Numerical Experiments Research Articles

A new cubic trigonometric Nu-Spline with shape control parameter and its applications

This study introduces a novel Cubic Trigonometric Nu-Spline (CTNS) with a shape parameter tailored for curve designing, ensuring geometric continuity of order 2. The CTNS possesses fundamental geometric properties such as convex hull, partition of unity, affine invariance, and variation diminishing, which are thoroughly discussed herein. Notably, our spline technique is enriched with Nu-Spline constraints, offering compelling local and global shape control capabilities. These capabilities encompass point tension, interval, or global tensions, enhancing versatility across various shape impacts. Beyond its curve designing prowess, the proposed technique exhibits commendable precision in estimating control points. Furthermore, its utility extends to diverse fields including electronics, medical image interpolation, manipulator path planning, and discrete time signal processing. Through numerical experimentation, we demonstrate the simplicity of implementing the CTNS algorithm alongside its superior accuracy compared to existing techniques.

On the splitting iteration method for Pareto eigenvalue complementarity problems of H +-matrices

We present a class of inexact splitting-modulus iteration methods for solving the Pareto Eigenvalue Complementarity Problem (EiCP) when the system matrix A is an H + -matrix. Our method first employs the matrix splitting technique to transform the original eigenvalue complementarity problem (EiCP) into an easily solvable Linear Complementarity Problem (LCP), and the inner iterative process corresponds to the inexact split iterative process when the modulus iteration method is used, where we employed an effective and fast inner iterative stopping criterion. We then provide a convergence proof for inexact matrix splitting iteration methods. Numerical experiments demonstrate that our proposed algorithms exhibit significant superiority over the classical matrix splitting iteration method in terms of computational time, especially for solving large-scale symmetric and asymmetric eigenvalue complementarity problems of H + -matrices.

Subnanoscale Ion Beam Modification-Assisted Smoothing of Heterostructure Surfaces.

Glass ceramic (GC) is the most promising material for objective lenses for extreme ultraviolet lithography that must meet the subnanometer precision, which is characterized by low values of high spatial frequency surface roughness (HSFR). However, the HSFR of GC is typically degraded during ion beam figuring (IBF). Herein, a developed method for constructing molecular dynamics (MD) models of GC was presented, and the formation mechanisms of surface morphologies were investigated. The results indicated that the generation of the dot-like microstructure was the result of the difference in the erosion rate caused by the difference in the intrinsic properties between ceramic phases (CPs) and glass phases (GPs). Further, the difference in the microstructure of the IBF surface under different beam angles was mainly caused by the difference in the two types of sputtering. Quantum mechanical calculations showed that the presence of interstitial atoms would result in electron rearrangement and that the electron localization can lead to a reduction in CP stability. To obtain a homogeneous surface, the effects of beam parameters on the heterogeneous surface were systematically investigated based on the proposed MD model. Then, a novel ion beam modification (IBM) method was proposed and demonstrated by TEM and GIXRD. The range of ion beam smoothing parameters that could effectively converge the HSFR of the modified surface was determined through numerous experiments. Using the optimized beam parameters, an ultrathin homogeneous modified surface within 3 nm was obtained. The HSFR of GC smoothed by ion beam modification-assisted smoothing (IBMS) dropped from 0.348 to 0.090 nm, a 74% reduction. These research results offer a deeper understanding of the morphology formation mechanisms of the GC surfaces involved in ion beam processing and may point to a new approach for achieving ultrasmooth heterostructure surfaces down to the subnanometer scale.

Impact of Model Resolution and Initial/Boundary Conditions in Forecasting Low-level Atmospheric Fields Over the Incheon International Airport

Abstract This study investigates the impact of initial/boundary conditions (IC/BCs) and horizontal resolutions on forecast for average weather conditions, focusing on low-level weather variables such as 2-m temperature (T2m), 2-m water vapor mixing ratio (Q2m), and 10-m wind speed (WS10). A Weather Research and Forecasting (WRF) model is used for regional mesoscale model simulations and large-eddy simulations (LES). The 6-h-interval forecast fields generated by the Global Forecast System of the National Centers for Environmental Prediction and the Korean Integrated Model of the Korea Meteorological Administration are utilized as IC/BCs for the regional models. Numerical experiments are performed for 24 h starting at 0000 UTC on each day in April 2021 when the average monthly wind speed was strongest during 10 years (2011-2020). Comparison of model simulations with observations obtained around the Yeong-Jong Island, where Incheon International Airport is situated, shows that the regional models capture the time series of T2m, Q2m, and WS10 more effectively than the global model forecasts. Moreover, the LES experiments with a 100-m horizontal grid spacing simulate higher Q2m and lower WS10 during the daytime compared to the 1-km WRF. This results in a deterioration of their time series correlation with the observations. Meanwhile, the 100-m LES forecasts time series of T2m over ocean stations and Q2m over land stations, as well as probability density functions of low-level weather variables, more accurately than that of the 1-km WRF. Our study also emphasizes the need for caution when comparing high-resolution model results with observation values at specific stations due to the high spatial variability in low-level meteorological fields.

