# Blog

Follow our research and recent news!

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.

Inês Guimarães

David Carvalho

In this 3rd post of the series, and before we dive into out-of-the-box disruptive methods, we close the first part by outlining some good old classical constructions of Hadamard matrices.

Inês Guimarães

David Carvalho

In this 2nd post of the series, we introduce Hadamard matrices and their unique properties in a more formal context and show how hard it is to find them.

Inês Guimarães

David Carvalho

In a series spanning six posts, we dive deep into the topic of Hadamard matrices and how Machine Learning can help us better understand these objects both theoretically and within the context of applications.

David Carvalho

In this Christmas special post, we dive into a remarkable connection between finding function roots and Newton fractals.