Stochastic projection based approach for gradient free physics informed learning

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