Rodent: Relevance determination in differential equations
This addresses the challenge of explainable ODE discovery from limited data, though it appears incremental as it builds on existing techniques like VAE and ARD.
The paper tackles the problem of identifying generating ordinary differential equations (ODEs) from partially observed trajectories without prescribed basis functions, using Neural Arithmetic Units and a sparsification method combining VAE and ARD to minimize state size and non-zero parameters. The result demonstrates learning manifolds of models for harmonic signals and Lotka-Volterra systems.
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.