mlsanityData to 7 Oct 2026

Advection Augmented Convolutional Neural Networks

arXiv 2406.19253 ↗First posted 27 Jun 2024cs.LGcited by 5

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Abstract (arXiv)

Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation and video prediction. Modern techniques for the solution of these problems typically combine Convolution Neural Networks (CNN) architecture with a time prediction mechanism. However, oftentimes, such approaches underperform in the long-range propagation of information and lack explainability. In this work, we introduce a physically inspired architecture for the solution of such problems. Namely, we propose to augment CNNs with advection by designing a novel semi-Lagrangian push operator. We show that the proposed operator allows for the non-local transformation of information compared with standard convolutional kernels. We then complement it with Reaction and Diffusion neural components to form a network that mimics the Reaction-Advection-Diffusion equation, in high dimensions. We demonstrate the effectiveness of our network on a number of spatio-temporal datasets that show their merit.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 46 of its 69 references that are in the map. First posted on arXiv 27 Jun 2024.

Builds on

46 of 69 references.

References · 46

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34 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 2.

5 papers.

  1. 2026Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecastingcited by 2
  2. 2025Probabilistic Forecasting for Dynamical Systems with Missing or Imperfect Datacited by 1
  3. 2026Flowers: A Warp Drive for Neural PDE Solverscited by 1
  4. 2024iiANET: Inception Inspired Attention Hybrid Network for efficient Long-Range Dependencycited by 0
  5. 2025Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbationcited by 0