Dielectric polymers for electrostatic energy storage are used in modern electronic and electrical systems, and their performance can be significantly enhanced through doping with ultralow content nanofillers to improve energy storage performance. Understanding the underlying physical mechanisms of polymer nanocomposites is essential for designing high-performance dielectric polymers. This paper presents a conduction model that integrates Richardson–Schottky emission and hopping conduction to describe charge injection and transport in polymer composites. Phase-field simulations, incorporating electrical, thermal, and mechanical breakdown mechanisms, investigate the influence of nanofiller volume fraction, size, and dielectric constant on the dielectric response and breakdown behaviors under high temperature and electric fields. We propose the Physics-Informed Neural Networks for phase-field simulation that integrates the physical rules of charge transport, phase evolution, and boundary conditions. By embedding phase field models within the Physics-Informed Neural Networks' structure, this method demonstrates the ability to predict the breakdown strength and energy density of polymer nanocomposites. This work provides crucial guidelines for designing high-performance dielectric energy storage capacitors under extreme conditions.