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math.NA2026
MATLAB-Based Layerwise Self-Adaptive Physics-Informed Neural Network in Applications to Multidimensional Coupled Burgers' Equations with High Reynolds Numbers
Harish P. Bhatt, Xi Chen, Jingsai Liang
This paper presents an improved physics-informed neural network for simulating the spatio-temporal solution profile of the multidimensional coupled Burgers' equations with high Rey…
math.NA2024
Efficiently and accurately simulating multi-dimensional M-coupled nonlinear Schrödinger equations with fourth-order time integrators and Fourier spectral method
Nate Lovett, Harish Bhatt
Coupled nonlinear Schrödinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow wate…