Stochastic Projection Based Gradient Free PINN for Reliability Analysis of System using PDEM

In this paper, a reliability analysis of stochastic systems is presented using probability density evolution method (PDEM).In PDEM, generalized density evolution equations (GDEEs) are completely decoupled between physical and probability space, which is developed based on the idea of probability conservation.Using the GF-discrepancy technique, a collection of representative points of random variables are constructed in order to provide an accurate estimate of the probability density function.Sufficient precision requires a large number of sample points, which becomes computationally costly.Physics-informed neural network (PINN)-based PDEM is one of promising methods which reduce the computational cost.Beside the advantages of PINN for solving GDEEs in PDEM, PINN may suffer from gradient estimation using Automatic Differentiation.In this study, stochastic projection based PINN, a gradient free method, is a coupled framework of stochastic projection theory and traditional PINN, for solving GDEEs.To illustrate the efficiency of the method, two numerical examples are investigated for estimating probability density function which is utilized for reliability analysis of stochastic systems.