  Partial differential equation parameter estimation is a mathematical and
computational process used to estimate the unknown parameters in a partial
differential equation model from observational data. This paper employs a
greedy sampling approach based on the Discrete Empirical Interpolation Method
to identify the most informative samples in a dataset associated with a partial
differential equation to estimate its parameters. Greedy samples are used to
train a physics-informed neural network architecture which maps the nonlinear
relation between spatio-temporal data and the measured values. To prove the
impact of greedy samples on the training of the physics-informed neural network
for parameter estimation of a partial differential equation, their performance
is compared with random samples taken from the given dataset. Our simulation
results show that for all considered partial differential equations, greedy
samples outperform random samples, i.e., we can estimate parameters with a
significantly lower number of samples while simultaneously reducing the
relative estimation error. A Python package is also prepared to support
different phases of the proposed algorithm, including data prepossessing,
greedy sampling, neural network training, and comparison.
