Combining Differential Equation Models with Deep Learning in an Undergraduate Modeling Course
0Day 2 | 5:00 PM–5:30 PM
"Combining Differential Equation Models with Deep Learning in an Undergraduate Modeling Course"
Presented by:
Victoria Rayskin, Optimum Solvers
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: We will discuss two types of projects in my course "Modeling for dynamic processes".The first type of projects is based on differential equation models. The second type of projects involves time series analysis. These two modeling techniques are related and can benefit from each other. While differential equations help to understand the physical nature of processes, time series analysis is related to statistical deep learning, can provide high fitting accuracy, and has gained popularity in the modern industrial world. Future AI developers and mathematical modelers may find it interesting to notice the connection between these two subjects.
The study of the interplay between dynamical systems and time series analysis has been carried out in many research directions. For example:
How can we construct a dynamical system using time series data? This question has been studied from a variety of view points (Koopman operator's inspired techniques, Brunton-Proctor-Kutz framework, etc.). One can also utilize some TS methods for the dynamical system construction. This is the subject of my research.
One can also try using a dynamical system (fitted to time series data) for predictions of the process. In my research, I developed such methods and applied them to COVID data and Internet traffic data.
Even though these research projects are not part of this presentation (an external funding proposal is pending), they inspired the idea of discussing with students the connection between Dynamical Systems and Time Series analysis.