In this talk, we first introduce convolutional neural networks designed to predict and analyze damage patterns on a disk resulting from molecular dynamic collision simulations. We propose the use of neural network approximations to complement peridynamic simulations by providing quick estimates which maintain much of the accuracy of the full simulations while reducing simulation times by a factor of 1500. We propose two distinct convolutional neural networks: one trained to perform the forward problem of predicting the damage pattern on a disk provided the location of a colliding object’s impact, and another trained to solve the inverse problem of identifying the collision location, angle, velocity, and size given the resulting damage pattern. Second, we introduce a Physics-informed DeepONet model to solve the multi-term time-fractional mixed diffusion equations. Deep Operator networks such as DeepONet can approximate nonlinear operators between infinite dimensional Banach spaces. PINN-DeepONet employs deep neural operator networks with the PDEs explicitly encoded into the Neural Networks using automatic differentiation to impose the underlying physical laws via soft penalty constraints during model training. Here we extend PINN-DeepONet to fractional physics-informed DeepONets to solve multi-term time-fractional mixed diffusion-wave equations. We demonstrate that the proposed method can not only yield a significant improvement in predictive accuracy but also reduce the need for large training data sets.