טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLinial Ori
SubjectGenerative ODE Modeling with Known Unknowns
DepartmentDepartment of Electrical Engineering
Supervisors Professor Ron Meir
Dr. Uri Shalit
Full Thesis textFull thesis text - English Version


Abstract

In several crucial applications, domain knowledge is encoded by a system of ordinary differ- ential 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 compli- ance 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. Im- portantly, 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 vari- ables 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. We test our method on videos of pendulums with unknown length, and a model of the cardiovascular system.