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Adaptive multiconfigurational wave functions

A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N{sub 2} and the potential energy curves for the first three singlet states of C{sub 2}. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu{sub 2}O{sub 2}{sup 2+} core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.

74 ATOMIC AND MOLECULAR PHYSICS↗

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗

Prior-based artifact correction (PBAC) in computed tomography

Purpose: Image quality in computed tomography (CT) often suffers from artifacts which may reduce the diagnostic value of the image. In many cases, these artifacts result from missing or corrupt regions in the projection data, e.g., in the case of metal, truncation, and limited angle artifacts. The authors propose a generalized correction method for different kinds of artifacts resulting from missing or corrupt data by making use of available prior knowledge to perform data completion. Methods: The proposed prior-based artifact correction (PBAC) method requires prior knowledge in form of a planning CT of the same patient or in form of a CT scan of a different patient showing the same body region. In both cases, the prior image is registered to the patient image using a deformable transformation. The registered prior is forward projected and data completion of the patient projections is performed using smooth sinogram inpainting. The obtained projection data are used to reconstruct the corrected image. Results: The authors investigate metal and truncation artifacts in patient data sets acquired with a clinical CT and limited angle artifacts in an anthropomorphic head phantom data set acquired with a gantry-based flat detector CT device. In all cases, the corrected images obtained by PBAC are nearly artifact-free. Compared to conventional correction methods, PBAC achieves better artifact suppression while preserving the patient-specific anatomy at the same time. Further, the authors show that prominent anatomical details in the prior image seem to have only minor impact on the correction result. Conclusions: The results show that PBAC has the potential to effectively correct for metal, truncation, and limited angle artifacts if adequate prior data are available. Since the proposed method makes use of a generalized algorithm, PBAC may also be applicable to other artifacts resulting from missing or corrupt data.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Analysis of the Radiative Transfer Equation with Highly Asymmetric Phase Function

This paper considers a scalar radiative transfer problem with high scattering anisotropy, Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal. which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2 + is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.

Korkin, Sergey V.↗

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗

SU-E-J-16: Automatic Image Contrast Enhancement Based On Automatic Parameter Optimization for Radiation Therapy Setup Verification

Purpose: In RT patient setup 2D images, tissues often cannot be seen well due to the lack of image contrast. Contrast enhancement features provided by image reviewing software, e.g. Mosaiq and ARIA, require manual selection of the image processing filters and parameters thus inefficient and cannot be automated. In this work, we developed a novel method to automatically enhance the 2D RT image contrast to allow automatic verification of patient daily setups as a prerequisite step of automatic patient safety assurance. Methods: The new method is based on contrast limited adaptive histogram equalization (CLAHE) and high-pass filtering algorithms. The most important innovation is to automatically select the optimal parameters by optimizing the image contrast. The image processing procedure includes the following steps: 1) background and noise removal, 2) hi-pass filtering by subtracting the Gaussian smoothed Result, and 3) histogram equalization using CLAHE algorithm. Three parameters were determined through an iterative optimization which was based on the interior-point constrained optimization algorithm: the Gaussian smoothing weighting factor, the CLAHE algorithm block size and clip limiting parameters. The goal of the optimization is to maximize the entropy of the processed Result. Results: A total 42 RT images were processed. The results were visually evaluated by RT physicians and physicists. About 48% of the images processed by the new method were ranked as excellent. In comparison, only 29% and 18% of the images processed by the basic CLAHE algorithm and by the basic window level adjustment process, were ranked as excellent. Conclusion: This new image contrast enhancement method is robust and automatic, and is able to significantly outperform the basic CLAHE algorithm and the manual window-level adjustment process that are currently used in clinical 2D image review software tools.

