Data-Driven Discovery of Ordinary Differential Equations
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Authors
Cox, Terry
Advisor
Eric Sullivan
Kelly Cline
Ted Wendt
Kelly Cline
Ted Wendt
Editor
Date of Issue
2019-04-01
Subject Keywords
ordinary differential equation, ODE, sensor data
Publisher
Citation
Series/Report No.
item.page.identifier
Title
Data-Driven Discovery of Ordinary Differential Equations
Other Titles
Type
thesis
Description
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.
Sponsors
Degree Awarded
Bachelor's
Semester
Spring
Department
Mathematics, Engineering & Computer Science