PODNO: Proper Orthogonal Decomposition Neural Operators
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Abstract (arXiv)
In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Building on the structure of Fourier Neural Operators (FNO), PODNO replaces the Fourier transform with (inverse) orthonormal transforms derived from the Proper Orthogonal Decomposition (POD) method to construct the integral kernel. Due to the optimality of POD basis, the PODNO has potential to outperform FNO in both accuracy and computational efficiency for high-frequency problems. From analysis point of view, we established the universality of a generalization of PODNO, termed as Generalized Spectral Operator (GSO). In addition, we evaluate PODNO's performance numerically on dispersive equations such as the Nonlinear Schrodinger (NLS) equation and the Kadomtsev-Petviashvili (KP) equation.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 12 of its 53 references that are in the map. First posted on arXiv 25 Apr 2025.
Builds on
12 of 53 references.
References · 12
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
- 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
- 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
- 2020Model Reduction and Neural Networks for Parametric PDEscited by 257
- 2020The Random Feature Model for Input-Output Maps between Banach Spacescited by 90
- 2023Nonlocality and Nonlinearity Implies Universality in Operator Learningcited by 43
- 2023A DeepONet multi-fidelity approach for residual learning in reduced order modelingcited by 14
- 2021DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle methodcited by 9
- 2022A variational neural network approach for glacier modelling with nonlinear rheologycited by 2
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Citing papers per year: 2026: 2.
2 papers.