Pedro Ferro Pereira
David Carvalho
Ivan Pombo
Fábio Cruz
In this grand finale, we explore how the Graph Network simulator fits into test scenarios of fluid dynamics, generalising from simple to chaotic ones, passing through a real experimental case.
Pedro Ferro Pereira
David Carvalho
Ivan Pombo
Fábio Cruz
In this blog post, we delve in to the architecture behind the Deep Learning model we will use --- an Encoder-Processor-Decoder (E-P-D) model and how a Graph Network Simulator can be devised from it.
Pedro Ferro Pereira
David Carvalho
Fábio Cruz
Ivan Pombo
In this third post of the series, we establish graphs as appropriate data structures to handle Smoothed Particle Hydrodynamics (SPH) data. We then construct own graphs with the aim of encoding the input of our Deep Learning model.
Pedro Ferro Pereira
Fábio Cruz
David Carvalho
Ivan Pombo
In this second post of the series, we dive deeper into the theoretical and implementational foundations of Smoothed Particle Hydrodynamics (SPH) as a Computational Fluid Dynamics framework.
Pedro Ferro Pereira
Fábio Cruz
David Carvalho
In the debut of a series on learning Computational Fluid Dynamics (CFD) using Machine Learning, we start off precisely by making sense of what a fluid is, which equations dictate how they evolve physically and how computational methods can help us simulate their solutions.
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.