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DOE OSTI2020

Methods for delineating cellular regions and classifying regions of histopathology and microanatomy

Embodiments disclosed herein provide methods and systems for delineating cell nuclei and classifying regions of histopathology or microanatomy while remaining invariant to batch effects. These systems and methods can include providing a plurality of reference images of histology sections. A first set of basis functions can then be determined from the reference images. Then, the histopathology or microanatomy of the histology sections can be classified by reference to the first set of basis functions, or reference to human engineered features. A second set of basis functions can then be calculated for delineating cell nuclei from the reference images and delineating the nuclear regions of the histology sections based on the second set of basis functions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2014

Multichannel response analysis on 2D projection views for detection of clustered microcalcifications in digital breast tomosynthesis

Purpose: To investigate the feasibility of a new two-dimensional (2D) multichannel response (MCR) analysis approach for the detection of clustered microcalcifications (MCs) in digital breast tomosynthesis (DBT). Methods: With IRB approval and informed consent, a data set of two-view DBTs from 42 breasts containing biopsy-proven MC clusters was collected in this study. The authors developed a 2D approach for MC detection using projection view (PV) images rather than the reconstructed three-dimensional (3D) DBT volume. Signal-to-noise ratio (SNR) enhancement processing was first applied to each PV to enhance the potential MCs. The locations of MC candidates were then identified with iterative thresholding. The individual MCs were decomposed with Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) basis functions and the channelized Hotelling model was trained to produce the MCRs for each MC on the 2D images. The MCRs from the PVs were fused in 3D by a coincidence counting method that backprojects the MC candidates on the PVs and traces the coincidence of their ray paths in 3D. The 3D MCR was used to differentiate the true MCs from false positives (FPs). Finally a dynamic clustering method was used to identify the potential MC clusters in the DBT volume based on the fact that true MCs of clinical significance appear in clusters. Using two-fold cross validation, the performance of the 3D MCR for classification of true and false MCs was estimated by the area under the receiver operating characteristic (ROC) curve and the overall performance of the MCR approach for detection of clustered MCs was assessed by free response receiver operating characteristic (FROC) analysis. Results: When the HG basis function was used for MCR analysis, the detection of MC cluster achieved case-based test sensitivities of 80% and 90% at the average FP rates of 0.65 and 1.55 FPs per DBT volume, respectively. With LG basis function, the average FP rates were 0.62 and 1.57 per DBT volume at the same sensitivity levels. The difference in the two sets of basis functions for detection of MCs did not show statistical significance. Conclusions: The authors' experimental results indicate that the MCR approach is promising for the detection of MCs on PV images. The HG or LG basis functions are both effective in characterizing the signal response of MCs using the channelized Hotelling model. The coincidence counting method for fusion of the 2D MCR in 3D is an important step for FP reduction. Further study is underway to improve the MCR approach for microcalcification detection in DBT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2016

Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Uncertainty reduction in residual stress measurements by an optimised inverse solution using nonconsecutive polynomials

Many destructive methods for measuring residual stresses such as the slitting method require an inverse analysis to solve the problem. The accuracy of the result as well as an uncertainty component (the model uncertainty) depends on the basis functions used in the inverse solution. The use of a series expansion as the basis functions for the inverse solution was analysed in a previous work for the particular case where functions orders grew consecutively. The present work presents a new estimation of the model uncertainty and a new improved methodology to select the final basis functions for the case where the basis is composed of polynomials. Including nonconsecutive polynomial orders in the basis generates a larger space of possible solutions to be evaluated and allows the possibility to include higher-order polynomials. The paper includes a comparison with two other inverse analyses methodologies applied to synthetically generated data. With the new methodology, the final error is reduced and the uncertainty estimation improved.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Daubechies wavelets for linear scaling density functional theory

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 method and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Novel Histogram Based Unsupervised Classification Technique to Determine Natural Classes From Biophysically Relevant Fit Parameters to Hyperspectral Data

Hyperspectral image analysis has benefited from an array of methods that take advantage of the increased spectral depth compared to multispectral sensors; however, the focus of these developments has been on supervised classification methods. Lack of a priori knowledge regarding land cover characteristics can make unsupervised classification methods preferable under certain circumstances. An unsupervised classification technique is presented in this paper that utilizes physically relevant basis functions to model the reflectance spectra. These fit parameters used to generate the basis functions allow clustering based on spectral characteristics rather than spectral channels and provide both noise and data reduction. Histogram splitting of the fit parameters is then used as a means of producing an unsupervised classification. Unlike current unsupervised classification techniques that rely primarily on Euclidian distance measures to determine similarity, the unsupervised classification technique uses the natural splitting of the fit parameters associated with the basis functions creating clusters that are similar in terms of physical parameters. The data set used in this work utilizes the publicly available data collected at Indian Pines, Indiana. This data set provides reference data allowing for comparisons of the efficacy of different unsupervised data analysis. The unsupervised histogram splitting technique presented in this paper is shown to be better than the standard unsupervised ISODATA clustering technique with an overall accuracy of 34.3/19.0% before merging and 40.9/39.2% after merging. Finally, this improvement is also seen as an improvement of kappa before/after merging of 24.8/30.5 for the histogram splitting technique compared to 15.8/28.5 for ISODATA.

