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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.05800 |
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Table of Contents:
- For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a perturbation-correction framework based on Loacal Randomized Neural Networks(LRaNNs) to overcome this limitation. In the initialization step, a satisisfactory based approximation is obtained by minimizing the original nonconvex residual, typically stagnating at a moderate accuracy level. Subsequently, in the correction step, a correction term is determined by solving a subproblem governed by a perturbation expansion around the base approximation. This reformulation yields a convex optimization problem for the output coefficients, which guarantees rapic convergence. We rigorously derive an a posteriori error estitmate, demonstrating that the total generalization error is governed by the discrete residual norm, quadrature error, and a controllable truncation error. Numerical experiments on nonlinear diffusion problems with irregular moving interfaces, gradient-dependent diffusivities, and high-contrast media demonstrate that the proposed method effectively overcomes the optimization plateau. The correction step yields a significant improvement of 4-6 order of magnitude in L^2 accuracy.