Numerical Experiments Research Articles

Fast hybrid method for solving variational inequalities beyond monotonicity in real Banach spaces

In this work, we introduce a new inertial hybrid algorithm that combines the subgradient extragradient, Halpern, and S-iteration methods. We provide an approximate solution to variational inequality and common fixed point problem of relatively non-expansive mappings in real Banach spaces, where our cost operator is Lipschitz continuous and quasimonotone, and our step size is self-adaptive, non-monotone, and non-reliant on any line-search principle. We provide two strong convergence results with (and without) recourse to the monotonicity property, and further conduct several relevant numerical experiments to reveal the efficiency of our method over others in the literature.

Neural interval‐censored survival regression with feature selection

AbstractSurvival analysis is a fundamental area of focus in biomedical research, particularly in the context of personalized medicine. This prominence is due to the increasing prevalence of large and high‐dimensional datasets, such as omics and medical image data. However, the literature on nonlinear regression algorithms and variable selection techniques for interval‐censoring is either limited or nonexistent, particularly in the context of neural networks. Our objective is to introduce a novel predictive framework tailored for interval‐censored regression tasks, rooted in Accelerated Failure Time (AFT) models. Our strategy comprises two key components: (i) a variable selection phase leveraging recent advances on sparse neural network architectures; (ii) a regression model targeting prediction of the interval‐censored response. To assess the performance of our novel algorithm, we conducted a comprehensive evaluation through both numerical experiments and real‐world applications that encompass scenarios related to diabetes and physical activity. Our results outperform traditional AFT algorithms, particularly in scenarios featuring nonlinear relationships.

Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates

We compare sparse grid stochastic collocation and Gaussian process emulation as surrogates for the parameter-to-observation map of a groundwater flow problem related to the Waste Isolation Pilot Plant in Carlsbad, NM. The goal is the computation of the probability distribution of a contaminant particle travel time resulting from uncertain knowledge about the transmissivity field. The latter is modelled as a lognormal random field which is fitted by restricted maximum likelihood estimation and universal kriging to observational data as well as geological information including site-specific trend regression functions obtained from technical documentation. The resulting random transmissivity field leads to a random groundwater flow and particle transport problem which is solved realization-wise using a mixed finite element discretization. Computational surrogates, once constructed, allow sampling the quantities of interest in the uncertainty analysis at substantially reduced computational cost. Special emphasis is placed on explaining the differences between the two surrogates in terms of computational realization and interpretation of the results. Numerical experiments are given for illustration.

Imaging a two-layered conductive medium by a modified factorization method

In this paper, we consider the inverse acoustic scattering problem of determining a two-layered inhomogeneous medium with a conductive transmission condition from far-field measurements. The well-posedness of the direct problem can be established by applying a variational method. For the inverse problem, we shall develop a modified factorization method for recovering the shape and location of the two-layered conductive medium. Finally, we provide some numerical experiments to demonstrate the practicability of the inversion algorithms.

A fluid–particle decomposition approach to matching market design for crowdsourced delivery systems

This paper considers a crowdsourced delivery (CSD) system that effectively utilizes the existing trips to fulfill parcel delivery as a matching problem between CSD drivers and delivery tasks. This matching problem has two major challenges. First, it is a large-scale combinatorial optimization problem that is hard to solve in a reasonable computational time. Second, the evaluation of the objective function for socially optimal matching contains the utility of drivers for performing the tasks, which is generally unobservable private information. To address these challenges, this paper proposes a hierarchical distribution mechanism of CSD tasks that decomposes the matching problem into the task partition (master problem) and individual task-driver matching within smaller groups of drivers (sub-problems). We incorporate an auction mechanism with truth-telling and efficiency into the sub-problems so that the drivers’ perceived utilities are revealed through their bids. Furthermore, we formulate the master problem as a fluid model based on continuously approximated decision variables. By exploiting the random utility framework, we analytically represent the objective function of the problem using continuous variables, without explicitly knowing the drivers’ utilities. The numerical experiment shows that the proposed approach solved large-scale matching problems at least 100 times faster than a naive LP solver and approximated the original objective value with errors of less than 1%. The code of this work is available at https://github.com/yuki-oyama/fluid-particle-csd.

