Research Overview

My research bridges computational mathematics, electromagnetics, and scientific machine learning. I develop stable, high-order numerical methods—particularly FDTD schemes—for simulating nonlinear electromagnetic wave propagation in media governed by the Maxwell–Duffing system. My work captures complex phenomena like soliton dynamics and anharmonic polarization, supported by analytical benchmarks using the tanh method. I also design physics-informed neural networks (PINNs) with theoretical proofs  that preserve physical invariants such as mass, energy, and momentum. My long-term goal is to unify rigorous numerical analysis with deep learning to build hybrid solvers for nonlinear wave dynamics in electromagnetics and optics.