PINNs Introductory Code for the Heat Equation This repository provides some basic insights on Physics Informed Neural Networks (PINNs) and their implementation. PINNs are numerical methods based on the universal approximation capacity of neural networks, aiming to approximate solutions of partial differential equations. Recently, extensive focus has been on approximating […]
Math Martin Hernandez
3 posts
Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd’s algorithm. Also called Voronoid iteration, this is an iterative algorithm finding for equispaced convex cells in euclidean space. Lloyd’s algorithm finds the distribution of the cells computing their center of mass and iteratively applying the […]
Uniform Turnpike Property 1 Introduction In this post, we analyze a heat equation with rapidly oscillating coefficients dependent on a parameter , with a distributed control. We show that the uniform null controllability implies the uniform turnpike property, i.e., the turnpike property with constants independent of the -parameter. The main […]