Which direction does this shape point to? As a human, it is natural to identify when a shape points in a certain direction, but how do we do it algorithmically? In other words, in which direction is this polygon pointing? A way to find this direction is to fit an ellipse to the shape and use the major axis as the direction it’s pointing. Fitting an ellipse can be done by doing an eigenvector decomposition of the covariance matrix.

Introduction Physics informed neural networks (PINNs) is a framework for solving PDEs first introduced in 1998 by Lagaris et al. and later in 2019 where reintroduced to the DL community by Raissi et al. The main idea is to train an artificial neural network that follow physics given by a PDE. Sample problem In this article I will be using the logistic equation known to model population growth as a one dimensional example problem.

Introduction Diffusion probabilistic model (DPM) or just diffusion models are a generative model that has received a lot of attention in the last couple of years in models DALL-E2 and Imagen. In this blog post I will give a short introduction and a minimal implementation of this model. The task we are going to solve is to recover a 2D shape from a random set of points. The diffusion framework consist of a forward diffusion process were random noise is added to the input until the it has no reassembles to the input.