60 APPLIED LIFE SCIENCES↗

Adaptive enhanced sampling by force-biasing using neural networks

A machine learning assisted method is presented for molecular simulation of systems with rugged free energy landscapes. The method is general and can be combined with other advanced sampling techniques. In the particular implementation proposed here, it is illustrated in the context of an adaptive biasing force approach where, rather than relying on discrete force estimates, one can resort to a self-regularizing artificial neural network to generate continuous, estimated generalized forces. By doing so, the proposed approach addresses several shortcomings common to adaptive biasing force and other algorithms. Specifically, the neural network enables smooth estimates of generalized forces in sparsely sampled regions, force estimates in previously unexplored regions, and continuous force estimates with which to bias the simulation, as opposed to biases generated at specific points of a discrete grid. The usefulness of the method is illustrated with three different examples, chosen to highlight the wide range of applicability of the underlying concepts. In all three cases, the new method is found to enhance considerably the underlying traditional adaptive biasing force approach. Furthermore, the method is also found to provide improvements over previous implementations of neural network assisted algorithms.

97 MATHEMATICS AND COMPUTING↗

Space-Related Applications of Intelligent Control: Which Algorithm to Choose? (Theoretical Analysis of the Problem)

For a space mission to be successful it is vitally important to have a good control strategy. For example, with the Space Shuttle it is necessary to guarantee the success and smoothness of docking, the smoothness and fuel efficiency of trajectory control, etc. For an automated planetary mission it is important to control the spacecraft's trajectory, and after that, to control the planetary rover so that it would be operable for the longest possible period of time. In many complicated control situations, traditional methods of control theory are difficult or even impossible to apply. In general, in uncertain situations, where no routine methods are directly applicable, we must rely on the creativity and skill of the human operators. In order to simulate these experts, an intelligent control methodology must be developed. The research objectives of this project were: to analyze existing control techniques; to find out which of these techniques is the best with respect to the basic optimality criteria (stability, smoothness, robustness); and, if for some problems, none of the existing techniques is satisfactory, to design new, better intelligent control techniques.

Kreinovich, Vladik↗

Image-Based Digital Twin for Assessing the Coupled Electro-Chemo-Mechanical Behavior of Li-Ion Batteries

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The discrete nature of the images' pixel points is employed throughout the model and approximation construction. The mechanical model is verified using an image-based microstructure under tensile loading. A transient electro-chemo-mechanical coupled simulation is performed to evaluate the potential micro-cracking induced degradation of the battery cathode material subjected to charge/discharge cycling.

battery degradation↗

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

SANE: strategic autonomous non-smooth exploration for multiple optima discovery in multi-modal and non-differentiable black-box functions

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and multimodal parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, material structure image spaces, and molecular embedding spaces. Often these systems are black-boxes and time-consuming to evaluate, which resulted in strong interest towards active learning methods such as Bayesian optimization (BO). However, these systems are often noisy which make the black box function severely multi-modal and non-differentiable, where a vanilla BO can get overly focused near a single or faux optimum, deviating from the broader goal of scientific discovery. To address these limitations, here we developed Strategic Autonomous Non-Smooth Exploration (SANE) to facilitate an intelligent Bayesian optimized navigation with a proposed cost-driven probabilistic acquisition function to find multiple global and local optimal regions, avoiding the tendency to becoming trapped in a single optimum. To distinguish between a true and false optimal region due to noisy experimental measurements, a human (domain) knowledge driven dynamic surrogate gate is integrated with SANE. We implemented the gate-SANE into pre-acquired piezoresponse spectroscopy data of a ferroelectric combinatorial library with high noise levels in specific regions, and piezoresponse force microscopy (PFM) hyperspectral data. SANE demonstrated better performance than classical BO to facilitate the exploration of multiple optimal regions and thereby prioritized learning with higher coverage of scientific values in autonomous experiments. Our work showcases the potential application of this method to real-world experiments, where such combined strategic and human intervening approaches can be critical to unlocking new discoveries in autonomous research.

