  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 paper, we focus on the model discovery problem when
the data is not efficiently sampled in time. 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. 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.

Numerical Analysis;Machine Learning;Numerical Analysis;Computational Physics