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At least 811 records · Page 45

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Shaykhian, Gholam Ali↗

Validation for 2D/3D registration II: The comparison of intensity- and gradient-based merit functions using a new gold standard data set

Purpose: A new gold standard data set for validation of 2D/3D registration based on a porcine cadaver head with attached fiducial markers was presented in the first part of this article. The advantage of this new phantom is the large amount of soft tissue, which simulates realistic conditions for registration. This article tests the performance of intensity- and gradient-based algorithms for 2D/3D registration using the new phantom data set. Methods: Intensity-based methods with four merit functions, namely, cross correlation, rank correlation, correlation ratio, and mutual information (MI), and two gradient-based algorithms, the backprojection gradient-based (BGB) registration method and the reconstruction gradient-based (RGB) registration method, were compared. Four volumes consisting of CBCT with two fields of view, 64 slice multidetector CT, and magnetic resonance-T1 weighted images were registered to a pair of kV x-ray images and a pair of MV images. A standardized evaluation methodology was employed. Targets were evenly spread over the volumes and 250 starting positions of the 3D volumes with initial displacements of up to 25 mm from the gold standard position were calculated. After the registration, the displacement from the gold standard was retrieved and the root mean square (RMS), mean, and standard deviation mean target registration errors (mTREs) over 250 registrations were derived. Additionally, the following merit properties were computed: Accuracy, capture range, number of minima, risk of nonconvergence, and distinctiveness of optimum for better comparison of the robustness of each merit. Results: Among the merit functions used for the intensity-based method, MI reached the best accuracy with an RMS mTRE down to 1.30 mm. Furthermore, it was the only merit function that could accurately register the CT to the kV x rays with the presence of tissue deformation. As for the gradient-based methods, BGB and RGB methods achieved subvoxel accuracy (RMS mTRE down to 0.56 and 0.70 mm, respectively). Overall, gradient-based similarity measures were found to be substantially more accurate than intensity-based methods and could cope with soft tissue deformation and enabled also accurate registrations of the MR-T1 volume to the kV x-ray image. Conclusions: In this article, the authors demonstrate the usefulness of a new phantom image data set for the evaluation of 2D/3D registration methods, which featured soft tissue deformation. The author's evaluation shows that gradient-based methods are more accurate than intensity-based methods, especially when soft tissue deformation is present. However, the current nonoptimized implementations make them prohibitively slow for practical applications. On the other hand, the speed of the intensity-based method renders these more suitable for clinical use, while the accuracy is still competitive.

60 APPLIED LIFE SCIENCES↗

Distance‐based reconstruction of protein quaternary structures from inter‐chain contacts

Abstract Predicting the quaternary structure of protein complex is an important problem. Inter‐chain residue‐residue contact prediction can provide useful information to guide the ab initio reconstruction of quaternary structures. However, few methods have been developed to build quaternary structures from predicted inter‐chain contacts. Here, we develop the first method based on gradient descent optimization (GD) to build quaternary structures of protein dimers utilizing inter‐chain contacts as distance restraints. We evaluate GD on several datasets of homodimers and heterodimers using true/predicted contacts and monomer structures as input. GD consistently performs better than both simulated annealing and Markov Chain Monte Carlo simulation. Starting from an arbitrarily quaternary structure randomly initialized from the tertiary structures of protein chains and using true inter‐chain contacts as input, GD can reconstruct high‐quality structural models for homodimers and heterodimers with average TM‐score ranging from 0.92 to 0.99 and average interface root mean square distance from 0.72 Å to 1.64 Å. On a dataset of 115 homodimers, using predicted inter‐chain contacts as restraints, the average TM‐score of the structural models built by GD is 0.76. For 46% of the homodimers, high‐quality structural models with TM‐score ≥ 0.9 are reconstructed from predicted contacts. There is a strong correlation between the quality of the reconstructed models and the precision and recall of predicted contacts. Only a moderate precision or recall of inter‐chain contact prediction is needed to build good structural models for most homodimers. Moreover, GD improves the quality of quaternary structures predicted by AlphaFold2 on a Critical Assessment of Techniques for Protein Structure Prediction–Critical Assessments of Predictions of Interactions dataset.

