LD-GTransNet turns interface problems into a linear least-squares solve via lift-and-decoupling with preset hidden parameters, outperforming existing neural and classical numerical methods on 2D and 3D high-contrast benchmarks
The authors propose LD-GTransNet: building on the multi-layer GTransNet approach, it adds a lift-and-decoupling strategy with preset hidden-layer neuron parameters and separate subnetworks for physical coordinates and an added auxiliary variable, giving a unified global approximation of piecewise smooth solutions without explicit domain decomposition and reducing the formulation to a linear least-squares problem that removes nonlinear training; numerical experiments on 2D and 3D benchmark interface problems show better accuracy and efficiency than existing neural-network and traditional numerical methods, especially for high-contrast coefficients and complex interface geometries.