Energy-Based Adaptive Deep Unfitted Nitsche Method for Elliptic Interface Problems

Abstract

The paper proposes an energy-based adaptive sampling strategy to enhance the performance of the deep unfitted Nitsche method (DUNM) for elliptic interface problems. Instead of relying on fixed or random training points, the proposed refinement indicator dynamically concentrates samples in high-energy regions, including sharp coefficient jumps and interface singularities. This targeted allocation improves both accuracy and efficiency compared to random sampling. Numerical experiments in both two- and three-dimensional settings demonstrate that the method achieves robust accuracy and efficiency across diverse scenarios, from standard geometries to highly irregular interfaces, while effectively handling high-contrast coefficients and multi-subdomain configurations. These results confirm that the proposed adaptive strategy not only reduces training cost but also ensures reliable performance in complex interface problems.