Biswas, Arpan [University of Tennessee, Knoxville,↗

Feasibility of kilovoltage x-ray energy modulation by gaseous media and its application in contrast-enhanced radiotherapy

Purpose: To present a method to modulate the energy contents of a kilovoltage x-ray beam that makes use of a gas as the modulating medium. The method is capable of producing arbitrary x-ray spectra by varying the pressure of the modulating gas and the peak kilovoltage (kVp) of the x-ray beams whose energy is being modulated.Methods: An aluminum chamber was machined with a 0.5 cm wall thickness, designed to withstand pressures of more than 80 atm. A pressure sensor and electrovalves were used to monitor and regulate the gas pressure. Argon was used as the modulating gas. A CdTe spectrometer was used to measure x-ray spectra for different combinations of kVp and gas pressure, thus obtaining a set of basis x-ray functions. An arbitrary x-ray spectrum can then be formed by the linear combination of such basis functions. In order to show one possible application of the modulation method, a contrast-enhanced radiotherapy prostate treatment was optimized with respect to the x-ray beam energy, without restrictions on the possible shape of the resultant x-ray spectra.Results: The x-ray spectra basis functions obtained display a smooth and gradual variation of their average energy as a function of the gas pressure for a given kVp, sometimes in the order of 1 or 2 keV. This gradual variation would be difficult to obtain with a conventional aluminum or copper filters, as the change in thickness necessary to reproduce the data presented would be in the order of micrometers, making necessary the use of a large number of such filters. Using the modulation method presented here, the authors were able to reconstruct the optimized x-ray spectra from the measured basis functions, for different optimization objectives.Conclusions: A method has been developed that allows for the controlled modulation of the energy contents of kilovoltage x-ray spectra. The method has been shown to be able to reproduce spectra of arbitrary shape, such as those obtained from the optimization of contrast-enhanced radiotherapy. The method may have other applications as well, such as in the precise matching of diagnostic x-ray catalog spectra.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Energetics and the Role of Defects in Fe(II)-Catalyzed Goethite Recrystallization from Molecular Simulations

Goethite is one of the most stable and common iron (III) minerals at the Earth’s near surface. However, recent isotope- tracer studies suggest that goethite continuously recrystallizes in the presence of aqueous Fe(II) ions. Such studies often indicate the presence of two regimes of atom exchange kinetics, a rapid stage assigned to reactive defect sites initially available at particle surfaces, followed by slower continuous exchange. An autocatalytic solid-state electron conduction model coupling Fe(II) oxidative adsorption to its reductive release at spatially distinct sites has been proposed, but the thermodynamic driving force has yet to be pinpointed. Here, using a novel hybrid/reactive molecular simulation method, for goethite (110) surfaces at circumneutral pH, we rigorously tested whether surface free energy minimization, including examining the role of structural defects, is sufficient to overcome the activation energy for interfacial electron transfer and conduction. The simulations quantitatively show that: (i). on smooth stable surfaces the available thermal energy at dynamic equilibrium is sufficient to sustain the slow continuous regime of atom exchange kinetics via short intra-surface electron conduction pathways of 1-2 nm (3-5 Fe site hops); (ii). in this slower regime, the model converges to atom exchange kinetics of 10 -5 Fe s -1 cm -2 , a rate recently deduced from stochastic modeling of experimental data and linked to the reductive dissolution rate of goethite; (iii). the driving force for initially rough defective goethite surfaces to smoothen can accelerate atom exchange to an extent quantitatively consistent with that observed in the initial rapid stage, in this case accessing conduction pathways of up to 8 nm. The findings suggest that the interaction of Fe(II) with initially defective goethite surfaces can drive, by the conduction model, atom exchange that is capable of recrystallizing the interiors of nanoscale particles, and that, closer to equilibrium on smooth surfaces, slower atom exchange continues in perpetuity but likely involving only the outermost atomic layers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗

Revealing the Predominant Surface Facets of Rough Cu Electrodes under Electrochemical Conditions

