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Nonlinear Dynamics - In this paper, we investigate the asymptotic stability of the probability density function (pdf) of the states of a class of nonlinear SDEs. We use the Detailed-balance... 相似文献
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Ali Namadchian Mehdi Ramezani 《Numerical Methods for Partial Differential Equations》2020,36(3):637-653
The Fokker–Planck equation is a useful tool to analyze the transient probability density function of the states of a stochastic differential equation. In this paper, a multilayer perceptron neural network is utilized to approximate the solution of the Fokker–Planck equation. To use unconstrained optimization in neural network training, a special form of the trial solution is considered to satisfy the initial and boundary conditions. The weights of the neural network are calculated by Levenberg–Marquardt training algorithm with Bayesian regularization. Three practical examples demonstrate the efficiency of the proposed method. 相似文献
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