  Partial differential equations (PDEs) with multiple scales or those defined
over sufficiently large domains arise in various areas of science and
engineering and often present problems when approximating the solutions
numerically. Machine learning techniques are a relatively recent method for
solving PDEs. Despite the increasing number of machine learning strategies
developed to approximate PDEs, many remain focused on relatively small domains.
When scaling the equations, a large domain is naturally obtained, especially
when the solution exhibits multiscale characteristics. This study examines
two-scale equations whose solution structures exhibit distinct characteristics:
highly localized in some regions and significantly flat in others. These two
regions must be adequately addressed over a large domain to approximate the
solution more accurately. We focus on the vanishing gradient problem given by
the diminishing gradient zone of the activation function over large domains and
propose a stratified sampling algorithm to address this problem. We compare the
uniform random classical sampling method over the entire domain and the
proposed stratified sampling method. The numerical results confirm that the
proposed method yields more accurate and consistent solutions than classical
methods.