Enhanced Quantitative Wavefront Imaging for Nano-Object Characterization.

Quantitative phase imaging enables precise and label-free characterizations of individual nano-objects within a large volume, without a priori knowledge of the sample or imaging system. While emerging common path implementations are simple enough to promise a broad dissemination, their phase sensitivity still falls short of precisely estimating the mass or polarizability of vesicles, viruses, or nanoparticles in single-shot acquisitions. In this paper, we revisit the Zernike filtering concept, originally crafted for intensity-only detectors, with the aim of adapting it to wavefront imaging. We demonstrate, through numerical simulation and experiments based on high-resolution wavefront sensing, that a simple Fourier-plane add-on can significantly enhance phase sensitivity for subdiffraction objects─achieving over an order of magnitude increase (×12)─while allowing the quantitative retrieval of both intensity and phase. This advancement allows for more precise nano-object detection and metrology.

Assessment of water mass distribution and intrusions of circumpolar deep water in the Amundsen Sea based on the ocean reanalysis product FOAM-GLOSEA5v13

The Amundsen Sea of West Antarctica is one of the regions of particularly interest to the oceanography community due to accelerated basal melting of its ice shelves. Quantitative estimates of the composition of water masses and their sources are essential for understanding the heat and salt budgets and the stability of ice shelves in this region. In this study, the water mass distributions on the Amundsen Sea continental shelf are estimated based on FOAM-GLOSEA5v13, a global oceanographic reanalysis product, using a modified statistical based optimal water mass analysis method. The reanalysis product effectively captures the signal of primary water masses, including the Winter Water (WW) and the Circumpolar Deep Water (CDW) below the Antarctic Summer Surface Water (SSW). The horizontal and vertical distributions and temporal evolution of three water mass endmembers (WW, CDW and DSW) and their mixing ratios are calculated, based on which an intrusion location detection method was established. Using the reanalysis product and intrusion detection method, all potential CDW intrusion sites along the shelf break are identified. Based on the reanalysis product, an intrusion site over the shelf break, away from major deep troughs was captured and confirmed by numerical particle tracking experiments.

Ground-truth-free Deep Learning for 3-D Seismic Denoising and Reconstruction with Channel Attention Mechanism

Seismic denoising methods using supervised methods rely on a large number of high-quality paired training datasets to reach satisfactory performances. There are two ways to generate labels for network training: one is to simulate the synthetic data using the wave equation, and the other is to utilize denoised data obtained via conventional methods. However, using these labels will limit the networks' noise attenuation performance compared with using large volumes of noise-free data as labels. Here, we propose a ground-truth-free way for three-dimensional (3-D) seismic data processing. First, we use the 3-D patch scheme to divide the noisy seismic data into many fixed-size blocks and then flatten the obtained 3-D patches to expand the training set and capture more higher-order waveform characteristics from the input noisy data. Next, the obtained training dataset is sent into the proposed deep learning (DL) network, where the encoder blocks compress the feature map to extract the waveform features, and the decoder blocks reconstruct the denoised feature map. Notably, the convolutional bottleneck attention module (CBAM) and efficient channel attention (ECA) module are applied to guide the network to focus on signal fluctuation features with fewer network parameters. In addition, the concatenation mechanism is used to enable deep networks to reuse shallow-layer waveform features and mitigate overfitting during training. Finally, the unpatching scheme is used to reconstruct the denoised 3-D seismic data. Numerical experiments demonstrate that the proposed method outperforms benchmark approaches in terms of signal-to-noise ratio (SNR) improvement and useful signal preservation.

