Stochastic Method Research Articles

Convergence of Numerical Methods for the Navier–Stokes–Fourier System Driven by Uncertain Initial/Boundary Data

AbstractWe consider the Navier–Stokes–Fourier system governing the motion of a general compressible, heat conducting, Newtonian fluid driven by random initial/boundary data. Convergence of the stochastic collocation and Monte Carlo numerical methods is shown under the hypothesis that approximate solutions are bounded in probability. Abstract results are illustrated by numerical experiments for the Rayleigh–Bénard convection problem.

On the multi‐parameters identification of concrete dams: A novel stochastic inverse approach

AbstractThis paper introduces a novel stochastic inverse method that utilizes perturbation theory and advanced intelligence techniques to solve the multi‐parameter identification problem of concrete dams using displacement field monitoring data. The proposed method considers the uncertainties associated with the dam displacement monitoring data, which are comprised of two distinct sources: the first is related to stochastic mechanical properties of the dam, and the second is due to observation errors. The displacements at different measuring points generated by dam mechanical properties exhibit spatial correlation, while the observation errors at different points can be considered statistically random. In this context, the inversion formulas are derived for unknown stochastic parameters of the dam by combining perturbation equations and Taylor expansion methods. An improved meta‐heuristic optimization method is employed to identify the mean of stochastic parameters, while mathematical and statistical methods are used to determine the variance of stochastic parameters. The feasibility of the proposed method is verified through numerical examples of a typical dam section under different conditions. Additionally, the paper discusses and demonstrates the applicability of this method in a practical dam project. Results indicate that this method can effectively capture the uncertainty of dam's mechanical properties and separates them from observation errors.

Stochastic Initial States Randomization Method for Robust Knowledge Transfer in Multi-Agent Reinforcement Learning

Reinforcement learning, which are also studied in the field of defense, face the problem of sample efficiency, which requires a large amount of data to train. Transfer learning has been introduced to address this problem, but its effectiveness is sometimes marginal because the model does not effectively leverage prior knowledge. In this study, we propose a stochastic initial state randomization(SISR) method to enable robust knowledge transfer that promote generalized and sufficient knowledge transfer. We developed a simulation environment involving a cooperative robot transportation task. Experimental results show that successful tasks are achieved when SISR is applied, while tasks fail when SISR is not applied. We also analyzed how the amount of state information collected by the agents changes with the application of SISR.

Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions

Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions

Random walk algorithms for solving nonlinear chemotaxis problems

Abstract Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

Variance Reduction Techniques for Stochastic Proximal Point Algorithms

In the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties. Stochastic proximal point algorithms have been studied as an alternative to stochastic gradient algorithms since they are more stable with respect to the choice of the step size. However, their variance-reduced versions are not as well studied as the gradient ones. In this work, we propose the first unified study of variance reduction techniques for stochastic proximal point algorithms. We introduce a generic stochastic proximal-based algorithm that can be specified to give the proximal version of SVRG, SAGA, and some of their variants. For this algorithm, in the smooth setting, we provide several convergence rates for the iterates and the objective function values, which are faster than those of the vanilla stochastic proximal point algorithm. More specifically, for convex functions, we prove a sublinear convergence rate of O(1/k). In addition, under the Polyak-łojasiewicz condition, we obtain linear convergence rates. Finally, our numerical experiments demonstrate the advantages of the proximal variance reduction methods over their gradient counterparts in terms of the stability with respect to the choice of the step size in most cases, especially for difficult problems.

Characterisation of basalt/glass/kevlar-29 hybrid fibre-reinforced plastic composite material through Nd: YAG laser drilling and optimisation using stochastic methods

Characterisation of basalt/glass/kevlar-29 hybrid fibre-reinforced plastic composite material through Nd: YAG laser drilling and optimisation using stochastic methods

