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This research paper introduces a neural operator leveraging Dynamic Mode Decomposition (DMD) to efficiently model spatiotemporal processes and solve partial differential equations with reduced computational costs. By combining DMD with deep learning, the method extracts key system dynamics to achieve high reconstruction accuracy on standard physics benchmarks like the heat and Burgers equations, offering a lightweight alternative to traditional numerical methods and existing neural operators like DeepONet.
A Neural Operator based on Dynamic Mode Decomposition
arXiv:2507.01117v2 Announce Type: replace Abstract: 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.
Abstract: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.
30 pages, 10 figures. Manuscript unchanged; added a link to the full text on ResearchGate: this https URL
Machine Learning (cs.LG)
arXiv:2507.01117 [cs.LG]
(or arXiv:2507.01117v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2507.01117 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1007/s11227-026-08918-3 Focus to learn more DOI(s) linking to related resources
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