An Astronomer’s perspective on Deep Learning

This blog contains notes and notebooks of a researcher in Astronomy diving deep into the study of deep learning. What I found during my quest, and what I report here, is meant to be purely anecdotical and it is not necessarily following a logical and sound educational path. The hope, with which I build this blog, is that it will eventually become a useful reference for me to look back at and that also other people, with a similar background to mine, may find some use out of these notes and notebooks.

My name is Lorenzo Posti and I’m currently a postdoctoral researcher at the Strasbourg Observatory (France) specialized in models of galaxy dynamics, which I use to study the origin of galaxies and the nature of dark matter. Find my list of poublications on ADS

This site is built using fastpages. The diagram of the neural network in the banner was made using NN-SVG, the input image shows isophotal contours of the galaxy NGC 4342 rendered from Hubble observations.

Posts

• Intro to diffusion models from scratch

  This notebook is an introduction to diffusion models that are currently state-of-the-art in computer vision and in image generation. I build from scratch a diffusion model able to generate realistic rotation curves starting from purely random noise.

  Jan 19, 2023

• Conditioning diffusion models

  After the intro to diffusion models, let's take them to the next step by introducing conditioning in these simplified models and let's do it from scratch. We will build a model able to generate rotation curves with peculiar features that we can specify upfront.

  Jan 19, 2023

• `vcdisk`: a python package for galaxy rotation curves

  This notebook presents a minimal python package that I wrote to solve Poisson's equation in galactic disks. `vcdisk` is an handy toolbox of essential functions to compute the circular velocity of thick disks and flattened bulges of arbitrary surface density.

  Dec 8, 2022

• A simple neural network to predict galaxy rotation curves from photometry

  Designing a simple feedforward neural network, made with just linear layers, activations, and batch normalization, to predict rotation curves from galaxy surface brightness profiles. Comparison to the MOND empirical law.

  Nov 16, 2022

• Rotation curve decompositions with Gaussian Processes: taking into account data correlations leads to unbiased results

  Correlations between velocity measurements in disk galaxy rotation curves are usually neglected when fitting dynamical models. This notebook, which accompanies the paper Posti (2022), Res. Notes AAS, 6, 233, shows how data correlations can be taken into account in rotation curve decompositions using Gaussian Processes.

  Nov 2, 2022

• Gaussian Processes: modelling correlated noise in a dataset

  Independent datapoints are most often just a convenient idealisation which can even hamper your model inference at times and bias your results. Learn how to embrace the reality of correlated noise in the data and marginalize the parameter posteriors with Gaussian Processes.

  Oct 17, 2022

• Variational Autoencoder: learning an underlying distribution and generating new data

  Constructing an autoencoder that learns the underlying distribution of the input data, generated from a multi-dimensional smooth function `f=f(x_1,x_2,x_3,x_4)`. This can be used to generate new data, sampling from the learned distribution

  Oct 7, 2022

• Autoencoder represents a multi-dimensional smooth function

  Setting up a simple `Autoencoder` neural network to reproduce a dataset obtained by sampling a multi-dimensional smooth function `f=f(x_1,x_2,x_3,x_4)`. As an example I'm using a disc+halo rotation curve model where both components are described by 2-parameters circular velocities

  Jun 10, 2022

• Ground-up construction of a simple neural network

  Constructing a simple multi-layered neural network (NN) from scratch using pure `python` and a bit of `pytorch`. This is mostly my personal re-writing of the fantastic lesson 1 of the `fast.ai` course Part 2

  Mar 22, 2022

• Understanding how basic linear NNs handle non-linearities

  A deep exploration, an visualization, of how a single-layer linear neural network (NN) is able to approximate non linear behaviours with a just handful of neurons and the magic of activation functions.

  Mar 18, 2022