58 GEOSCIENCES↗

DOE OSTI2019

A high-order multiscale finite-element method for time-domain elastic wave modeling in strongly heterogeneous media

Efficient and accurate numerical methods for elastic wave modeling in complex media have many important applications. However, it is fairly challenging to model elastic wave propagation in strongly heterogeneous media with high computational efficiency and high-order accuracy simultaneously. We develop a novel high-order multiscale finite-element method to model elastic wave propagation in strongly heterogeneous media in the time domain. The most important feature of our method is a generalization of standard multiscale finite element method by using high-order multiscale finite-element basis functions to capture the fine-scale heterogeneities on the coarse mesh, in contrast to conventional finite-element basis functions that are merely determined by the order of polynomials. These multiscale basis functions leads to a system matrix with significantly reduced dimension, thus enable us to solve the elastic wave equation on the coarse mesh with high-order accuracy and very low computational time cost. In conclusion, we use 2D and 3D numerical examples to demonstrate the superior efficiency and accuracy of our new modeling method compared with the conventional spectral-element method.

58 GEOSCIENCES↗

DOE OSTI2016

Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation

Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Multiscale analysis and computation for flows in heterogeneous media

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Energy conservation in real-time nuclear–electronic orbital Ehrenfest dynamics

Real-time nuclear–electronic orbital Ehrenfest (RT-NEO-Ehrenfest) dynamics methods provide a first-principles approach for describing nonadiabatic molecular processes with nuclear quantum effects. For an efficient description of proton transfer within RT-NEO-Ehrenfest dynamics, the basis function center associated with the quantum proton can be allowed to move classically. Here, this traveling proton basis (TPB) approach effectively captures proton quantum dynamics, although its energy conservation behavior is not yet fully satisfactory. Two recently proposed TPB approaches, in principle, conserve the extended energy, which includes both the system energy and the kinetic energy associated with the proton basis function center. Herein, a thermostatted TPB approach is proposed to improve the conservation of the system energy, excluding the kinetic energy associated with the proton basis function center. In this approach, the quantum proton dynamics are modulated by dynamically rescaling the proton momentum operator to maintain the system energy conservation. With the excited-state intramolecular proton transfer of o-hydroxybenzaldehyde as an example, this approach is shown to significantly improve the system energy conservation while preserving the accuracy of the quantum proton dynamics as achieved in the original TPB approach.

Ehrenfest dynamics↗

DOE OSTI2012

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

A novel algorithm, based on a hybrid Gaussian and plane waves (GPW) approach, is developed for the canonical second-order Møller–Plesset perturbation energy (MP 2 ) of finite and extended systems. The key aspect of the method is that the electron repulsion integrals (ia|λσ) are computed by direct integration between the products of Gaussian basis functions λσ and the electrostatic potential arising from a given occupied-virtual pair density ia. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. In particular, for condensed phase systems, this scheme is highly efficient. Furthermore, our implementation has low memory requirements and displays excellent parallel scalability up to 100 000 processes. In this way, canonical MP 2 calculations for condensed phase systems containing hundreds of atoms or more than 5000 basis functions can be performed within minutes, while systems up to 1000 atoms and 10 000 basis functions remain feasible. Solid LiH has been employed as a benchmark to study basis set and system size convergence. Lattice constants and cohesive energies of various molecular crystals have been studied with MP 2 and double-hybrid functionals.

Chemistry↗

DOE OSTI2018

Coarse-Grained Hydrodynamics from Correlation Functions

This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.

HPC↗

DOE OSTI2020

Data-driven predictive probability density function control of fiber length stochastic distribution shaping in refining process

Pulp is the most important raw material in paper in paper industries, whose Fiber Length Stochastic Distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the output FLSD shaping, which display non-Gaussian distribution properties. Therefore, the traditional control, method based on the mean and variance of fiber length is difficult to control the FLSD shaping effectively. In this paper, a novel data-driven predictive probability density function (PDF) control method is proposed for output FLSD shaping in refining process. Primarily, in order to improve the approximation accuracy of the PDF employing RBF neural network, the parameters (center value and width) of each RBF basis functions are tuned via utilizing iterative learning control (ILC) law, and the corresponding estimations of weights law can be obtained. Secondly, considering that the conventional linear model of weights vector has drawbacks of low accuracy and weak generalization ability, random vector functional link networks (RVFLNs) based data driven nonlinear modelling method is employed to characterize the prediction model between the input variables and weights vector. Finally, in order to reduce the randomness of the output FLSD, a minimum entropy control method under mean constraint is employed to design the predictive PDF controller for the output FLSD shaping with the help of the established nonlinear stochastic distribution model. Both simulations and experiments are given to illustrate the effectiveness and practicability of the proposed method.

Probability debsity function, Fiber length distrib↗