Integrated scheduling of multi-objective lot-streaming hybrid flowshop with AGV based on deep reinforcement learning

The conventional approach to shop floor scheduling often overlooks handling time, either neglecting it or assimilating it into processing time. This results in inadequate information sharing, hindering operational synergy and impeding overall optimisation. Addressing this issue, this study focuses on the three-stage lot-streaming hybrid flowshop scheduling problem with automated guided vehicles (LSHFSP-AGV). It introduces a multi-objective scheduling model to enhance collaboration between machine production and AGV distribution, three objectives of minimum maximum completion time, minimum total machine idle time, and shortest AGV transportation distance are set. An improved multi-objective double-depth Q learning algorithm (NSGA2-MDDQN) based on NSGA-II is proposed to solve the problem. Taguchi experiments were conducted to determine the optimal parameter combination among alternative parameter combinations, and extensive numerical experiments involving 27 instances demonstrated the superiority of NSGA2-MDDQN over combinatorial scheduling rules, MDDQN, and NSGA-II, proving the superiority of the algorithm. The experimental results show that on the objective of minimising makespan, NSGA2-MDDQN reduces by an average of 23.17% compared to the composite scheduling rule, NSGA-II and MDDQN. And achieving an average reduction of 43.78% in machine idle time, and 9.12% in AGV transport distance.

Impacts of Local and Remote SST Warming on Summer Circulation Changes in the Western North Pacific

Abstract This study explores how future SST warming in remote ocean basins may affect the western North Pacific (WNP) wet season climate by applying a high-resolution atmospheric general circulation model to conduct a series of numerical experiments. A marked precipitation and tropical cyclone (TC) activity reduction, as well as enhanced anticyclonic circulation, in the WNP is projected in AMIP experiments forced by SST change in a future warming scenario. The sensitivity experiments reveal that various SST warming phenomena (e.g., in the global SST warming pattern, the tropical ocean belt, the Indian Ocean, tropical Atlantic, the subtropical northeast Pacific) and the increase of greenhouse gas concentration could weaken the precipitation, TC activity, and circulation. By contrast, the SST warming in the WNP and eastern equatorial Pacific have opposite and mixed effects, respectively, and tend to weakly offset the dominant influences of remote ocean warming. These results indicate that the WNP, being the epicenter of the global teleconnection of divergent and rotational flow, is susceptible to the influence of the SST warming in remote ocean basins. The remote forcing as projected in future scenarios would overwhelm the enhancing effect of local SST warming and weaken the circulation, convection, and TC activity in the WNP. These findings further the understanding of how the decreased precipitation and enhanced subtropical high in the WNP may be easily triggered by remote SST warming as revealed in the AMIP-type simulations. How this effect would be affected by air-sea coupling needs further investigation.

Convolutional encoding and normalizing flows: a deep learning approach for offshore wind speed probabilistic forecasting in the Mediterranean Sea

Abstract The safe and efficient execution of offshore operations requires short-term (1 to 6 hours ahead) high-quality probabilistic forecasts of metocean variables. The development areas for offshore wind projects, potentially in high depths, make it difficult to gather measurement data. This paper explores the use of deep learning for wind speed forecasting at an unobserved offshore location. The proposed convolutional architecture jointly exploits coastal measurements and numerical weather predictions to emulate multivariate probabilistic short-term forecasts. We explore both Gaussian and non-Gaussian neural representations using normalizing flows. We benchmark these approaches with respect to state-of-art data-driven schemes, including analog methods and quantile forecasting. The performance of the models, and resulting forecast quality, are analyzed in terms of probabilistic calibration, probabilistic and deterministic metrics, and as a function of weather situations. We report numerical experiments for a real case-study off the French Mediterranean coast. Our results highlight the role of regional numerical weather prediction and coastal in situ measurement in the performance of the post-processing. For single-valued forecasts, a 40% decrease in RMSE is observed compared to the direct use of numerical weather predictions. Significant skill improvements are also obtained for the probabilistic forecasts, in terms of various scores, as well as an acceptable probabilistic calibration. The proposed architecture can process a large amount of heterogeneous input data, and offers a versatile probabilistic framework for multivariate forecasting.

Approximation error estimates by noise‐injected neural networks

One‐hidden‐layer feedforward neural networks are described as functions having many real‐valued parameters. Approximation properties of neural networks are established (universal approximation property), and the approximation error is related to the number of parameters in the network. The essentially optimal order of approximation error bounds was already derived in 1996. We focused on the numerical experiment that indicates the neural networks whose parameters contain stochastic perturbations gain better performance than ordinary neural networks and explored the approximation property of neural networks with stochastic perturbations. In this paper, we derived the quantitative order of variance of stochastic perturbations to achieve the essentially optimal approximation order and verified the justifiability of our theory by numerical experiments.

