For over six decades, the finite element method (FEM) has been a powerful numerical technique for simulating phenomena across a wide range of engineering applications. However, modeling fracture remains computationally expensive, as it requires substantial mesh refinement along anticipated crack paths to accurately capture complex fracture topologies. In failure analyses of heterogeneous materials, the cost increases further due to spatially varying properties that influence crack initiation and propagation. With the advent of scientific machine learning (ML), neural networks (NNs) have emerged as promising tools to accelerate FEM-based fracture simulations through data-driven or physics-informed approaches. In this talk, we present a hybrid framework called the Integrated Finite Element Neural Network (I-FENN), which combines the FEM with physics-informed convolutional neural networks (PI-CNNs) for efficient crack prediction in multiphase materials containing inclusions. The key idea is to solve the mechanical equilibrium equation using FEM, while the phase-field fracture equation is solved using pre-trained PI-CNNs in a staggered manner. The neural network is trained using a physics-informed loss function based on the dimensionless strong-form residual of the phase-field equation, explicitly accounting for spatially varying critical energy release rates. Only minimal data are required, consisting of history-variable profiles from two load increments of a single-inclusion problem. During inference, the history variables are interpolated onto a uniform pixel grid for the PI-CNN and subsequently mapped back to the finite element mesh to update the nodal phase-field variable. The trained PI-CNN is then used to simulate fracture in geometries with multiple inclusions under varying loads, boundary conditions, and inclusion shapes. Comparisons with standard FEM simulations demonstrate accurate crack paths, reaction forces, and significantly reduced computational cost.