7 papers
IGA-ODIL: Optimizing DIscretre robust Loss with Isogeometric Analysis to solve forward and inverse problems faster using machine learning tools
Maciej Paszyński, Tomasz Służalec
Physics-informed neural networks (PINNs) formulate the solution of partial differential equations as residual minimization problems over neural network parameterizations. Although…
CO sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)
Askold Vilkha, Tomasz Służalec, Marcin Łoś +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 Służalec, 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 Służalec, Marcin Łoś, 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…
Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen
Maciej Sikora, Leszek Siwik, Natalia Leszczyńska +7
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…
Stabilization of isogeometric finite element method with optimal test functions computed from norm residual minimization
Marcin Łoś, Tomasz Służalec, Maciej Paszyński +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…
Matrix-by-matrix multiplication algorithm with computational complexity for variable precision arithmetic
Maciej Paszyński
We show that assuming the availability of the processor with variable precision arithmetic, we can compute matrix-by-matrix multiplications in computational complexi…