4 papers
G-PINNs: Gaussian-based spatially weighted formulation for PINNs: 1D low-viscous Burgers
Kheir-eddine Otmani, Abdelhalim Azzouz, Nourelhouda Groun +1
We introduce a Gaussian-based spatially weighted loss framework (G-PINNs) for physics-informed neural networks (PINNs) to improve the resolution of sharp discontinuities and shock…
Towards a Gagliardo-Type Theory of Fractional Sobolev Spaces on Arbitrary Time Scales
Hafida Abbas, Abdelhalim Azzouz, Praveen Agarwal +1
We propose a systematic Gagliardo-type formulation of fractional Sobolev spaces on arbitrary time scales, based on the Lebesgue Delta-measure and the off-diagonal interaction domai…
A nonlocal transmission problem on a hybrid continuous-discrete domain
Hafida Abbas, Abdelhalim Azzouz
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, d…
Fractional Sobolev Spaces and Variational Problems with Variable-Order Operators on Time Scales
Hafida Abbas, Abdelhalim Azzouz
We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define thro…