From the 2 of 5 linked papers with an AI index.
5 papers
Operator-Split Bayesian Learning for Elliptic PDEs with Unequal Interior and Boundary Data
Emmanuel E. Oguadimma
The paper introduces an operator-split Bayesian learning framework that uses independent Bayesian neural‑network priors for interior source and boundary data to solve second‑order…
Structure-Informed Neural Operators for Long-Time Prediction of Parametric Hamiltonian PDEs
Victory C. Obieke, Christopher Chukwuemeka, Emmanuel E. Oguadimma
The paper introduces an energy‑projection Fourier neural operator that incorporates invariant projection to improve long‑time predictions of parametric Hamiltonian PDEs, preserving…
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 Fou…
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…