  Many scientific phenomena are modeled by Partial Differential Equations
(PDEs). The development of data gathering tools along with the advances in
machine learning (ML) techniques have raised opportunities for data-driven
identification of governing equations from experimentally observed data. We
propose an ML method to discover the terms involved in the equation from
two-dimensional spatiotemporal data. Robust and useful physical features are
extracted from data samples to represent the specific behaviors imposed by each
mathematical term in the equation. Compared to the previous models, this idea
provides us with the ability to discover 2D equations with time derivatives of
different orders, and also to identify new underlying physics on which the
model has not been trained. Moreover, the model can work with small sets of
low-resolution data while avoiding numerical differentiations. The results
indicate robustness of the features extracted based on prior knowledge in
comparison to automatically detected features by a Three-dimensional
Convolutional Neural Network (3D CNN) given the same amounts of data. Although
particular PDEs are studied in this work, the idea of the proposed approach
could be extended for reliable identification of various PDEs.
