Classical Methods

Heat #1

Research Heat #1: The Heat Equation (and a Classical Solver)

February 14, 2022

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.

Heat Equation Finite Difference Methods PDEs PINNs Classical Methods Numerical Methods

Research Hadamard Matrices #3: It's Construction Time

February 7, 2022

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.

Hadamard matrices Combinatorial Optimization Linear Algebra Group Theory Classical Methods

Research Newton Fractals (oh-oh-oh!)

December 20, 2021

David Carvalho

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

Newton Fractals Fractals Root Finding Newton-Raphson Method Classical Methods Numerical Methods