  We propose a stochastic projection-based gradient free physics-informed
neural network. The proposed approach, referred to as the stochastic projection
based physics informed neural network (SP-PINN), blends upscaled stochastic
projection theory with the recently proposed physics-informed neural network.
This results in a framework that is robust and can solve problems involving
complex solution domain and discontinuities. SP-PINN is a gradient-free
approach which addresses the computational bottleneck associated with automatic
differentiation in conventional PINN. Efficacy of the proposed approach is
illustrated by a number of examples involving regular domain, complex domain,
complex response and phase field based fracture mechanics problems. Case
studies by varying network architecture (activation function) and number of
collocation points have also been presented.
