Advancing the dynamics inference of power electronic systems (PES) to the real-time edge-side holds transformative potential for testing, control, and monitoring. However, efficiently inferring the inherent hybrid continuous-discrete dynamics on resource-constrained edge hardware remains a significant challenge. This letter proposes a neural substitute solver (NSS) approach, which is a neural-network-based framework aimed at rapid accurate inference with significantly reduced computational costs. Specifically, NSS leverages lightweight neural networks to substitute time-consuming matrix operation and high-order numerical integration steps in traditional solvers, which transforms sequential bottlenecks into highly parallel operation suitable for edge hardware. Experimental validation on a multi-stage DC-DC converter demonstrates that NSS achieves 23x speedup and 60% hardware resource reduction compared to traditional solvers, paving the way for deploying edge inference of high-fidelity PES dynamics.