Data-Driven Discovery of Ordinary Differential Equations

Abstract

We suggest that using data-driven methods on collected sensor data, we can recreate the ordinary differential equation. In this case we are applying data to find the ODE as opposed to deriving an ODE from basic principles. To do this, we use the machine learning variable selection technique lasso regression to select which derivative terms are important in a linear model of possible/likely derivative terms. To confirm this method, we explore two know differential equations: a mass spring oscillator and a double mass spring oscillator. We explore both simulated and collected sensor data for both these equations. Following the machine learning methods, we correctly recreate the differential equations. Exploring further, we use cheap smart phone sensors as a way of measuring the concentration of Lipton Black Tea brewing over time. Without knowing the true differential equation, we create one using our data-driven methods. From our findings we can say that applying these methods verify and by pass the physics of the true equations.