59 BASIC BIOLOGICAL SCIENCES↗

Quasi parton distributions and the gradient flow

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.

42 ENGINEERING↗

Multi-component Reynolds-averaged Navier–Stokes simulations of Richtmyer–Meshkov instability and mixing induced by reshock at different times

Turbulent mixing generated by shock-driven acceleration of a perturbed interface is simulated using a new multi-component Reynolds-averaged Navier–Stokes (RANS) model closed with a two-equation K–ϵ model. Here, the model is implemented in a hydrodynamics code using a third-order weighted essentially non-oscillatory finite-difference method for the advection terms and a second-order central difference method for the gradients in the source and diffusion terms. In the present reshocked Richtmyer–Meshkov instability and mixing study, an incident shock with Mach number Ma s = 1.20 is generated in air and progresses into a sulfur hexafluoride test section. The time evolution of the predicted mixing layer widths corresponding to six shock tube test section lengths are compared with experimental measurements and three-dimensional multi-mode numerical simulations. The mixing layer widths are also compared with the analytical self-similar power-law solution of the simplified model equations prior to reshock. A set of model coefficients and initial conditions specific to these six experiments is established, for which the widths before and after reshock agree very well with experimental and numerical simulation data. A second set of general coefficients that accommodates a broader range of incident shock Mach numbers, Atwood numbers, and test section lengths is also established by incorporating additional experimental data for Ma s = 1.24, 1.50, and 1.98 with At = 0.67 and Ma s = 1.45 with At = –0.67 and previous RANS modeling. Terms in the budgets of the turbulent kinetic energy and dissipation rate equations are examined to evaluate the relative importance of turbulence production, dissipation and diffusion mechanisms during mixing. Convergence results for the mixing layer widths, mean fields, and turbulent fields under grid refinement are presented for each of the Ma s = 1.20 cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Machine Learning Analysis of Impact of Western US Fires on Central US Hailstorms

Fires, including wildfires, harm air quality and essential public services like transportation, communication, and utilities. These fires can also influence atmospheric conditions, including temperature and aerosols, potentially affecting severe convective storms. Here, we investigate the remote impacts of fires in the western United States (WUS) on the occurrence of large hail (size: $\geqslant$ 2.54 cm) in the central US (CUS) over the 20-year period of 2001–20 using the machine learning (ML), Random Forest (RF), and Extreme Gradient Boosting (XGB) methods. The developed RF and XGB models demonstrate high accuracy (> 90%) and F1 scores of up to 0.78 in predicting large hail occurrences when WUS fires and CUS hailstorms coincide, particularly in four states (Wyoming, South Dakota, Nebraska, and Kansas). The key contributing variables identified from both ML models include the meteorological variables in the fire region (temperature and moisture), the westerly wind over the plume transport path, and the fire features (i.e., the maximum fire power and burned area). Importantly, the results confirm a linkage between WUS fires and severe weather in the CUS, corroborating the findings of our previous modeling study conducted on case simulations with a detailed physics model.

54 ENVIRONMENTAL SCIENCES↗

Strong Correlation Effect in Ferrimagnetic Half-Metallic V{sub 2}CoAl and V{sub 2}CoGa Heusler Compounds