Exploring sensitive area in the whole pacific for two types of El Niño predictions and their implication for targeted observations

Based on the initial errors in the whole Pacific that are most likely to affect the predictions of two types of El Niño events, the sensitive area of ocean temperature in the whole Pacific for El Niño prediction starting from January is identified by using the Geophysical Fluid Dynamic Laboratory CM2P1, a fully coupled global climate model. The error growth analysis and the numerical experiments illustrated that, the initial ocean temperature in the Victoria mode (VM) region in the North Pacific will affect the intensity predictions of the CP-El Niño while that in the subsurface layer of the west equatorial Pacific and the surface layer of southeast Pacific will modulate the spatial structure predictions of CP-El Niño. But for EP-El Niño, the former plus the surface layer of the equatorial central eastern pacific will modulate the spatial structure predictions of the event while the latter is shown to be more effective in predictions of the intensity of the event. Furthermore, if targeted observations are conducted in the sensitive area of the whole Pacific, the El Niño prediction skills, including intensity and spatial structure predictions, could be greatly improved for both EP- and CP-El Niño events. Neither the sensitive area of subtropical Pacific nor the tropical Pacific can be precluded as accurate indicators when forecasting particular flavors and the intensity of El Niño events.

Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaranteeing physical properties like mass conservation. In this paper, we develop the first model reduction for the hyperbolic shallow water moment equations and achieve mass conservation. This is accomplished using a macro-micro decomposition of the model into a macroscopic (conservative) part and a microscopic (non-conservative) part with subsequent model reduction using either POD-Galerkin or dynamical low-rank approximation only on the microscopic (non-conservative) part. Numerical experiments showcase the performance of the new model reduction methods including high accuracy and fast computation times together with guaranteed conservation and consistency properties.

A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws

AbstractWe propose a numerical method to solve parameter-dependent scalar hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020). This approach relies on a very weak notion of solution of nonlinear equations, namely parametric entropy measure-valued (MV) solutions, satisfying linear equations in the space of Borel measures. The infinite-dimensional linear problem is approximated by a hierarchy of convex, finite-dimensional, semidefinite programming problems, called Lasserre’s hierarchy. This gives us a sequence of approximations of the moments of the occupation measure associated with the parametric entropy MV solution, which is proved to converge. In the end, several post-treatments can be performed from this approximate moments sequence. In particular, the graph of the solution can be reconstructed from an optimization of the Christoffel–Darboux kernel associated with the approximate measure, that is a powerful approximation tool able to capture a large class of irregular functions. Also, for uncertainty quantification problems, several quantities of interest can be estimated, sometimes directly such as the expectation of smooth functionals of the solutions. The performance of our approach is evaluated through numerical experiments on the inviscid Burgers equation with parametrised initial conditions or parametrised flux function.

Sinusoidal control strategy applied to continuous stirred‐tank reactors: Asymptotic and exponential convergence

AbstractThe main goal of this proposal is to present a class of nonlinear controllers for regulation and set point changes in continuous chemical reactors. The proposed control law has in its mathematical structure a proportional term of the regulation error to provide closed‐loop stability and a sinusoidal term, which can compensate for the nonlinearities of the plant. The closed‐loop stability of the plant is demonstrated via Lyapunov analysis, which reveals an asymptotic convergence of the control output to the required set points. Furthermore, the analysis of the regulation error's dynamic under the considered assumptions leads us to conclude that exponential stability is also reached. The controller is implemented via numerical experiments in two examples to generalize the applicability of the proposed approach by considering continuous stirred‐tank reactors models. The first case considers autocatalytic chemical oscillatory reactions that induce chaotic behaviour. For the second case, a process of acetone, butanol, and ethanol (ABE) fermentation through Clostridium acetobutylicum is considered. The proposed strategy shows an adequate performance because it can reach the required set point without long time settings and overshoot. A comparison with a smooth sliding‐mode and a standard proportional‐integral (PI) controller indicates the advantages of the proposed control approach.

Towards unified land data assimilation at ECMWF: Soil and snow temperature analysis in the SEKF

AbstractWeather centres use a variety of data assimilation schemes to analyze different land variables in their operational forecast systems. Current activities at the European Centre for Medium‐Range Weather Forecasts (ECMWF) are working towards a unified and more consistent land data assimilation system to provide more accurate initial conditions for the atmospheric forecasts. The first step is to replace the current 1D optimal interpolation (1D‐OI) used for first‐layer soil and snow temperature analyses, and integrate multi‐layer soil and first‐layer snow temperature into the ensemble‐based simplified extended Kalman filter (SEKF) currently used for multi‐layer soil moisture. This work focuses on the technical developments and the evaluation of the atmospheric forecast skill of a series of numerical weather prediction experiments to compare different SEKF configurations with the former 1D‐OI over a three‐month summer and winter period. Using the SEKF leads to seasonally varying significant improvements in the 2‐m temperature forecast in the verification against own analyses and to slightly improved results in the validation using independent synoptic observations. This work lays the foundation for integrating additional land variables into the SEKF and investigating stronger land–atmosphere coupling.

