mlsanityData to 14 Oct 2026

A Neural Operator based on Dynamic Mode Decomposition

arXiv 2507.01117 ↗First posted 1 Jul 2025cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 23 of its 40 references that are in the map. First posted on arXiv 1 Jul 2025.

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References · 23

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  3. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
  4. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  5. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
  6. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  7. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  8. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  9. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  10. 2021Factorized Fourier Neural Operatorscited by 249
  11. 2022U-NO: U-shaped Neural Operatorscited by 230
  12. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 221
11 more
  1. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214
  2. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  3. 2014Dynamic mode decomposition with controlcited by 129
  4. 2022Wavelet neural operator: a neural operator for parametric partial differential equationscited by 78
  5. 2021Seismic wave propagation and inversion with Neural Operatorscited by 51
  6. 2023Super-Resolution Neural Operatorcited by 49
  7. 2023Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networkscited by 32
  8. 2023Koopman neural operator as a mesh-free solver of non-linear partial differential equationscited by 29
  9. 2024DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domainscited by 16
  10. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  11. 2020Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamicscited by 9

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