# Solving Traveltime Tomography with Deep Learning

arXiv: https://arxiv.org/abs/1911.11636 · HTML: https://mlsanity.com/paper/1911.11636/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

## Built on by (most cited first, 7 of 7)

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- [Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime](https://mlsanity.com/paper/2106.01143/) (2021)
- [Disentangled Representation Learning for Parametric Partial Differential Equations](https://mlsanity.com/paper/2410.02136/) (2024)
- [Solving the inverse problem of microscopy deconvolution with a residual Beylkin-Coifman-Rokhlin neural network](https://mlsanity.com/paper/2407.03239/) (2024)
- [Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery](https://mlsanity.com/paper/2505.23106/) (2025)

## Abstract (arXiv)

This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the medium. This inverse map is high-dimensional and nonlinear. For the circular tomography geometry, a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction. Motivated by this and filtered back-projection, we propose an effective neural network architecture for the inverse map using the recently proposed BCR-Net, with weights learned from training datasets. Numerical results demonstrate the efficiency of the proposed neural networks.