6 papers
Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest
Muhammad Luthfi Shahab, Gabriella Alfa Indahsari, Imam Mukhlash +1
This paper introduces a hybrid joint-selective optimization (HJSO) framework for large-scale numerical problems in which a small subset of trainable quantities is of primary intere…
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…
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…
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…
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 Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations
Endah Rokhmati Merdika Putri, Muhammad Luthfi Shahab, Mohammad Iqbal +4
We propose a new method, called a deep-genetic algorithm (deep-GA), to accelerate the performance of the so-called deep-BSDE method, which is a deep learning algorithm to solve hig…