The paper presents a numerical method for solving a class of high-dimensional stochastic control systems based on tensor decomposition and parallel computing.The HJB solution provides a globally optimal controller to ...The paper presents a numerical method for solving a class of high-dimensional stochastic control systems based on tensor decomposition and parallel computing.The HJB solution provides a globally optimal controller to the associated dynamical system.Variable substitution is used to simplify the nonlinear HJB equation.The curse of dimensionality is avoided by representing the HJB equation using separated representation.Alternating least squares(ALS)is used to reduced the separation rank.The experiment is conducted and the numerical solution is obtained.A high-performance algorithm is designed to reduce the separation rank in the parallel environment,solving the high-dimensional HJB equation with high efficiency.展开更多
Within the framework of zero-curvature representation theory, the decompositions of eachequation in a hierarchy of zero-curvature equations associated with loop algebra 81(2) by meansof higher-order constraints on pot...Within the framework of zero-curvature representation theory, the decompositions of eachequation in a hierarchy of zero-curvature equations associated with loop algebra 81(2) by meansof higher-order constraints on potential are given a unified treatment, and the general schemeand uniform formulas for the decompositions are proposed. This provides a method of separationof variables to solve a hierarchy of (1+1)-dimensional integrable systems. TO illustrate the general scheme, new higher-order decompositions of two hierarchies of zero-curvature equations arepresented.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61873254。
文摘The paper presents a numerical method for solving a class of high-dimensional stochastic control systems based on tensor decomposition and parallel computing.The HJB solution provides a globally optimal controller to the associated dynamical system.Variable substitution is used to simplify the nonlinear HJB equation.The curse of dimensionality is avoided by representing the HJB equation using separated representation.Alternating least squares(ALS)is used to reduced the separation rank.The experiment is conducted and the numerical solution is obtained.A high-performance algorithm is designed to reduce the separation rank in the parallel environment,solving the high-dimensional HJB equation with high efficiency.
文摘Within the framework of zero-curvature representation theory, the decompositions of eachequation in a hierarchy of zero-curvature equations associated with loop algebra 81(2) by meansof higher-order constraints on potential are given a unified treatment, and the general schemeand uniform formulas for the decompositions are proposed. This provides a method of separationof variables to solve a hierarchy of (1+1)-dimensional integrable systems. TO illustrate the general scheme, new higher-order decompositions of two hierarchies of zero-curvature equations arepresented.
