  In recent years, machine learning methods have been widely used to study
physical systems that are challenging to solve with governing equations.
Physicists and engineers are framing the data-driven paradigm as an alternative
approach to physical sciences. In this paradigm change, the deep learning
approach is playing a pivotal role. However, most learning architectures do not
inherently incorporate conservation laws in the form of continuity equations,
and they require dense data to learn the dynamics of conserved quantities. In
this study, we introduce a clever mathematical transform to represent the
classical dynamics as a point-wise process of disappearance and reappearance of
a quantity, which dramatically reduces model complexity and training data for
machine learning of transport phenomena. We demonstrate that just a few
observational data and a simple learning model can be enough to learn the
dynamics of real-world objects. The approach does not require the explicit use
of governing equations and only depends on observation data. Because the
continuity equation is a general equation that any conserved quantity should
obey, the applicability may range from physical to social and medical sciences
or any field where data are conserved quantities.
