  In this paper, a new asymptotic preserving (AP) scheme is proposed for the
anisotropic elliptic equations. Different from previous AP schemes, the actual
one is based on first-order system least-squares for second-order partial
differential equations, and it is uniformly well-posed with respect to
anisotropic strength. The numerical computation is realized by a deep neural
network (DNN), where least-squares functionals are employed as loss functions
to determine parameters of DNN. Numerical results show that the current AP
scheme is easy for implementation and is robust to approximate solutions or to
identify anisotropic strength in various 2D and 3D tests.