Metal electrodes with rough surfaces are frequently found to convert CO or CO 2 to hydrocarbons and oxygenates with high selectivity and at high reaction rates in comparison with their smooth counterparts. The atomic-level morphology of a rough electrode is likely one key factor responsible for its comparatively high catalytic selectivity and activity. However, few methods are capable of probing the atomic-level structure of rough metal electrodes under electrocatalytic conditions. As a result, the nuances in the atomic-level surface morphology that control the catalytic characteristics of these electrodes have remained largely unexplored. Because the C≡O stretching frequency of atop-bound CO (CO atop ) depends on the coordination of the underlying metal atom, the IR spectrum of this reaction intermediate on the copper electrode could, in principle, provide structural information about the catalytic surface during electrolysis. However, other effects, such as dynamic dipole coupling, easily obscure the dependence of the frequency on the surface morphology. Further, in the limit of low CO atop coverage, where coupling effects are small, the C≡O stretching frequencies of CO atop on Cu(111) and Cu(100) facets are virtually identical. Therefore, on the basis of the C≡O stretching frequency, it is not straightforward to distinguish between these two ubiquitous surface facets, which exhibit vastly different CO reduction activities. Herein, we show that key features of the atomic-level surface morphology of rough copper electrodes can be inferred from the potential dependence of the line shape of the C≡O stretching band of CO atop . Specifically, we compared two types of rough copper thin-film electrodes that are routinely employed in the context of surface-enhanced infrared absorption spectroscopy (SEIRAS). We found that copper films that are electrochemically deposited on Si-supported Au films (CuAu–Si) are poor catalysts for the reduction of CO to ethylene in comparison to copper films (Cu–Si) that are electrolessly deposited onto Si crystals. As quantified by differential electrochemical mass spectrometry (DEMS), the onset potential for ethylene is ~200 ± 65 mV more cathodic for CuAu–Si than that for Cu–Si. To reveal the origin of the disparate catalytic properties of Cu–Si and CuAu–Si, we probed the surfaces of the electrodes with cyclic voltammetry (CV) and SEIRAS. The CV characterization suggests that the (111) surface facet predominates on CuAu–Si, whereas the (100) facet is more common on Cu–Si. SEIRAS reveals that the line shape of the C≡O stretching of CO atop is composed of two bands that are attributable to CO atop on terrace and defect sites. The different surface structures manifest themselves in the form of starkly different potential dependences of the line shape of the C≡O stretching mode of CO atop on the two types of electrodes. With a simple Boltzmann model that considers the different adsorption energies of CO atop on terrace and defect sites, and the resulting CO atop populations on terrace and defect sites, we deduced that the observed electrode-specific potential dependence of the line shape is consistent with the presence of different predominant terrace sites on the two types of films. This strategy for assessing the atomic-level morphology is not restricted to SEIRAS but could also be applied to the C≡O stretching bands recorded with surface-enhanced Raman spectroscopy (SERS), which is suitable for probing a wide range of rough copper electrodes. Therefore, with this work, we establish the potential dependence of the C≡O stretching band of CO atop as a probe of the atomic-level surface structure of rough metal electrodes under electrochemical conditions. When it is coupled with complementary techniques, this methodology provides essential structural information for further improvement in the reaction selectivity of rough metal electrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A RIGOROUS FREE-FORM LENS MODEL OF A2744 TO MEET THE HUBBLE FRONTIER FIELDS CHALLENGE

Hubble Frontier Fields (HFF) imaging of the most powerful lensing clusters provides access to the most magnified distant galaxies. The challenge is to construct lens models capable of describing these complex massive, merging clusters so that individual lensed systems can be reliably identified and their intrinsic properties accurately derived. We apply the free-form lensing method (WSLAP+) to A2744, providing a model independent map of the cluster mass, magnification, and geometric distance estimates to multiply lensed sources. We solve simultaneously for a smooth cluster component on a pixel grid, together with local deflections by the cluster member galaxies. Combining model prediction with photometric redshift measurements, we correct and complete several systems recently claimed and identify four new systems totaling 65 images of 21 systems spanning a redshift range of 1.4 < z < 9.8. The reconstructed mass shows small enhancements in the directions where significant amounts of hot plasma can be seen in X-ray. We compare photometric redshifts with ''geometric redshifts'', finding a high level of self-consistency. We find excellent agreement between predicted and observed fluxes with a best-fit slope of 0.999 ± 0.013 and an rms of ∼0.25 mag, demonstrating that our magnification correction of the lensed background galaxies is very reliable. Intriguingly, few multiply lensed galaxies are detected beyond z ≅ 7.0, despite the high magnification and the limiting redshift of z ≅ 11.5 permitted by the HFF filters. With the additional HFF clusters, we can better examine the plausibility of any pronounced high-z deficit with potentially important implications for the reionization epoch and the nature of dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