arXiv:2605.24876v1 Announce Type: cross Abstract: 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 problem
The continuous advancements in AI and specifically neural operators are leading to more sophisticated methods for solving complex scientific and engineering problems.
This development allows for faster and more accurate simulations of physical phenomena, critical for applications in various scientific and industrial fields.
The ability to approximate solutions for challenging PDEs with random and highly varying coefficients could significantly reduce computational time and resources for complex modeling.
- · AI researchers
- · Engineering simulation software providers
- · Materials science
- · Climate modeling
- · Traditional numerical solvers
- · High-performance computing centers reliant on older simulation methods
More efficient and accurate scientific simulations become widely accessible.
Accelerated discovery of new materials or optimization of complex physical systems due to improved modeling.
The development of 'digital twin' technologies becomes more robust and widespread across industries.
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Read at arXiv cs.LG