We propose a solver for 2D parametric transmission problems that combines neural networks with a low-dimensional eigenvalue solver. It is named “Least-Squares-Based Regularity-Conforming Neural Network (LS-ReCoNN)” method. The method employs a quadratic loss function that enforces the PDE residual and flux continuity conditions and provides a consistent upper bound for the energy-norm error. Then, it decomposes the solution into a singular part and a regular part that also contains jumps in the gradients. The singular part is approximated using basis functions obtained from a one-dimensional finite element (FE) eigenvalue problem. For the regular part, we employ a separated representation, leading to a sum of terms that are multiplications of a parameter-dependent coefficient times a space-dependent function. The space-dependent functions are approximated with a deep neural network, while the parameter-dependent coefficients of the regular part are solved by using a least-squares approach, in which the optimal approximation for each parameter instance is obtained online by solving a small least-squares problem [2]. This construction embeds prior analytical knowledge into the approximation space, avoiding Gibbs-type instabilities and improving accuracy near interfaces and junction singularities [1]. Numerical experiments demonstrate that LS-ReCoNN accurately captures low-regularity features while maintaining robustness and efficiency across wide parameter ranges, delivering solutions with energy-norm errors below 1%.