From the 1 of 5 linked papers with an AI index.
5 papers
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…
Communication Strategy Selection for Multi-GPU 3D FDTD with Convolutional Perfectly Matched Boundary Layers
Victory C. Obieke
In this paper we describe a communication-strategy study for multi-GPU three-dimensional finite-difference time-domain computation with convolutional perfectly matched layer bounda…
An Energy Stable Approach for Learning Derivative Operators from Noisy Data for Maxwells Equations
Victory C. Obieke, Ameh Emmanuel Sunday
We develop a structure-preserving ADMM method, denoted SP-ADMM, for learning energy-stable spatial derivative stencils for Maxwell equations from noisy data. Starting from the sour…
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…