mlsanityData to 14 Oct 2026

Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions

arXiv 2504.10932 ↗First posted 15 Apr 2025cs.LG cs.NA math.NAcited by 3

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Abstract (arXiv)

In this paper, a multi-scale DeepOnet (Mscale-DeepOnet) is proposed to reduce the spectral bias of the DeepOnet in learning high-frequency mapping between highly oscillatory functions, with an application to the nonlinear mapping between the coefficient of the Helmholtz equation and its solution. The Mscale-DeepOnet introduces the multiscale neural network in the branch and trunk networks of the original DeepOnet, the resulting Mscale-DeepOnet is shown to be able to capture various high-frequency components of the mapping itself and its image. Numerical results demonstrate the substantial improvement of the Mscale-DeepOnet for the problem of wave scattering in the high-frequency regime over the normal DeepOnet with a similar number of network parameters.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 5 of its 14 references that are in the map. First posted on arXiv 15 Apr 2025.

Builds on

5 of 14 references.

References · 5

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2018On the Spectral Bias of Neural Networkscited by 1,341
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  4. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
  5. 2020Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domainscited by 79

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Diagnosing Failure Modes of Neural Operators Across Diverse PDE Familiescited by 6
  2. 2026The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositionscited by 0
  3. 2026Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactorcited by 0