Manuel Madeira
David Carvalho
Fábio Cruz
In this 3rd and final part of the Heat series, we delve into the idea of enhancing generalizational power in Neural Networks so they can learn more complex aspects. We exemplify these ideas by running Physics Informed Neural Networks (PINNs) on a custom-designed domain and boundary condition.
Manuel Madeira
David Carvalho
Fábio Cruz
In this 2nd part of the series, we show that Neural Networks can learn how to solve Partial Differential Equations! In particular, we use a PINN (Physics-Informed Neural Network) architecture to obtain the results we obtained with classical algorithms in Heat #1.
Manuel Madeira
David Carvalho
Fábio Cruz
In the debut of a 3-post series on solving Partial Differential Equations (PDEs) using Machine Learning, we start by introducing the Heat Equation and then we solve it with a classical algorithm - a Finite Difference Method (FDM) method in a FTCS (Forward in Time, Centered in Space) scheme.