Neural Ordinary Differential Equations

This is a repository of code developed within the framework of a Bachelor's Thesis at the University of Barcelona on Neural Ordinary Differential Equations. It serves as a final degree project for the joint degrees of Mathematics and Computer Science.

As part of the project, this code provides examples and illustrations of how neural ODEs can be used with various purposes. Additionally, it intends to be a bridge between the theoretical results presented in the main text and the practical applications of this kind of model.

Folder structure

• support contains additional resources used in the creation of the project's main document memoria.pdf
• experiments contains the code for all the demonstrations and proofs-of-concept used in the project
  • helpers is an internal library for training and visualisation
  • continuous_normalising_flows contains the experiments about CNF models.
    • circles_results, and triangle_results have images generated when experimenting with different distributions
    • results contains the trained models
    • cnf_one_images and cnf_one_images_2 have gif illustrations of the evolution of a one-dimensional CNF
    • modelling contains auxiliary classes used in cnf_mnist.ipynb to generate hand-written digits
  • neural_odes contains examples of simple neural ODEs architectures
    • adjoint_comparison compares the efficiency of training neural ODEs using discretise-then-optimise or optimise-then-discretise approaches
    • augmentation shows the difference between augmented and unaugmented models
    • linear_ode illustrates how neural ODEs can be used to learn a linear continuous dynamical system