turkmath.org

The main purpose of this talk is to propose a newly developed stochastic Monte Carlo (MC) linear solver for some large-scale modeling problems that require special linear solvers due to the specific characteristics of these types of problems. The newly developed MC method offers an alternative to costly deterministic linear solvers, presenting advantages in computational time and complexity, including superior features such as parallelization capability. 
In this presentation, we propose employing the stochastic MC method for initial value problems with time-dependent coefficients, resulting in a hybrid numerical-stochastic approach that demonstrates superior efficiency compared to corresponding numerical methods. However, this method exhibits broad applicability to diverse classes of dynamic mathematical modeling problems, particularly at large scales. Additionally, we aim to explore integrating this method into the well-known Adaptive Neural-Fuzzy Inference System (ANFIS), thereby reducing computational complexity in computing the pseudo-inverse matrix within the iterative least square estimator (LSE) sub-method of the main ANFIS algorithm. It is known that the ANFIS method offers a powerful tool for data science analysis across various domains and applications such as predictive modeling, control systems, data fusion decision-making, and so on. Indeed, this method is a versatile tool, but its specific application depends on the data and problem at hand. In this research, we applied three classes of the newly modified ANFIS method, incorporating enhancements to their respective generating function structures. These models were utilized to forecast the daily prices of target fuel products using datasets sourced from the Thomson Reuters Eikon Refinitiv database.