  Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been
widely applied in diverse disciplines, including thermodynamics, continuum
mechanics, mathematical analysis, machine learning, etc. In this paper, we
propose a new method for solving the inverse XDE (ODE, PDE, SDE) problems by
utilizing the entropy balance equation instead of the original differential
equations. This distinguishing feature constitutes a major difference between
our current method and other previous classical methods (e.g. SINDy). Despite
concerns about the potential information loss during the compression procedure
from the original XDEs to single entropy balance equation, various examples
from MM reactions, Schlogl model and chemical Lorenz equations in the form of
ODEs to nonlinear porous medium equation and Fokker-Planck equation with a
double-well potential in the PDE form all well confirm the accuracy, robustness
and reliability of our method, as well as its comparable performance with
respect to SINDy.
