I will discuss the derivative-free loss method (DFLM), a stochastic approach for solving PDEs.  The method uses the stochastic representation of the PDE in the spirit of the Feynman-Kac formula. It characterizes the averaging of collective information from stochastic walkers’ paths exploring the neighborhood of a point of interest. While exploring the domain with an iterative averaging process, a neural network is reinforced to approximate the PDE solution. I will cover its analysis regarding trainability and highlight its effectiveness in non-intrusively tackling multiscale problems with highly oscillating coefficients and perforated domain problems.