional measurements. However, relative uncertainties vary among the allometric equations based on the vegetation parameters used for parameterization. We report the error metrics for measurements of tree diameter and tree height and discuss the consequences for estimated biomass. Despite methodological differences detected in this study, we conclude that laser-based electronic devices could complement conventional measurement techniques, thereby potentially improving estimates of tropical vegetation biomass.

54 ENVIRONMENTAL SCIENCES↗

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 OSTI2021

Comparison of Conventional and Constrained Variational Methods for Computing Large-Scale Budgets and Forcing Fields

Analyses of atmospheric heat and moisture budgets serve as an effective tool to study convective characteristics over a region and to provide large-scale forcing fields for various modeling applications. This paper examines two popular methods for computing large-scale atmospheric budgets: the conventional budget method (CBM) using objectively gridded analyses based primarily on radiosonde data and the constrained variational analysis (CVA) approach which supplements vertical profiles of atmospheric fields with measurements at the top of the atmosphere and at the surface to conserve mass, water, energy, and momentum. Successful budget computations are dependent on accurate sampling and analyses of the thermodynamic state of the atmosphere and the divergence field associated with convection and the large-scale circulation that influences it. Utilizing analyses generated from data taken during Dynamics of the Madden-Julian Oscillation (DYNAMO) field campaign conducted over the central Indian Ocean from October to December 2011, we evaluate the merits of these budget approaches and examine their limitations. While many of the shortcomings of the CBM, in particular effects of sampling errors in sounding data, are effectively minimized with CVA, accurate large-scale diagnostics in CVA are dependent on reliable background fields and rainfall constraints. Finally, for the DYNAMO analyses examined, the operational model fields used as the CVA background state provided wind fields that accurately resolved the vertical structure of convection in the vicinity of Gan Island. However, biases in the model thermodynamic fields were somewhat amplified in CVA resulting in a convective environment much weaker than observed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Model-observation discrepancies in Arctic moisture intrusions: causes and pathways for improved simulation

Arctic moisture intrusions (MIs), narrow filaments of strong moisture transport, are key drivers of poleward moisture flux and Arctic weather extremes, yet their representation in climate models is poorly understood. Using a new Arctic MI detection algorithm, we document persistent biases across three CMIP generations (CMIP3–CMIP6): models overestimate MI occurrence over the Pacific sector and underestimate it over the Atlantic sector. These errors stem from misrepresented midlatitude westerly jets, with an equatorward North Atlantic jet associated with too few Atlantic MIs, and a poleward, weakened North Pacific jet linked to too many Pacific MIs. Experiments that correct sea surface temperature and sea ice concentration biases and increase atmospheric resolution improve jet structure and MI statistics, while a cloud-locking simulation indicates that better high-frequency cloud–radiation–circulation interactions can yield further gains. Our results clarify pathways to reducing long-standing MI and jet biases, providing guidance for improving simulations of Arctic and midlatitude climate.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

A generalized Ewald decomposition for screened Coulomb interactions

Medium-range interactions occur in a wide range of systems, including charged-particle systems with varying screening lengths. We generalize the Ewald method to charged systems described by interactions involving an arbitrary dielectric response function ϵ(𝐤). We provide an error estimate and optimize the generalization to find the break-even parameters that separate a neighbor list-only algorithm from the particle-particle particle-mesh algorithm. We examine the implications of different choices of the screening length for the computational cost of computing the dynamic structure factor. We then use our new method in molecular dynamics simulations to compute the dynamic structure factor for a model plasma system and examine the wave-dispersion properties of this system.

Dharuman, Gautham↗

DOE OSTI2018

Atomic-position independent descriptor for machine learning of material properties

The high-throughput screening of periodic inorganic solids using machine learning methods requires atomic positions to encode structural and compositional details into appropriate material descriptors. These atomic positions are not available a priori for new materials, which severely limits exploration of novel materials. In this work, we overcome this limitation by using only crystallographic symmetry information in the structural description of materials. We show that for materials with identical structural symmetry, machine learning is trivial, and accuracies similar to that of density functional theory calculations can be achieved by using only atomic numbers in the material description. For machine learning of formation energies of bulk crystalline solids, this simple material descriptor is able to achieve prediction mean absolute errors of only 0.07 eV/at on a test dataset consisting of more than 85 000 diverse materials. Finally, this atomic-position independent material descriptor presents a new route of materials discovery wherein millions of materials can be screened by training a machine learning model over a drastically reduced subspace of materials.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Crystal growth, microstructure, and physical properties of SrMnSb 2

