scholarly journals General solutions for nonlinear differential equations: a rule-based self-learning approach using deep reinforcement learning

2019 ◽  
Vol 64 (5) ◽  
pp. 1361-1374 ◽  
Author(s):  
Shiyin Wei ◽  
Xiaowei Jin ◽  
Hui Li
Keyword(s):  
Reinforcement Learning ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Learning Approach ◽  
Rule Based ◽  
General Solutions ◽  
Self Learning

scholarly journals Creation and implementation of a set of game strategies based on training neural networks with reinforcement learning

2021 ◽  
Vol 2134 (1) ◽  
pp. 012005
Author(s):  
D S Kozlov ◽  
O N Polovikova
Keyword(s):  
Neural Networks ◽  
Reinforcement Learning ◽  
The Self ◽  
Learning Approach ◽  
Self Learning

Abstract The study explores the problems of reinforcement learning and finding non-obvious play strategies using reinforcement learning. Two approaches to agent training (blind and pattern-based) are considered and implemented. The advantage of the self-learning approach with reinforcement using patterns as applied to a specific game (tic-tac-toe five in a row) is shown. Recorded and analyzed the use of unusual strategies by an agent using a pattern-based approach.

scholarly journals Elementary Quadrature for the Riccati equation

2020 ◽  
Author(s):  
Ji-Xiang Zhao
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Analytical Method ◽  
Nonlinear Differential Equations ◽  
Integrability Condition ◽  
Type Equation ◽  
Abel Equation ◽  
General Solutions ◽  
Suitable Transformation ◽  
Elementary Quadrature

Abstract Using suitable transformation in combination with a specific Riccati-type equation solvable, the problem of solving Riccati equation can be transformed into that of a quasi-Abel equation of the second kind. By the extended Julia’s integrability condition, the general solutions of Riccati equation in the form of elementary quadrature are obtained, which contains numerous. This method opens up a new prospect for the study of nonlinear differential equations by analytical method.

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