./episode_179.sh
📚 “An investment in knowledge pays the best interest.” – Benjamin Franklin
💦 But How DO Fluid Simulations Work?
Fluid simulations. How on is it possible that a computer can recreate the crashing waves, the rolling clouds and the swirling smoke that we see in our daily lives, phenomena which seem characterized by randomness and chaos? This video will attempt to explain exactly how the mathematics behind fluid simulations work.
💦 The Navier-Stokes Equations
In 1845, Sir George Stokes had derived the equation of motion of a viscous flow by adding Newtonian viscous terms, thereby the Navier-Stokes Equations had been brought to their final form which has been used to generate numerical solutions for fluid flow ever since.
In this equation, the formula for mass continuity is missing and other assumptions go into this equation. You can find the full derivation of the equation here.
🦴 Finite Element Method for Medicine
In this numerical method, a complex shape is divided into many small, simple geometries, such as cuboids.
The finite element method easily calculates the simple geometries' physical behavior. The individual simple geometries‘ results are then combined to recreate the physical behavior of the entire body.
📚 Can Physics-Informed Neural Networks beat the Finite Element Method?
TL;DR: “Considering the solution time and accuracy, PINNs are not able to beat the finite element method in our study.”
The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of partial differential equations. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other.
💻 Engineering Tool of the Week – COOLFluiD
The object-oriented HPC platform for CFD, plasma and multi-physics simulations whose development started in 2002 at the Von Karman Institute for Fluid Dynamics (www.vki.ac.be) in collaboration with the KU Leuven Center for mathematical Plasma Astrophysics (CmPA) dept. (https://wis.kuleuven.be/CmPA) is open.
📚Book of the Week
Automated Machine Learning in Action
Automated Machine Learning in Action reveals how you can automate the burdensome elements of designing and tuning your machine learning systems. It’s written in a math-lite and accessible style, and filled with hands-on examples for applying AutoML techniques to every stage of a pipeline. AutoML can even be implemented by machine learning novices! If you’re new to ML, you’ll appreciate how the book primes you on machine learning basics. Experienced practitioners will love learning how automated tools like AutoKeras and KerasTuner can create pipelines that automatically select the best approach for your task, or tune any customized search space with user-defined hyperparameters, which removes the burden of manual tuning.
❤️ Support the Blog & Newsletter
Let’s connect on Twitter or Instagram or LinkedIn!
For any business-related issues or collaborations, feel free to write me an email to support@jousefmurad.com!
Keep engineering your mind! 🧠
Jousef