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    Data-Driven Discovery of Ordinary Differential Equations

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    CoxT_2019_Final.pdf (45.60Mb)
    Author
    Cox, Terry
    Advisor
    Eric Sullivan; Kelly Cline; Ted Wendt
    Date of Issue
    2019-04-01
    Subject Keywords
    ordinary differential equation, ODE, sensor data
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    URI
    https://scholars.carroll.edu/handle/20.500.12647/3513
    Title
    Data-Driven Discovery of Ordinary Differential Equations
    Type
    thesis
    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.
    Degree Awarded
    Bachelor's
    Semester
    Spring
    Department
    Mathematics, Engineering & Computer Science
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