AUTOMATED SYNTHESIS OF OPTIMAL SCHEMES LOCATION OF PRODUCTION FACILITIES ON RUGGED TERRAIN

An automated method has been developed to synthesize layouts of industrial facilities on rugged terrains, aimed at minimizing costs associated with utilities routes development (construction and operation). Additional conditions of optimization synthesis include constraints on the regulatory minimum permissible clear distances between facilities and requirements that prevent facilities from being placed in restricted zones. Three characteristic types of terrain surface relief sufficient to solve the optimization problem presented under automated design conditions have been identified. The terrain allocated for enterprise placement is specified in the conditions of the optimization problem being solved by a regular grid created based on Delaunay triangulation. To calculate the elevation (applicate) of the center of the geometric image of the facility’s base at any position, a secondary approximation of a local small area is applied using a second-order Lagrange interpolation polynomial. Due to the multimodal nature of the objective function, partly caused by the complexity of the topography of the territory designated for facility location, the use of one of the stochastic population methods, specifically the modified method of differential evolution, is proposed to ensure a search for the global minimum of the objective function. A numerical example of synthesizing facilities layouts is provided, assuming their location on different slopes of a depression. The results of the numerical experiment confirmed the possibility of using the method presented in the paper for automated search of optimal (close to optimal) layouts for facilities on rugged terrains.

Stochastic Characteristic Simulation Method of Inertial Devices Based on Allan Variance Matching

Stochastic Characteristic Simulation Method of Inertial Devices Based on Allan Variance Matching

Martingale solutions and asymptotic behaviors for a stochastic cross-diffusion three-species food chain model with prey-taxis.

The stochastic food chain model is an important model within the field of ecological research. Since existing models are difficult to describe the influence of cross-diffusion and random factors on the evolution of species populations, this work is concerned with a stochastic cross-diffusion three-species food chain model with prey-taxis, in which the direction of predators' movement is opposite to the gradient of prey, i.e., a higher density of prey. The existence and uniqueness of martingale solutions are established in a Hilbert space by using the stochastic Galerkin approximation method, the tightness criterion, Jakubowski's generalization of the Skorokhod theorem, and the Vitali convergence theorem. Furthermore, asymptotic behaviors around the steady states of the stochastic cross-diffusion three-species food chain model in the time mean sense are investigated. Finally, numerical simulations are carried out to illustrate the results of our analysis.

Efisiensi Perbankan Syariah Di Indonesia Dengan Stochasitic Frontier Analysis (SFA)

This study aims to examine the effect of Total Assets, Third Party Funds and Operating Costs on Total financing and measure the efficiency level of Bank Aladin Syariah in the 2020-2022 period. This research uses a quantitative approach with a causal associative research type. The data used in this study comes from the financial statements of Bank Aladin Syariah. The results showed that partially Total Assets had a significant effect on Total Financing of Bank Aladin Syariah. While Third Party Funds and Operating Costs have no effect on Total Financing. The highest efficiency value of Bank Aladin Syariah according to the Stochastic Frontier Analysis method occurred in the 2022 period. The implication of the research results is that the Bank Aladin Syariah policy improves its operational performance by being able to rationalize its operating costs. The highest efficiency value in 2022, the bank can concentrate policies by maintaining and improving efficiency through sustainable policies, regular evaluation, and adaptation to changes in the business environment. Bank Aladin Syariah can ensure the sustainability and improvement of its operational performance

Stochastic Linear Programming Method in Housing Investment Feasibility in West Jakarta

This research was conducted in light of a planned investment for residential development in West Jakarta, given the very limited availability of land in the area in terms of land size, price, shape, and other factors, necessitating an investment feasibility study. The purpose of the investment feasibility study is to analyze the viability of this investment. Besides the limited land availability, there is often uncertainty during the sales stage. Thus, this study employs a two-stage stochastic programming model. The houses to be built are divided into two types, namely houses with a width of 4 meters and houses with a width of 4.5 meters. The two-stage stochastic programming model created consists of 2 steps, namely step 1 during housing construction and step 2 during home sales. The objective function is to get the maximum net present value (Zmax). The overall time required in this investment is 4 years. After creating a two-stage stochastic programming model, the analysis was carried out using the Solver Add-in in Microsoft Excel. The analysis concluded that the maximum net present value expected in this investment is 4,092.036 million Rupiah, with a positive net present value, this investment is acceptable. This analysis was added with the calculation of IRR as a supporter of the net present value which resulted in an interest rate of 23,63%. With a large enough IRR interest rate, it can be concluded that this housing development investment is acceptable.

