6 papers
Structure Preserving High-Order FDTD Methods for the Nonlinear Kerr-Debye Model with Lorentz Dispersion
Emmanuel E. Oguadimma, Vrushali A. Bokil, Nathan L. Gibson
We develop and analyze several families of fully discrete, high-order methods in the finite difference time domain (FDTD) framework for a nonlinear dispersive electromagnetic model…
Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domains
Emmanuel E. Oguadimma, Victory C. Obieke, Xueying Yu
We consider the cubic nonlinear Schrödinger (NLS) equation on two-dimensional flat tori with varying aspect ratios. In this formulation, the choice of aspect ratio governs the Four…
Structure-Informed Neural Operators for Long-Time Prediction of Parametric Hamiltonian PDEs
Victory C. Obieke, Christopher Chukwuemeka, Emmanuel E. Oguadimma
Hamiltonian partial differential equations (PDEs) often exhibit long-time dynamics governed by conserved quantities such as mass, momentum, and Hamiltonian energy. Standard Fourier…
Operator-Split Bayesian Learning for Elliptic PDEs with Unequal Interior and Boundary Data
Emmanuel E. Oguadimma
We propose an operator-split Bayesian learning framework for second-order uniformly elliptic Dirichlet problems with unequal numbers of interior and boundary observations. The data…
Analysis of Nonlinear Random Polarization in Dispersive Dielectrics
Nathan L. Gibson, Emmanuel E. Oguadimma
We present a study on the time-domain propagation of electromagnetic waves in dielectric materials modeled by a nonlinear Debye medium with random perturbations. Polynomial Chaos E…
Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation
Victory Obieke, Emmanuel Oguadimma
Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to pres…