IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients
We introduce a novel neural operator architecture designed to approximate solutions of linear elliptic partial differential equations with high-contrast, spatially varying coefficients. The network, termed the Iterated V-shaped Net (IV-Net), realizes a mapping from the input coefficients and righthand side to the corresponding solution field. The architecture of IV-Net is informed by, and closely resembles, a V-cycle multigrid solver. The IV-Net model is parameterized via convolutional layers defined in the physical domain. For coercive problems with highly heterogeneous coefficients, the proposed network exhibits superior performance relative to a proper orthogonal decomposition (POD) ap...
| Authors | Shan Zhong, George Biros |
|---|---|
| Primary category | math.NA |
| Published | 24 May 2026 |
| Last updated at source | 24 May 2026 |
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