Physics of microscale freeform 3D printing of ice

Ice is emerging as a promising sacrificial material in the rapidly expanding area of advanced manufacturing for creating precise 3D internal geometries. Freeform 3D printing of ice (3D-ICE) can produce microscale ice structures with smooth walls, hierarchical transitions, and curved and overhang features. However, controlling 3D-ICE is challenging due to an incomplete understanding of its complex physics involving heat transfer, fluid dynamics, and phase changes. This work aims to advance our understanding of 3D-ICE physics by combining numerical modeling and experimentation. We developed a 2D thermo-fluidic model to analyze the transition from layered to continuous printing and a 3D thermo-fluidic model for the oblique deposition, which enables curved and overhang geometries. Experiments are conducted and compared with model simulations. We found that high droplet deposition rates enable the continuous deposition mode with a sustained liquid cap on top of the ice, facilitating smooth geometries. The diameter of ice structures is controlled by the droplet deposition frequency. Oblique deposition causes unidirectional spillover of the liquid cap and asymmetric heat transfer at the freeze front, rotating the freeze front. These results provide valuable insights for reproducible 3D-ICE printing that could be applied across various fields, including tissue engineering, microfluidics, and soft robotics.

Performance of surge-induced synchronized switch harvesting on inductor as an efficient technique under strong electromechanical coupling and low amplitudes of vibration

Abstract The process of harvesting energy from ambient sources is key for various applications. This study examined the performance of two representative techniques from the surge-induced synchronized switch harvesting on inductor (S3HI) family under strong electromechanical coupling and compared this performance with that of some established techniques. S3HI techniques exploit the surge voltage to overcome the voltage barrier of diodes for rectifiers and storage capacitor voltages. One of their features, revealed in a previous study on weakly coupled systems, is that they can harvest substantial energy from low-level vibrations. This feature is desirable for certain use cases. This study aimed to clarify whether this feature is applicable even when the coupling is strong. The performance of various established techniques and two representatives from the S3HI group was studied by formulating an approximate analytical solution and performing numerical simulations and experiments. The theoretical results were confirmed to be consistent, and the discrepancy between experimental and theoretical results was minor. These results clearly demonstrate that the techniques from the S3HI family can effectively harvest substantial energy from small-amplitude vibrations, even when the coupling is strong. Moreover, the performance advantage of S3HI methods is even greater when the coupling is strong.

High-quality phase imaging by phase-shifting digital holography and deep learning

Quantitative phase imaging (QPI) technology is widely used in biomedical imaging and other fields because it can realize exact imaging for transparent phase-type samples, which is of great research significance. The complex amplitude distribution of the object wave obtained by phase-shifting digital holography (PSDH) reproduction can provide phase information for QPI, but its existence of phase wrapping and other problems limits its practical application. Although the traditional phase unwrapping algorithm provides a solution, it has problems such as low unwrapping accuracy or long time running. To solve these problems in QPI, a high-quality phase imaging (HQPI) method by PSDH and deep learning (DL) is proposed, where QPI is achieved by extracting the unknown phase shift using a generalized non-iterative phase shift extraction algorithm and unwrapping the wrapped phase by a DL network. Both numerical simulations and optical experiments verify the feasibility of the method. By comparing with the traditional phase unwrapping algorithm, it is demonstrated that the DL unwrapping method has higher unwrapping accuracy and more efficiency. The results show that the method of HQPI is capable of realizing comparatively fast and accurate QPI.

Dynamic pricing strategy for efficient electric vehicle charging and discharging in microgrids using multi-objective jaya algorithm

Abstract The rising demand for electric vehicle (EV) charging is spurring their increased integration into microgrids. With significant advancements, EVs have become widely adopted and integrated into various settings for charging/discharging. EVs integrated with the microgrids possess the capability to serve as variable loads and the various energy suppliers present it as a dual opportunity. However, a primary challenge in EV deployment lies in efficiently managing charging stations (CSs) to minimize waiting times for users and reduce charging costs for EV owners. In addressing these challenges require consideration of dynamic pricing mechanisms and the diverse characteristics of EVs to achieve optimal scheduling. A novel approach that combines dynamic pricing strategies with optimized scheduling for effective EV charging operations using multi-objective Jaya algorithm. To evaluate its performance, we conducted a numerical experiment using real-time data and the Nissan Leaf model EV. The results demonstrate that our multi-objective Jaya-based approach outperforms existing methods by achieving a remarkable cost saving rate of 16.013 % and an average profit of ₹ 243.6331 per kilowatt-hour with a network convergence time of 112 seconds. Also, our proposed algorithm provides a correlation between minimized EV charging costs and maximized EV aggregator profits. These findings validate the effectiveness and practical applicability of our proposed EV scheduling algorithm in real-world scenarios.

