Rodent: Relevance determination in differential equations

Niklas Heim; Václav Šmídl; Tomáš Pevný

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arXiv · 1912.00656

Rodent: Relevance determination in differential equations

Niklas Heim·Václav Šmídl·Tomáš Pevný

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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.

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BibTeX RIS

Niklas Heim, Václav Šmídl, Tomáš Pevný. 2019-12-02. Rodent: Relevance determination in differential equations. https://arxiv.org/abs/1912.00656

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