An Inverse Modeling Approach for Retrieving High-Resolution Surface Fluxes of Greenhouse Gases from Measurements of Their Concentrations in the Atmospheric Boundary Layer

This study explores the potential of using Unmanned Aircraft Vehicles (UAVs) as a measurement platform for estimating greenhouse gas (GHG) fluxes over complex terrain. We proposed and tested an inverse modeling approach for retrieving GHG fluxes based on two-level measurements of GHG concentrations and airflow properties over complex terrain with high spatial resolution. Our approach is based on a three-dimensional hydrodynamic model capable of determining the airflow parameters that affect the spatial distribution of GHG concentrations within the atmospheric boundary layer. The model is primarily designed to solve the forward problem of calculating the steady-state distribution of GHG concentrations and fluxes at different levels over an inhomogeneous land surface within the model domain. The inverse problem deals with determining the unknown surface GHG fluxes by minimizing the difference between measured and modeled GHG concentrations at two selected levels above the land surface. Several numerical experiments were conducted using surrogate data that mimicked UAV observations of varying accuracies and density of GHG concentration measurements to test the robustness of the approach. Our primary modeling target was a 6 km2 forested area in the foothills of the Greater Caucasus Mountains in Russia, characterized by complex topography and mosaic vegetation. The numerical experiments show that the proposed inverse modeling approach can effectively solve the inverse problem, with the resulting flux distribution having the same spatial pattern as the required flux. However, the approach tends to overestimate the mean value of the required flux over the domain, with the maximum errors in flux estimation associated with areas of maximum steepness in the surface topography. The accuracy of flux estimates improves as the number of points and the accuracy of the concentration measurements increase. Therefore, the density of UAV measurements should be adjusted according to the complexity of the terrain to improve the accuracy of the modeling results.

Randomized low‐rank approximation of parameter‐dependent matrices

AbstractThis work considers the low‐rank approximation of a matrix depending on a parameter in a compact set . Application areas that give rise to such problems include computational statistics and dynamical systems. Randomized algorithms are an increasingly popular approach for performing low‐rank approximation and they usually proceed by multiplying the matrix with random dimension reduction matrices (DRMs). Applying such algorithms directly to would involve different, independent DRMs for every , which is not only expensive but also leads to inherently non‐smooth approximations. In this work, we propose to use constant DRMs, that is, is multiplied with the same DRM for every . The resulting parameter‐dependent extensions of two popular randomized algorithms, the randomized singular value decomposition and the generalized Nyström method, are computationally attractive, especially when admits an affine linear decomposition with respect to . We perform a probabilistic analysis for both algorithms, deriving bounds on the expected value as well as failure probabilities for the approximation error when using Gaussian random DRMs. Both, the theoretical results and numerical experiments, show that the use of constant DRMs does not impair their effectiveness; our methods reliably return quasi‐best low‐rank approximations.

Potency Assay Variability Estimation in Practice.

During the drug development process, testing potency plays an important role in the quality assessment required for the manufacturing and marketing of biologics. Due to multiple operational and biological factors, higher variability is usually observed in bioassays compared with physicochemical methods. In this paper, we discuss different sources of bioassay variability and how this variability can be statistically estimated. In addition, we propose an algorithm to estimate the variability of reportable results associated with different numbers of runs and their corresponding OOS rates under a given specification. Numerical experiments are conducted on multiple assay formats to elucidate the empirical distribution of bioassay variability.

A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem

The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution, is often used to address the challenge. Built on a recently proposed day-to-day discrete-time dynamical model called cumulative logit (CumLog), this study provides a new behavioral underpinning for the maximum-entropy user equilibrium (MEUE) route flow. It has been proven that CumLog can reach a UE state without presuming that travelers are perfectly rational. Here, we further establish that CumLog always converges to the MEUE route flow if (i) travelers have no prior information about routes and thus, are forced to give all routes an equal initial choice probability or if (ii) all travelers gather information from the same source such that the general proportionality condition is satisfied. Thus, CumLog may be used as a practical solution algorithm for the MEUE problem. To put this idea into practice, we propose to eliminate the route enumeration requirement of the original CumLog model through an iterative route discovery scheme. We also examine the discrete-time versions of four popular continuous-time dynamical models and compare them with CumLog. The analysis shows that the replicator dynamic is the only one that has the potential to reach the MEUE solution with some regularity. The analytical results are confirmed through numerical experiments. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This research was funded by the United States National Science Foundation’s Division of Civil, Mechanical and Manufacturing Innovation [Grant 2225087]. The work of J. Xie was funded by the National Natural Science Foundation of China [Grant 72371205]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0525 .

