4 papers
Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm
Muhammad Luthfi Shahab, Imam Mukhlash, Hadi Susanto
This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partial differential equations (PDEs). By for…
Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations
Muhammad Luthfi Shahab, Hadi Susanto
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength…
A finite difference method with symmetry properties for the high-dimensional Bratu equation
Muhammad Luthfi Shahab, Hadi Susanto, Haralampos Hatzikirou
Solving the three-dimensional (3D) Bratu equation is highly challenging due to the presence of multiple and sharp solutions. Research on this equation began in the late 1990s, but…
Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices
Muhammad Luthfi Shahab, Fidya Almira Suheri, Rudy Kusdiantara +1
This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcati…