Phase-field modeling is a physics-based computational approach for simulating physics at interfaces. It has prominent uses in powder melting, additive manufacturing, and modeling dendrite formation on metal electrodes. The direct numerical simulation using the phase-field method is computationally expensive, as meshes will get sufficiently small in order to get a reasonably smooth solution. Recent work has shown that, in the additive manufacturing case, using machine learning techniques can solve the problem at least 50 times faster than the regular direct approaches, while still capturing the relevant physics. This project focuses on phase-field modeling of dendrite formation on metal electrodes. First, the bottlenecks using direct computational approaches will be determined. Next, similar to additive manufacturing, machine learning will be used in an attempt to alleviate these bottlenecks. The end goal is to use both Physics-Informed Neural Networks (PINNs), as well as Phyiscs-Informed Neural Operators (PINOs) to solve the underlying system of partial differential equations (PDEs) of the phase-field model.