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arXiv Machine Learning By Tianhao Hu, Bangti Jin, Fengru Wang, Yifeng Xu

A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems

Read the original on arXiv Machine Learning →

The paper introduces a hybrid iterative deep Ritz method (H-IDRM) for solving interface problems involving second-order elliptic operators. It uses a mixed formulation that reduces the problem to a sequence of convex minimization tasks and employs a level‑set neural network to represent the interface, thereby handling piecewise smooth solutions without explicit interface sampling. The authors analyze errors from neural network, Monte Carlo, iterative, and penalty sources, and demonstrate through numerical experiments that H-IDRM outperforms existing neural solvers on high‑dimensional, complex interface problems.

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