no code implementations • 4 Jan 2024 • Marcin Łoś, Maciej Paszyński
This loss function in PINNs is generally not robust with respect to the true error.
no code implementations • 24 Sep 2023 • Paweł Maczuga, Maciej Sikora, Maciej Skoczeń, Przemysław Rożnawski, Filip Tłuszcz, Marcin Szubert, Marcin Łoś, Witold Dzwinel, Keshav Pingali, Maciej Paszyński
We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic execution on cloud environment; (2) it supports two dimensional time-dependent PDEs; (3) it provides simple interface for definition of the residual loss, boundary condition and initial loss, together with their weights; (4) it support Neumann and Dirichlet boundary conditions; (5) it allows for customizing the number of layers and neurons per layer, as well as for arbitrary activation function; (6) the learning rate and number of epochs are available as parameters; (7) it automatically differentiates PINN with respect to spatial and temporal variables; (8) it provides routines for plotting the convergence (with running average), initial conditions learnt, 2D and 3D snapshots from the simulation and movies (9) it includes a library of problems: (a) non-stationary heat transfer; (b) wave equation modeling a tsunami; (c) atmospheric simulations including thermal inversion; (d) tumor growth simulations.
no code implementations • 3 Jan 2022 • Kamil Doległo, Anna Paszyńska, Maciej Paszyński, Leszek Demkowicz
We present an alternative approach, where the physcial quantity is approximated as a linear combination of smooth B-spline basis functions, and the neural network approximates the coefficients of B-splines.
