5 papers
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…
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…