We present first-principles calculations based on the full-potential linearized augmented plane wave (FP-LAPW) method to investigate the structural, elastic, electronic, and magnetic properties of the Heusler compounds V{sub 2}CoAl and V{sub 2}CoGa. We explore different magnetic configurations in both regular and inverse Heusler structures: the Cu{sub 2}MnAl-type and Hg{sub 2}CuTi-type structures respectively. Our compounds are found to be ferrimagnets in the inverse Heusler structure. To take into account the effects of the strong correlation among the localized d-states, we perform a calculation using the GGA+U method (the general gradient approximation with the Hubbard on-site Coulomb correction U). Then we show that both compounds exhibit a half-metallic character and have a magnetic moment of 2.00 μ{sub B} per formula unit. This latter statement is coherent with the generalized Slater-Pauling rule (SP). In terms of the band structure calculations, we explain the formation of the indirect energy band gaps in the spin-majority channels. We also use the mean-field approximation (MFA) to discuss the magnetic exchange couplings and predict the Curie temperature for both compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of Fe Doping and O Vacancies on the Magnetic Properties of Rutile TiO{sub 2}

Magnetism sources of Fe doping and O vacancies, which coexist in the presence of rutile TiO{sub 2}, are controversial and require a resolution. The effects of Fe doping and point defect on the magnetism of rutile TiO{sub 2} were studied using geometry optimization and energy calculation based on the first principle generalized gradient approximation + U method (GGA+U) of density functional theory. Fe/Vo ratio is 1:1 in rutile TiO{sub 2}. The next closest distance between Fe and Vo is 0.04082 nm. The formation energy of the doping system is the smallest. This doping system has the highest stability. The coexistence of Fe doping and O vacancy achieved ferromagnetic long-range order. The different ratios of Fe/Vo are 1:1, 1:2, 2:1, and 2:2. The magnetic properties of the doping system are significantly different. At a ratio of 2:1, the magnetic moment is the largest among all doping systems. Moreover, the Curie temperature of the doping system can be higher than room temperature. These findings can obtain dilute magnetic semiconductors with potential application value. At a Fe/V{sub O} ratio of 2:2, the Ti{sub 14}Fe{sub 2}O{sub 30} system produces a half-metallic property of 100% electron spin polarizability. This is the most valuable application for designing and preparing novel spintronic injection source dilute magnetic semiconductors. The magnetic source is mainly mediated by the holes generated by Fe doping and O vacancy complexes, thereby causing the spin polarization double exchange effect on the electron of Ti–3d orbital atoms near the O vacancy, O–2p electron orbital, and Fe–3d electron orbital. This feature is consistent with the following theories: the mean field approximation and the double exchange mechanism theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optimal Wetting Angles in Lattice Boltzmann Simulations of Viscous Fingering

We conduct pore-scale simulations of two-phase flow using the 2D Rothman–Keller colour gradient lattice Boltzmann method to study the effect of wettability on saturation at breakthrough (sweep) when the injected fluid first passes through the right boundary of the model. We performed a suite of 189 simulations in which a “red” fluid is injected at the left side of a 2D porous model that is initially saturated with a “blue” fluid spanning viscosity ratios M=ν r /ν b ∈[0.001,100] and wetting angles θ w ∈[0°,180°]. As expected, at low-viscosity ratios M=ν r /ν b $\ll$1 we observe viscous fingering in which narrow tendrils of the red fluid span the model, and for high-viscosity ratios M$\gg$1, we observe stable displacement. The viscous finger morphology is affected by the wetting angle with a tendency for more rounded fingers when the injected fluid is wetting. However, rather than the expected result of increased saturation with increasing wettability, we observe a complex saturation landscape at breakthrough as a function of viscosity ratio and wetting angle that contains hills and valleys with specific wetting angles at given viscosity ratios that maximize sweep. This unexpected result that sweep does not necessarily increase with wettability has major implications to enhanced oil recovery and suggests that the dynamics of multiphase flow in porous media has a complex relationship with the geometry of the medium and the hydrodynamical parameters.

