We present a new scientific machine learning method that learns from data computationally inexpensive surrogate model for predicting the evolution of system governed by time-dependent nonlinear partial differential equation (PDE), an enabling technology many computational algorithms used in engineering settings. Our formulation generalizes to function space PDE setting Operator Inference previo...

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches applied. However, nonlinear partial (PDEs) pose substantial challenges from inferential perspective, most notably the absence explicit conditioning formula. This paper extends earlier work on linear PDEs a general class initial value problems specified by PDEs, motiv...