Generative ODE Modeling with Known Unknowns

Ori Linial, Uri Shalit

Keywords: generative models, variatonal autoencoder, physical system, ordinary differential equation, healthcare

TL;DR: How to integrate an apriori known ODE into the process of learning an apriori unknown generative function

Abstract: In several crucial applications, domain knowledge is encoded by a system of ordinary differential equations (ODE). A motivating example is intensive care unit patients: The dynamics of some vital physiological variables such as heart rate, blood pressure and arterial compliance can be approximately described by a known system of ODEs. Typically, some of the ODE variables are directly observed while some are unobserved, and in addition many other variables are observed but not modeled by the ODE, for example body temperature. Importantly, the unobserved ODE variables are “known-unknowns”: We know they exist and their functional dynamics, but cannot measure them directly, nor do we know the function tying them to all observed measurements. Estimating these known-unknowns is often highly valuable to physicians. Under this scenario we wish to: (i) learn the static parameters of the ODE generating each observed time-series (ii) infer the dynamic sequence of all ODE variables including the known-unknowns, and (iii) extrapolate the future of the ODE variables and the observations of the time-series. We address this task with a variational autoencoder incorporating the known ODE function, called GOKU-net for Generative ODE modeling with Known Unknowns.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2003.10775/code)