Facing multidimensional poverty in older adults: An artificial intelligence approach that reveals the variable relevance

Despite the rapid development in very recent years of Artificial Intelligence models to predict poverty risk, this problem still remains an unsolved open challenge, especially from a multidimensional perspective. One of the main challenges is related to the scarcity of labelled and high-quality data for training models coupled with the lack of a general reference model to build good predictors. This results in the proposal of a variety of approaches tailored to specific contexts. This paper presents our proposal to address multidimensional poverty prediction, starting from an unlabelled dataset. We focus on the case of a fragile population, the older adults; our approach is highly flexible and can be easily adapted to various scenarios. Firstly, starting from expert knowledge, we apply a stochastic method for estimating the probability of an individual being poor, and we use this probability to identify three levels of risk. Then, we train an XGBoost classification model and exploit its tree structure to define a ranking of feature relevance. This information is used to create a new set of aggregated features representative of different poverty dimensions. An explainable novel Naive Bayes model is then trained for predicting individuals’ deprivation level in our particular domain. The capacity to identify which variables are predominantly associated with poverty among older adults offers valuable insights for policymakers and decision-makers to address poverty effectively.

Computational Methods for Stationary and Nonstationary Fokker–Planck–Kolmogorov Equations with Random Coefficients

In this paper, methodological approaches for distribution functions of nonlinear stochastic differential equations (SDEs) with uncertain parameters are elaborated. The stationary and nonstationary Fokker–Planck–Kolmogorov (FPK) equations associated with the considered random equations are investigated. A semi-analytical approach based on the extended exponential closure handling the parameters uncertainty effects is presented. A new numerical method coupling the polynomial chaos with the differential quadrature method (DQM) is elaborated for the stationary case. A compact matrix formulation is established allowing considering a large number of generalized polynomial chaos. For nonstationary random FPK equations, the polynomial chaos is coupled with the quadrature discretization. A symmetric discretization of the main Fokker–Planck operator using a tensor product of the Hilbert state space and the Hilbert probabilistic space has resulted. The obtained eigenvalues and random eigenfunctions are used for a spectral decomposition. The time solution is obtained by the spectral expansion as well as by the random Euler stochastic method. The accuracy, effectiveness and advantages of the developed procedure in analyzing the stationary and nonstationary probabilistic solutions of nonlinear stochastic dynamical systems with uncertain parameters excited by a Gaussian white noise are demonstrated.

Stochastic Gauss-Newton method for estimating absorption and scattering in optical tomography with the Monte Carlo method for light transport.

Image reconstruction in optical tomography in the so-called transport regime, where the diffusion approximation is not valid, requires modeling of light transport using the radiative transfer equation. In this work, we approach this problem by utilizing the Monte Carlo method for light transport. In this work, we propose a methodology for absolute imaging of absorption and scattering in this regime utilizing a Monte Carlo method for light transport. The image reconstruction problem is formulated as a minimization problem that is solved using a stochastic Gauss-Newton method. In the construction of the Jacobian matrix for scattering, a perturbation approximation for Monte Carlo is utilized. The approach is evaluated with numerical simulations using an adaptive approach where the number of photon packets is adjusted during the iterations, and with different fixed numbers of photon packets. The simulations show that the Monte Carlo method for light transport can be utilized in the absolute imaging problem of optical tomography and that the absorption and scattering parameters can be estimated simultaneously with good accuracy.

Poincaré and SimBio: a versatile and extensible Python ecosystem for modeling systems.

Chemical reaction networks (CRNs) play a pivotal role in diverse fields such as systems biology, biochemistry, chemical engineering, and epidemiology. High-level definitions of CRNs enables to use various simulation approaches, including deterministic and stochastic methods, from the same model. However, existing Python tools for simulation of CRN typically wrap external C/C++ libraries for model definition, translation into equations and/or numerically solving them, limiting their extensibility and integration with the broader Python ecosystem. In response, we developed Poincaré and SimBio, two novel Python packages for simulation of dynamical systems and CRNs. Poincaré serves as a foundation for dynamical systems modeling, while SimBio extends this functionality to CRNs, including support for the Systems Biology Markup Language (SBML). Poincaré and SimBio are developed as pure Python packages enabling users to easily extend their simulation capabilities by writing new or leveraging other Python packages. Moreover, this does not compromise the performance, as code can be just-in-time compiled with Numba. Our benchmark tests using curated models from the BioModels repository demonstrate that these tools may provide a potentially superior performance advantage compared to other existing tools. In addition, to ensure a user-friendly experience, our packages use standard typed modern Python syntax that provides a seamless integration with integrated development environments. Our Python-centric approach significantly enhances code analysis, error detection, and refactoring capabilities, positioning Poincaré and SimBio as valuable tools for the modeling community. Poincaré and SimBio are released under the MIT license. Their source code is available on GitHub (https://github.com/maurosilber/poincare and https://github.com/hgrecco/simbio) and can be installed from PyPI or conda-forge.

