  In biomedical engineering, earthquake prediction, and underground energy
harvesting, it is crucial to indirectly estimate the physical properties of
porous media since the direct measurement of those are usually
impractical/prohibitive. Here we apply the physics-informed neural networks to
solve the inverse problem with regard to the nonlinear Biot's equations.
Specifically, we consider batch training and explore the effect of different
batch sizes. The results show that training with small batch sizes, i.e., a few
examples per batch, provides better approximations (lower percentage error) of
the physical parameters than using large batches or the full batch. The
increased accuracy of the physical parameters, comes at the cost of longer
training time. Specifically, we find the size should not be too small since a
very small batch size requires a very long training time without a
corresponding improvement in estimation accuracy. We find that a batch size of
8 or 32 is a good compromise, which is also robust to additive noise in the
data. The learning rate also plays an important role and should be used as a
hyperparameter.
