arXiv:2507.01117 · v2
A Neural Operator based on Dynamic Mode Decomposition
摘要
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction. The study presents a neural operator based on the dynamic mode decomposition algorithm (DMD), mapping functional spaces, which combines DMD and deep learning (DL) for spatiotemporal processes efficient modeling. Solving PDEs for various initial and boundary conditions requires significant computational resources. The method suggested automatically extracts key modes and system dynamics using them to construct predictions, reducing computational costs compared to traditional numerical methods. The approach has demonstrated its efficiency through comparative analysis of performance with closest analogues DeepONet and FNO in the heat equation, Laplaces equation, and Burgers equation solutions approximation, where it achieves high reconstruction accuracy.
作者备注：30 pages, 10 figures. Manuscript unchanged; added a link to the full text on ResearchGate: https://www.researchgate.net/publication/416771541_A_neural_operator_based_on_dynamic_mode_decomposition
期刊信息：The Journal of Supercomputing 82, 811 (2026)