##Statistics Seminar##\\ Department of Mathematics and Statistics
^ **DATE:**|Thursday, September 7, 2023 |
^ **TIME:**|1:15pm -- 2:15pm |
^ **LOCATION:**|WH 100E |
^ **SPEAKER:**|Jia Zhao, Binghamton University |
^ **TITLE:**|Discovery of Governing Equations with Recursive Deep Neural Networks |
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**Abstract**
Model discovery based on existing data has been one of the major focuses
of mathematical modelers for decades. Despite tremendous achievements of model
identification from adequate data, how to unravel the models from limited data is
less resolved. In this talk, I will focus on the model discovery problem when the
data is not efficiently sampled. This is common due to limited experimental
accessibility and labor/resource constraints. Specifically, we introduce a recursive
deep neural network (RDNN) for data-driven model discovery. By embedding the known
physics knowledge, this recursive approach can retrieve the governing equation in a
simple and efficient manner, and it can significantly improve the approximation
accuracy by increasing the recursive stages. In particular, our proposed approach
shows superior power when the existing data are sampled with a large time lag, from
which the traditional approach might not be able to recover the model well. Several
widely used examples of dynamical systems are used to benchmark this newly proposed
recursive approach. Numerical comparisons confirm the effectiveness of this
recursive neural network for model discovery.