  We present an application of Physics-Informed Neural Networks to handle
MultiPhase-Field simulations of microstructure evolution. It has been showcased
that a combination of optimization techniques extended and adapted from the
PINNs literature, and the introduction of specific techniques inspired by the
MPF Method background, is required. The numerical resolution is realized
through a multi-variable time-series problem by using fully discrete
resolution. Within each interval, space, time, and phases are treated
separately, constituting discrete subdomains. An extended multi-networking
concept is implemented to subdivide the simulation domain into multiple
batches, with each batch associated with an independent Neural Network trained
to predict the solution. To ensure efficient interaction across different
phasesand in the spatio-temporal-phasic subdomain, a Master NN handles
efficient interaction among the multiple networks, as well as the transfer of
learning in different directions. A set of systematic simulations with
increasing complexity was performed, that benchmarks various critical aspects
of MPF simulations, including different geometries, types of interface dynamics
and the evolution of an interfacial triple junction. A comprehensive approach
is adopted to specifically focus the attention on the interfacial regions
through an automatic and dynamic meshing process, significantly simplifying the
tuning of hyper-parameters and serving as a fundamental key for addressing MPF
problems using Machine Learning. The pyramidal training approach is proposed to
the PINN community as a dual-impact method: it facilitates the initialization
of training and allows an extended transfer of learning. The proposed PINNs-MPF
framework successfully reproduces benchmark tests with high fidelity and Mean
Squared Error loss values ranging from 10$^{-4}$ to 10$^{-6}$ compared to
ground truth solutions.
