Phase field modeling of fracture with isogeometric analysis and machine learning methods$nvon Somdatta Goswami This thesis presents the advances and applications of phase field modeling in fracture analysis. In this approach the sharp crack surface topology in a solid is approximated by a diffusive crack zone governed by a scalar auxiliary variable. The uniqueness of phase field modeling is that the crack paths are automatically determined as part of the solution and no interface tracking is required. The damage parameter varies continuously over the domain. But this flexibility comes with associated difficulties: (1) a very fine spatial discretization is required to represent sharp local gradients correctly; (2) fine discretization results in high computational cost; (3) computation of higher order derivatives for improved convergence rates and (4) curse of dimensionality in conventional numerical integration techniques. As a consequence the practical applicability of phase field models is severely limited. ...