  Identifying underlying governing equations and physical relevant information
from high-dimensional observable data has always been a challenge in physical
sciences. With the recent advances in sensing technology and available
datasets, various machine learning techniques have made it possible to distill
underlying mathematical models from sufficiently clean and usable datasets.
However, most of these techniques rely on prior knowledge of the system and
noise-free data obtained by simulation of physical system or by direct
measurements of the signals. Hence, the inference obtained by using these
techniques is often unreliable to be used in the real world where observed data
is noisy and requires feature engineering to extract relevant features. In this
work, we provide a deep-learning framework that extracts relevant information
from real-world videos of highly stochastic systems, with no prior knowledge
and distills the underlying governing equation representing the system. We
demonstrate this approach on videos of confined multi-agent/particle systems of
ants, termites, fishes as well as a simulated confined multi-particle system
with elastic collision interactions. Furthermore, we explore how these
seemingly diverse systems have predictable underlying behavior. In this study,
we have used computer vision and motion tracking to extract spatial
trajectories of individual agents/particles in a system, and by using LSTM VAE
we projected these features on a low-dimensional latent space from which the
underlying differential equation representing the data was extracted using
SINDy framework.