We report on the crystal and magnetic structures, magnetic, and transport properties of SrMnSb 2 single crystals grown by the self-flux method. Magnetic susceptibility measurements reveal an antiferromagnetic (AFM) transition at T N = 295(3) K. Above T N , the susceptibility slightly increases and forms a broad peak at T ~ 420 K, which is a typical feature of two-dimensional magnetic systems. Neutron diffraction measurements on single crystals confirm the previously reported C-type AFM structure below T N . Both de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) effects are observed in SrMnSb2 single crystals. Analysis of the oscillatory component by a Fourier transform shows that the prominent frequencies obtained by the two different techniques are practically the same within error regardless of sample size or saturated magnetic moment. Transmission electron microscopy (TEM) reveals the existence of stacking faults in the crystals, which result from a horizontal shift of Sb atomic layers suggesting possible ordering of Sb vacancies in the crystals. Increase of temperature in susceptibility measurements leads to the formation of a strong peak at T ~ 570 K that upon cooling under magnetic field the susceptibility shows a ferromagnetic transition at T C ~ 580 K. Neutron powder diffraction on crushed single-crystals does not support an FM phase above T N . Furthermore, X-ray magnetic circular dichroism (XMCD) measurements of a single crystal at the L 2,3 edge of Mn shows a signal due to induced canting of AFM moments by the applied magnetic field. All evidence strongly suggests that a chemical transformation at the surface of single crystals occurs above 500 K concurrently producing a minute amount of ferromagnetic impurity phase.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

Here, compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several compressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers l1_ls, SpaRSA, CGIST, FPC_AS, and ADMM, we develop techniques to mitigate overfitting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendations on parameter settings for these techniques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-crossflow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy, and computational trade-offs between polynomial bases of different degrees, and practicability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A Physical Model for Understanding the Activation of MoS 2 Basal-plane Sulfur Atoms for the Hydrogen Evolution Reaction

All the DFT calculations are done with the Vienna Ab Initio Simulation Package (VASP) using the projector augmented wave method. The Bayesian error estimation exchange-correlation functionals (BEEF) with van der Waals interactions are employed. A plane-wave cutoff energy of 400 eV is used together with PAW-PBE potentials where semi core p states are treated as valence. All the calculations allow for spin-polarization. The structures are relaxed until the force is converged to < 0.01 eV/Å. The lattice parameter of MoS 2 unit cell, optimized with this functional, is 3.19 Å. A (4×4) supercell is used to model all the transition metal doped MoS 2 systems studied here, including those with S vacancies. For calculations in the initial dopant structure exploration, the Brillouin zone is sampled with a 3x3x1 Monkhorst-Pack k-point mesh. A 6×6×1 Monkhorst-Pack k-point mesh is used for the H binding energy and density of states calculations. In all calculations, the vacuum layer is set as 15 Å to eliminate periodic interaction perpendicular to the basal plane.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗

DOE OSTI2021

DeepDist: real-value inter-residue distance prediction with deep residual convolutional network

Abstract Background Driven by deep learning, inter-residue contact/distance prediction has been significantly improved and substantially enhanced ab initio protein structure prediction. Currently, most of the distance prediction methods classify inter-residue distances into multiple distance intervals instead of directly predicting real-value distances. The output of the former has to be converted into real-value distances to be used in tertiary structure prediction. Results To explore the potentials of predicting real-value inter-residue distances, we develop a multi-task deep learning distance predictor (DeepDist) based on new residual convolutional network architectures to simultaneously predict real-value inter-residue distances and classify them into multiple distance intervals. Tested on 43 CASP13 hard domains, DeepDist achieves comparable performance in real-value distance prediction and multi-class distance prediction. The average mean square error (MSE) of DeepDist’s real-value distance prediction is 0.896 Å 2 when filtering out the predicted distance ≥ 16 Å, which is lower than 1.003 Å 2 of DeepDist’s multi-class distance prediction. When distance predictions are converted into contact predictions at 8 Å threshold (the standard threshold in the field), the precision of top L/5 and L/2 contact predictions of DeepDist’s multi-class distance prediction is 79.3% and 66.1%, respectively, higher than 78.6% and 64.5% of its real-value distance prediction and the best results in the CASP13 experiment. Conclusions DeepDist can predict inter-residue distances well and improve binary contact prediction over the existing state-of-the-art methods. Moreover, the predicted real-value distances can be directly used to reconstruct protein tertiary structures better than multi-class distance predictions due to the lower MSE. Finally, we demonstrate that predicting the real-value distance map and multi-class distance map at the same time performs better than predicting real-value distances alone.

59 BASIC BIOLOGICAL SCIENCES↗