A. Vilkha

collaborators

3 papers

math.NA2026

CO $_{2}$ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)

Askold Vilkha, Tomasz SÅuÅ¼alec, Marcin ÅoÅ +1

This paper presents the hybrid solver for a $C O_{2}$ sequestration problem. The solver uses the IGA-ADS (IsoGeometric Analysis Alternating Directions solver) to compute the saturatio…

cs.LG2026

Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN)

Tomasz SÅuÅ¼alec, Marcin ÅoÅ, Askold Vilkha +1

We explore the possibility of solving Partial Differential Equations (PDEs) using discrete weak formulations. We propose a programming environment for defining a discrete computati…

cs.LG2024

Collocation-based Robust Variational Physics-Informed Neural Networks (CRVPINN)

Marcin ÅoÅ, Tomasz SÅuÅ¼alec, PaweÅ Maczuga +3

Physics-Informed Neural Networks (PINNs) have been successfully applied to solve Partial Differential Equations (PDEs). Their loss function is founded on a strong residual minimiza…

CO2​ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)

Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN)

Collocation-based Robust Variational Physics-Informed Neural Networks (CRVPINN)

CO $_{2}$ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)