6 papers
IGA-ODIL: Optimizing DIscretre robust Loss with Isogeometric Analysis to solve forward and inverse problems faster using machine learning tools
Maciej PaszyÅski, Tomasz SÅużalec
Physics-informed neural networks (PINNs) formulate the solution of partial differential equations as residual minimization problems over neural network parameterizations. Although…
Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen
Leszek Siwik, Maciej Sikora, Natalia Leszczyńska +12
In this paper, we propose a Physics-Informed Neural Network framework for time-dependent simulations of pollution propagation originating from moving emission sources. We formulate…
CO sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)
Askold Vilkha, Tomasz SÅużalec, Marcin ÅoÅ +1
This paper presents the hybrid solver for a sequestration problem. The solver uses the IGA-ADS (IsoGeometric Analysis Alternating Directions solver) to compute the saturatio…
Wildfires Quasi-Implicit Alternative-Direction Simulations using Isogeometric Finite Element Method
Juliusz Wasieleski, Tomasz SÅużalec, Maciej Woźniak +7
We develop a wildfire simulation model that evolves the temperature scalar field using an energy balance equation accounting for heat generation, transport, and loss. For these equ…
Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN)
Tomasz SÅużalec, 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…
Stabilization of isogeometric finite element method with optimal test functions computed from norm residual minimization
Marcin ÅoÅ, Tomasz SÅużalec, 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…