PRODUCTIVITY, EFFICIENCY AND ENTREPRENEURIAL - INNOVATIVE UNIVERSITY INDEX: AN ANALYSIS FOR UNIVERSITIES IN TÜRKIYE

The productivity and efficiency of universities were analysed in this study. The data and results of the Entrepreneurial and Innovative University Index-EIUI, which is calculated by TÜBITAK every year by considering various information for universities, were used. The study aimed to discuss the index, productivity, and efficiency results comparatively. Four-year data (2019-2022) and the index values were used. Balanced panel data analysis was performed on universities consistently included in the list each year. In the calculation of the index, a weighted sum of values standardized by the min-max method was taken into account. This is available in the calculation methodology of the index. Total factor productivity and stochastic frontier model methods were used for the analysis of productivity and efficiency, respectively. Universities that enter the index list every year and are at the top are effective, but they could not increase their productivity in the previous years. Universities established before 1992 may have approached the saturation level in terms of the input-output relationship, but it can be said that they can maintain their effectiveness. Some public and private universities that were established in 1992 and later have raised their productivity and efficiency. Although the index value and efficiency values overlapped to a certain extent, the significant differences in productivity were remarkable. While the studies in the literature focused on the meta-analysis of the index and the efficiency analysis of universities with various methods, this study presented an inclusive and comparative analysis in terms of index, productivity, and efficiency with panel data analysis.

Dynamic stochastic projection method for multistage stochastic variational inequalities

Dynamic stochastic projection method for multistage stochastic variational inequalities

Numerical methods for distributed stochastic compositional optimization problems with aggregative structure

ABSTRACT The paper studies the distributed stochastic compositional optimization problems over networks, where all the agents' inner-level function is the sum of each agent's private expectation function. Focusing on the aggregative structure of the inner-level function, we employ the hybrid variance reduction method to obtain the information on each agent's private expectation function, and apply the dynamic consensus mechanism to track the information on each agent's inner-level function. Then by combining with the standard distributed stochastic gradient descent method, we propose a distributed aggregative stochastic compositional gradient descent method. When the objective function is smooth, the proposed method achieves the convergence rate O ( K − 1 / 2 ) . We further combine the proposed method with the communication compression and propose the communication compressed variant distributed aggregative stochastic compositional gradient descent method. The compressed variant of the proposed method maintains the convergence rate O ( K − 1 / 2 ) . Simulated experiments on decentralized reinforcement learning verify the effectiveness of the proposed methods.

An investigation of stochastic trust-region based algorithms for finite-sum minimization

This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in [F.E. Curtis, K. Scheinberg, and R. Shi, A stochastic trust region algorithm based on careful step normalization, INFORMS. J. Optim. 1(3) (2019), pp. 200–220; F.E. Curtis and R. Shi, A fully stochastic second-order trust region method, Optim. Methods Softw. 37(3) (2022), pp. 844–877]. A theoretical analysis that complements the results in the literature is presented, and the issue of tuning the involved hyper-parameters is investigated. Our study also focuses on a practical version of the method, which computes the stochastic gradient by means of the inner product test and the orthogonality test proposed by Bollapragada et al. in [R. Bollapragada, R. Byrd, and J. Nocedal, Adaptive sampling strategies for stochastic optimization, SIAM. J. Optim. 28(4) (2018), pp. 3312–3343]. It is shown experimentally that this implementation improves the performance of TRish and reduces its sensitivity to the choice of the hyper-parameters.