Deep Neural Network (DNN) 1 Deep neural network 1 Deep neural networks 1 Density evolution 1 Density evolution method 1 Differential equations 1 Evolution equations 1 General Density Evolution Equation (GDEE) 1 General density evolution equation 1 Learning systems 1 Network architecture 1 Neural-networks 1 Numerical methods 1 Physic informed neural network 1 Physics Informed Neural Network (PINN) 1 Probability 1 Probability Density Evolution Method (PDEM) 1 Probability density evolution method 1 Probability density evolutions 1 Probability evolution 1 Stochastic systems 1