Randomized Neural Networks for Partial Differential Equation on Static and Evolving Surfaces
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the need for repeated mesh updates and geometry or solution transfer. While neural-network-based methods offer mesh-free discretizations, approaches based on nonconvex training can be costly and may fail to deliver high accuracy in practice. In this work, we develop a randomized neural network (RaNN) method for solving PDEs on both static and evolving surfaces: the hidden-layer parameters are randomly generated and kept fixed, and the output-layer coefficients...
| Authors | Jingbo Sun, Fei Wang |
|---|---|
| Primary category | math.NA |
| Published | 2 March 2026 |
| Last updated at source | 2 March 2026 |
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