mlsanityData to 14 Oct 2026

Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets

arXiv 2306.15891 ↗First posted 28 Jun 2023cs.LGcited by 3

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Abstract (arXiv)

In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transport problem. We observe that the vanilla physics-informed DeepONets with modified MLP may exhibit instability in maintaining the desired limiting macroscopic behavior. Therefore, this necessitates the utilization of an asymptotic-preserving loss function. Drawing inspiration from the heat kernel in the diffusion equation, we propose a new architecture called Convolutional Deep Operator Networks, which employ multiple local convolution operations instead of a global heat kernel, along with pooling and activation operations in each filter layer. Our APCON methods possess a parameter count that is independent of the grid size and are capable of capturing the diffusive behavior of the linear transport problem. Finally, we validate the effectiveness of our methods through several numerical examples.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 20 of its 41 references that are in the map. First posted on arXiv 28 Jun 2023.

Builds on

20 of 41 references.

References · 20

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8 more
  1. 2022Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equationscited by 28
  2. 2021MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEscited by 24
  3. 2021Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equationcited by 16
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  5. 2022MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problemscited by 13
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  8. 2022A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equationscited by 2

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Cited by year

Citing papers per year: 2024: 2; 2025: 1.

3 papers.

  1. 2024An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learningcited by 6
  2. 2025Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systemscited by 1
  3. 2024Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equationscited by 0