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Value of risk aversion in perishable products supply chain management

AbstractIn this paper, we study optimal procurement and inventory decisions for a supply chain with a single perishable product under demand uncertainty. To control risk, on the one hand, we use a risk-averse objective, and on the other hand, we utilize a chance constraint to satisfy demand with a high probability. We formulate the problem as a two-stage stochastic program with a chance constraint and risk-averse objective, where long-term decisions on pre-positioning products are made in the first stage, while recourse decisions on reallocation and emergency procurement are made in the second stage. To allow for different risk preferences, we incorporate conditional value-at-risk into the objective function and study its combination with the expectation or worst-case of the second-stage costs. To solve the resulting models, we develop various variants of the L-shaped method, based on dual and primal decomposition, and by leveraging the connection between the optimization of coherent risk measures and distributionally robust optimization. Through extensive numerical experiments, we demonstrate the value of risk aversion and present a comparative computational study on the performance of different algorithms.

Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver

Abstract Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations only requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz (HVA) aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate its effectiveness, efficiency, and advantages with the two-dimensional Heisenberg model and the Fermi-Hubbard chain. Numerical experiments show that MBHVA can have similar performance as circuit-based ansatz, and is expected to reduce operation counts during execution compared to quantum circuits, bringing the advantage of running time. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in the noisy intermediate-scale quantum (NISQ) era, especially in the presence of large multi-qubit rotation operations.

Parameter Tuning of Agent-Based Models: Metaheuristic Algorithms

When it comes to modelling complex systems using an agent-based approach, there is a problem of choosing the appropriate parameter optimisation technique. This problem is further aggravated by the fact that the parameter space in complex agent-based systems can have a large dimension, and the time required to perform numerical experiments can be large. An alternative approach to traditional optimisation methods are the so-called metaheuristic algorithms, which provide an approximate solution in an acceptable time. The purpose of this study is to compare various metaheuristic algorithms for parameter tuning and to analyse their effectiveness applied to two agent-based models with different complexities. In this study, we considered commonly used metaheuristic algorithms for agent-based model optimisation: the Markov chain Monte Carlo method, the surrogate modelling approach, the particle swarm optimisation algorithm, and the genetic algorithm, as well as the more novel chaos game optimisation algorithm. The proposed algorithms were tested on two agent-based models, one of which was a simple toy model of the spread of contagious disease, and the other was a more complex model of the circulation of respiratory viruses in a city with 10 million agents and 26 calibrated parameters.

Convergence of lattice Boltzmann methods with overrelaxation for a nonlinear conservation law

We approximate a nonlinear multidimensional conservation law by Lattice Boltzmann Methods (LBM), based on underlying BGK type systems with finite number of velocities discretized by a transport-collision scheme. The collision part involves a relaxation parameter ω which value greatly influences the stability and accuracy of the method, as noted by many authors. In this article we clarify the relationship between ω and the parameters of the kinetic model and we highlight some new monotonicity properties which allow us to extend the previously obtained stability and convergence results. Numerical experiments are performed.

An adiabatic boundary condition with cylindrical perfect conductors for improved approximations from heat-pulse measurement near the soil-atmosphere interface

The cylindrical-perfect-conductors (CPC) theory, which assumes an infinite and homogeneous soil medium, can be used to analyze heat pulse (HP) measurements to estimate soil thermal property values. However, when a HP sensor is positioned near the soil surface, the CPC theory is not valid because of the change in media properties at the soil-atmosphere interface. In this study, a CPC solution considering an adiabatic boundary condition (CPC-ABC) is presented to account for the soil-atmosphere interface effect. Compared with the results from numerical simulations, the CPC-ABC solution gave more accurate soil temperature values at the sensing probe than did a CPC model. When a HP sensor was positioned horizontally at a depth of 1 mm below a sand soil surface, the relative errors (RE) of CPC estimated thermal property values were as large as 52%, while the RE values based on the CPC-ABC solution were about 8%. Results from numerical simulations and laboratory experiments both showed that the CPC model worked well for horizontally positioned HP sensors with probe lengths of 70-mm at burial depths greater than 15 mm. Soil-atmosphere interface effect was largely dependent on HP sensor dimensions and measurement volumes. Overall, the extended CPC-ABC theory provided accurate soil thermal property estimates by considering the effects of finite probe properties and the presence of the soil-atmosphere interface.