Maciej Paszynski

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20242026

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math.NA2026

IGA-ODIL: Optimizing DIscretre robust Loss with Isogeometric Analysis to solve forward and inverse problems faster using machine learning tools

Maciej PaszyÅski, Tomasz SÅuÅ¼alec

Physics-informed neural networks (PINNs) formulate the solution of partial differential equations as residual minimization problems over neural network parameterizations. Although…

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…

math.NA2024

Stabilization of isogeometric finite element method with optimal test functions computed from $L_{2}$ norm residual minimization

Marcin ÅoÅ, Tomasz SÅuÅ¼alec, Maciej PaszyÅski +1

We compare several stabilization methods in the context of isogeometric analysis and B-spline basis functions, using an advection-dominated advection\revision{-}diffusion as a mode…

IGA-ODIL: Optimizing DIscretre robust Loss with Isogeometric Analysis to solve forward and inverse problems faster using machine learning tools

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

Stabilization of isogeometric finite element method with optimal test functions computed from L2​ norm residual minimization

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

Stabilization of isogeometric finite element method with optimal test functions computed from $L_{2}$ norm residual minimization