Die Programmiersprache ist Python, und wir planen die Verwendung von modernen Python-Modulen für ML wie PyTorch oder ggf. JAX. Gute Python-Kenntnisse sind Voraussetzung. Das Softwareprojekt findet semesterbegleitend statt und kann auch auf Englisch durchgeführt werden.

Relevant resources

All the resources below are highly relevant, but if this is your first time being exposed to neural differential equations you should focus on the underlined items.

Theory

• Beginner friendly:
  • The best source covering the main flavors of neural differential equations in-depth: On Neural Differential Equations, https://arxiv.org/abs/2202.02435
  • Overview of the current state of the field: Comprehensive Review of Neural Differential Equations for Time Series Analysis, https://arxiv.org/abs/2502.09885
• Neural ODEs
  • The paper that started the whole field: Neural Ordinary Differential Equations, https://arxiv.org/abs/1806.07366
• Neural CDEs: 

  • Neural Controlled Differential Equations for Irregular Time Series, https://arxiv.org/abs/2005.08926

  • Neural Controlled Differential Equations for Online Prediction Tasks, https://arxiv.org/abs/2106.11028

• Neural SDEs:

  • Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data, https://openreview.net/forum?id=4VIgNuQ1pY

  • Scalable Gradients for Stochastic Differential Equations, https://arxiv.org/abs/2001.01328

Software

Neural differential equations = differential equations + Neural networks. We will be using Diffrax for differential equations and Equinox for neural networks, all written in JAX.

• JAX: https://docs.jax.dev/en/latest/notebooks/thinking_in_jax.html

• Diffrax: https://docs.kidger.site/diffrax/

• Equinox for Neural networks: https://docs.kidger.site/equinox/