Mathematical Modeling Support in a Distributed Problem Solving Environment for Scientific Computing

Abstract

In computing sciences (e-Sciences) we need computer power, excellent algorithms and programming power in order to solve scientific problems leading to discoveries and development of innovative new products. So far, the computer power and the computing algorithms have been developed incredibly, and have provided enormous contributions to e-Sciences and e-Productions. Problem solving environments (PSE) support the programming power in e-Sciences and e-Productions, and have been studied actively for a few decades. In this paper a distributed PSE, named D-NCAS is presented, and a computer-assisted mathematical modeling support is also discussed in D-NCAS, which helps users solve partial differential equation (PDE) based problems in scientific computing. The D-NCAS PSE inputs a problem description and outputs a program flow, a C-language source code for the problem and also a document for the program. Each PSE module is distributed on networklinked distributed computers. The PSE holds all the information of the problem: PDEs, discretization scheme, mesh information, equation manipulation results, designed program structure, variable and constant definitions and program itself. The PSE concept has been opening a new direction for the computer-assisted programming or development of scientific simulation programs or CAEs.

A problem solving environment that assists model development for reinforcement learning algorithms

“…Researchers are possible to utilize the system with only their technical term. As easy preparation of utilization the system for user, the system is based on web-based system [19][20].…”

Collecting data of human choice using Problem Solving Environment and modeling human behavior

“…(3) (4) where P is the number of periods, M is the number of facilities, is the capacity of Facility m, is the number of users who use Facility m at period p, N is the number of subjects, and is the number of visits for agent i who visits Facility m during P periods. Therefore the AverageDifference is a measure for the facilities that indicates the difference between the target capacity of a facility and the actual congestion.…”

“…To obtain the tables based on real data from with human subjects, we develop a PSE system to collect behavioral data for choice behavior. The system introduces the concept of PSEs [3][4][5]. Section II shows a design of our computational environment for the behavior.…”

Review of PSE (Problem Solving Environment) Study

“…In development of computer programs for high-performance computing (HPC) and simulations in science and technology, mathematical models are essentially important to obtain reasonable or correct results for the users' problems. PSE research also covers the mathematical modeling support [23][24][25][26]. If the users are not experts in the target scientific area, the mathematical modeling support is helpful to build up their mathematical models.…”