Engineering↗

Speeding up and reducing memory usage for scientific machine learning via mixed precision

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets) stand out as the leading techniques for solving partial differential equations by incorporating both physical equations and experimental data. However, training PINNs and DeepONets require significant computational resources, including long computational times and large amounts of memory. In search of computational efficiency, training neural networks using half precision (float16) rather than the conventional single (float32) or double (float64) precision has gained substantial interest, given the inherent benefits of reduced computational time and memory consumed. However, we find that float16 cannot be applied to SciML methods, because of gradient divergence at the start of training, weight updates going to zero, and the inability to converge to a local minima. To overcome these limitations, we explore mixed precision, which is an approach that combines the float16 and float32 numerical formats to reduce memory usage and increase computational speed. Our experiments showcase that mixed precision training not only substantially decreases training times and memory demands but also maintains model accuracy. Here, we also reinforce our empirical observations with a theoretical analysis. The research has broad implications for SciML in various computational applications.

97 MATHEMATICS AND COMPUTING↗

Phase-field modeling of dislocation–interstitial interactions

The mechanical behavior of body-centered cubic (BCC) materials can be dramatically affected by the presence of interstitial solute atoms. Here we present a new phase-field dislocation dynamics formulation to include the diffusion of interstitials. Short-range interactions are accounted for by a concentration-dependent lattice energy, and long-range interactions are accounted for by modifications to the elastic energy. The interstitial diffusion law introduces gradients that require methods for minimizing Gibbs oscillations, which is done via a modified Green’s function. The formulation is general to any solute-solvent system and is applied here to Nb-O as a model system, whose interstitial parameters are obtained from ab initio calculations. The effect of O on the core structures of Nb edge and screw dislocations is calculated. The diffusion of O to form interstitial atmospheres around dislocation cores is simulated, as well as the critical stresses required for dislocations to break away or cross slip from these atmospheres. Future applications of the method to simulate complex interstitial embrittlement mechanisms are discussed.

36 MATERIALS SCIENCE↗

Identifying common stored product insects using automated deep learning methods

Monitoring stored product insect pests is a common practice for post-harvest management of stored grain and grain-based commodities, which helps ensure product quality from harvest to final consumer. Current methods of sampling and monitoring can be time-consuming, labor-intensive, expensive and require expertise in insect identification. Therefore, this study aims to develop an image-based automated identification system for common stored product insect species using deep-learning methods. Top-down images of the common stored product adult insect species of Rhyzopertha dominica, Cryptolestes ferrugineus, Tribolium castaneum, Sitophilus oryzae, and Oryzaephilus surinamensis were acquired and analyzed. Deep learning-based, state-of-the-art Convolutional Neural Networks (CNN) models (ResNet-50, MobileNet-v2, DarkNet-53, and EfficientNet-b0) were fine-tuned with a transfer learning approach to classify the insect species. All models were able to correctly identify the insect species with at least 96% accuracy and with few misclassifications. One issue with trained CNNs is that they do not explain the reasoning for the classification and are often called a “black box”. Therefore, visualization methods called Gradient-weighted Class Activation Mapping (Grad-CAM) were implemented to explore the black box network. The Grad-CAM uses heat maps to highlight the major image features that the network focused on to make insect species predictions. The Grad-CAM verifies the network's prediction and also helps improve network performance. This study contributes to the overall goal of developing a camera-based system for monitoring stored grain insects. As a result, the developed system would empower warehouse, flour mills, and other food facilities with a tool to quickly and accurately identify insect species in stored product environments and could be implemented as part of a close to real-time monitoring system.

60 APPLIED LIFE SCIENCES↗

In-depth quantitative analysis of the microstructures produced by Surface Mechanical Attrition Treatment (SMAT)

Electron BackScattered Diffraction (EBSD) maps are used to characterize quantitatively the graded microstructure formed by Surface Mechanical Attrition Treatment (SMAT) and applied here to the 316L stainless steel. In particular, the analysis of GNDs – coupled with relevant and reliable criteria – was used to depict the thickness of each zone identified in the SMAT-affected layers: (i) the “ultrafine grain” (UFG) zone present at the extreme top surface, (ii), the “transition zone” where grains were fragmented under the heavy plastic deformation and, finally, (iii) the “deformed zone” where initial grains are simply deformed. The interest of this procedure is illustrated through the comparative analysis of the effect of some SMAT processing parameters (amplitude of vibration and treatment duration). The UFG and transition zones are more significantly modified than the overall affected thickness under our tested conditions. - Highlights: • EBSD maps are used to characterize quantitatively the microstructure of SMAT treated samples. • Calculation of the GND density to quantify strain gradients • A new method to depict the different zone thicknesses in the SMAT affected layer • Effects of SMAT processing parameters on the surface microstructure evolution.

