56 citations · 114 across the 15 of their papers we have counts for
15 papers
Solving higher-order Lane-Emden-Fowler type equations using physics-informed neural networks: benchmark tests comparing soft and hard constraints
Hubert Baty
In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, thi…
Solving stiff ordinary differential equations using physics informed neural networks (PINNs): simple recipes to improve training of vanilla-PINNs
Hubert Baty
Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex pr…
Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests
Hubert Baty, Leo Baty
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a…
Hyperbolic method to explore multiplicity flow solutions in a four-sided lid-driven cavity
Hubert Baty
In this study, the hyperbolic method is adopted to explore the flow field states of incompressible flow in a four-sided lid-driven square cavity. In particular, we focus on the flo…
On the Sweet-Parker model for incompressible visco-resistive magnetic reconnection in two dimensions associated to ideal magnetohydrodynamic instabilities
Hubert Baty
We revisit the well known Sweet-Parker (SP) model for magnetic reconnection in the framework of two dimensional incompressible magnetohydrodynamics. The steady-state solution is re…
On the explosive phase of the tearing mode in double current sheet plasmas: effect of the equilibrium magnetic configuration on the onset threshold and growth rate
Hubert Baty
Magnetic reconnection associated with the tearing instability occurring in double-current sheet systems is investigated within the framework of reduced resistive magnetohydrodynami…