Simultaneous measurement of solid concentration and solid moisture in gas–solid two-phase flow using a dual-modality electrical sensor

Abstract In a gas-solid two-phase flow system, simultaneous measurement of solid concentration and solid moisture is essential for some applications. However, during the measurement process, solid concentration and solid moisture are coupled in the measurement signals when the measurement signal is sensitive to both solid concentration and moisture. This makes it challenging to measure them simultaneously in the same measurement field. To solve this issue, a novel measurement method is proposed in this study, which uses a dual-modality electrical sensor to achieve simultaneous measurement of solid concentration and solid moisture in gas-solid two-phase flow. The dual-modality electrical sensor features a simple structure and captures measurement signals of capacitance and angle of dielectric loss within the same measurement section. With the above signals which are both sensitive to solid concentration and moisture, an iterative correction calculation method is adopted to achieve the simultaneous measurement of solid concentration and solid moisture. During the calculation process, the measured parameters are decoupled and continuously corrected until the related error values meet the threshold requirement. Numerical simulation experiments under three typical distributions and physical experiments under roping flow are carried out to verify the proposed measurement method. The results prove the effectiveness of the proposed measurement method in the simultaneous measurement of solid concentration and solid moisture for gas-solid two-phase flow.

Optimization Of Photophoretic Forces In Coated-Hollow Microspheres

Photophoresis, a thermal phenomenon, generates non-contact forces on microparticles in a fluid when exposed to a light beam, such as a laser. These forces depend on the geometrical, thermal, and optical properties of the particles, and aligning these properties in inhomogeneous particles can enhance photophoretic forces. The use of coated-hollow microspheres offers a promising approach to this challenge. This work presents a photophoresis model for a threelayered microsphere in the slip-flow regime, applying Navier-Stokes equations with corrected boundary conditions. We used numerical approaches to compute the heat source function using Lorenz-Mie theory and validated the results against previous works. Applied to a copper-coated glass bubble, the model analyzed the photophoretic force as a function of coating thickness, considering several shell thicknesses. Results show that nanometric scale coatings enhance the force up to a maximum, after which the high thermal conductivity of copper reduces it. For coatings above 100 nm, the force becomes insensitive to shell thickness, demonstrating copper’s dominance in optical and thermal phenomena. The study suggests depositing excess coating for higher photophoretic forces, providing a framework for optimizing microparticle design for photophoretic applications. Future work includes further validation through numerical models and experiments and finding analytical solutions for integrals associated with terms in the boundary coefficients using Lorenz-Mie Theory, which holds great promise for advancing our understanding of photophoresis.

Programmable XY-type couplings through parallel spin-dependent forces on the same trapped ion motional modes

We propose and experimentally demonstrate an analog scheme for generating XY-type (Jijxσxiσxj+Jijyσyiσyj) Hamiltonians on trapped ion spins with independent control over the Jijx and Jijy terms. The Ising-type interactions σxiσxj and σyiσyj are simultaneously generated by employing two spin-dependent forces operating in parallel on the same set of normal modes. We analytically calculate the region of validity of this scheme, and provide numerical and experimental validation with Yb+171 ions. This scheme inherits the programmability and scalability of the Ising-type interactions with trapped ions that have been explored in numerous quantum simulation experiments. Our approach extends the capabilities of existing trapped ion quantum simulators to access a large class of spin Hamiltonians relevant for exploring exotic quantum phases such as superfluidity and spin liquids. Published by the American Physical Society 2024

Efficient factored gradient descent algorithm for quantum state tomography

Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol that combines the state-factored with eigenvalue mapping to address the rank-deficient issue and incorporates a momentum-accelerated gradient descent algorithm to speed up the optimization process. We implement extensive numerical experiments to demonstrate that our factored gradient descent algorithm efficiently mitigates the rank-deficient problem and admits orders of magnitude better tomography accuracy and faster convergence. We also find that our method can accomplish the full-state tomography of random 11-qubit mixed states within one minute. Published by the American Physical Society 2024

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024