36 MATERIALS SCIENCE↗

Spontaneous imbibition in a square tube with corner films: theoretical model and numerical simulation

Spontaneous imbibition in an angular tube with corner films is a fundamental problem in many scientific and engineering processes. In this paper, a modified interacting capillary bundle model is developed to describe the liquid imbibition dynamics in a square tube with corner films. The square tube is decomposed into several interacting sub-capillaries and the local capillary pressure in each sub-capillary is derived based on the specific shape of its meniscus. The conductance of each sub-capillary is calculated using single-phase lattice Boltzmann simulation. The modified interacting capillary bundle model and color-gradient lattice Boltzmann method are used to simulate the liquid imbibition dynamics in the square tube with different fluid properties. The predictions by the modified interacting capillary bundle model match well with the lattice Boltzmann simulation results for different conditions, demonstrating the accuracy and robustness of the interacting capillary bundle model to describe the imbibition dynamics with corner films. In addition, the interacting capillary bundle model is helpful to investigate the mechanisms during spontaneous imbibition and the influences of fluid viscosity, surface tension, wetting phase contact angle and gravity on imbibition dynamics. Finally, a universal scaling law of imbibition dynamics for the main meniscus is developed and the scaling law for arc meniscus is also analyzed.

42 ENGINEERING↗

Localized Opto-Mechanical Control of Protein Adsorption onto Carbon Nanotubes

Chemical reactions can be described by an energy diagram along a reaction coordinate in which an activation barrier limits the rate at which reactants can be transformed into products. This reaction impedance can be overcome by reducing the magnitude of the barrier through the use of catalysis, increasing the thermal energy of the system, or through macroscopic mechanical processes. Here, we demonstrate direct molecular-scale control of a reaction through the precise application of opto-mechanical work. The method uses optical gradient forces generated in the evanescent field surrounding hybrid photonic-plasmonic structures to drive an otherwise unlikely adsorption reaction between proteins and carbon nanotubes. The adsorption of immunoglobulins on carbon nanotubes is used as a model reaction and investigated with an extended DLVO theory. The technique is also used to force a Förster resonance energy transfer between fluorophores on mismatched immunoglobulin proteins and is expected to lead to novel forms of chemical synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-speed adaptive contact-mode atomic force microscopy imaging with near-minimum-force

In this paper, an adaptive contact-mode imaging approach is proposed to replace the traditional contact-mode imaging by addressing the major concerns in both the speed and the force exerted to the sample. The speed of the traditional contact-mode imaging is largely limited by the need to maintain precision tracking of the sample topography over the entire imaged sample surface, while large image distortion and excessive probe-sample interaction force occur during high-speed imaging. In this work, first, the image distortion caused by the topography tracking error is accounted for in the topography quantification. Second, the quantified sample topography is utilized in a gradient-based optimization method to adjust the cantilever deflection set-point for each scanline closely around the minimal level needed for maintaining stable probe-sample contact, and a data-driven iterative feedforward control that utilizes a prediction of the next-line topography is integrated to the topography feeedback loop to enhance the sample topography tracking. The proposed approach is demonstrated and evaluated through imaging a calibration sample of square pitches at both high speeds (e.g., scan rate of 75 Hz and 130 Hz) and large sizes (e.g., scan size of 30 μm and 80 μm). The experimental results show that compared to the traditional constant-force contact-mode imaging, the imaging speed can be increased by over 30 folds (with the scanning speed at 13 mm/s), and the probe-sample interaction force can be reduced by more than 15% while maintaining the same image quality.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