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A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems

arXiv · AI, language, vision and robotics · article · Sep 23, 2026 · UTC

In this work, we propose a hybrid iterative deep Ritz method (H-IDRM) for a class of interface problems for second-order elliptic operators. It is based on a new mixed formulation of the problem and involves solving a sequence of convex minimization problems. We employ a level-set neural network architecture, featuring a level-set representation of the interface, to accommodate the piecewise smoothness of the solution and the flux. The approach involves only volumetric representations instead of duality pairing on the interface and avoids explicit interface sampling that is inconvenient for co

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