Rodent: Relevance determination in differential equations

TL;DR

This paper introduces Rodent, a neural approach that identifies underlying differential equations from observed trajectories without predefined basis functions, emphasizing interpretability and sparsity.

Contribution

It presents a novel method combining neural arithmetic units with VAE and ARD to learn sparse, interpretable ODE models from data, capturing diverse dynamical systems.

Findings

Successfully learns models for harmonic signals.

Effectively captures Lotka-Volterra systems.

Achieves sparse and interpretable ODE representations.

Abstract

We aim to identify the generating, ordinary differential equation (ODE) from a set of trajectories of a partially observed system. Our approach does not need prescribed basis functions to learn the ODE model, but only a rich set of Neural Arithmetic Units. For maximal explainability of the learnt model, we minimise the state size of the ODE as well as the number of non-zero parameters that are needed to solve the problem. This sparsification is realized through a combination of the Variational Auto-Encoder (VAE) and Automatic Relevance Determination (ARD). We show that it is possible to learn not only one specific model for a single process, but a manifold of models representing harmonic signals as well as a manifold of Lotka-Volterra systems.