# Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography

arXiv: https://arxiv.org/abs/2605.09960 · HTML: https://mlsanity.com/paper/2605.09960/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 8 of 8)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [Machine learning in acoustics: theory and applications](https://mlsanity.com/paper/1905.04418/) (2019)
- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [Total-variation regularization strategies in full-waveform inversion](https://mlsanity.com/paper/1608.06159/) (2016)

## Abstract (arXiv)

Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a Fourier-feature neural network, replacing the grid-based slowness vector with a continuous, infinitely differentiable function. Prior neural-field tomography has staircased smooth fields under total-variation (TV) priors or oscillated near interfaces under L2 Laplacian smoothing. We adopt second-order total generalized variation (TGV2) and parametrize its auxiliary vector field as a second neural network jointly optimized with the velocity field, eliminating the inner Chambolle-Pock primal-dual loop that classically dominates TGV computation. On three synthetic benchmarks (Gaussian, horizontally layered, curved-fault inspired by OpenFWI) using cross-well acquisition, 5% travel-time noise, and five seeds, MIMIR-TGV2 ties a classical FMM-LSMR baseline with auto-tuned hyperparameters on the Gaussian (p=0.134, paired t-test) and significantly outperforms it on layered (p<0.0001, 44% RMSE reduction) and curved-fault (p=0.0002, 33% reduction). Replacing TGV2 with TV degrades performance on Gaussian (p=0.004) and layered (p=0.003); curriculum-annealed TV improves Gaussian RMSE by only 5.4%, confirming that TV's staircase bias is intrinsic to the regularizer rather than a scheduling artifact. The results empirically validate the Bredies-Kunisch-Pock prediction that piecewise-affine priors are better suited to subsurface velocity recovery than piecewise-constant TV priors. We argue that the central design choice in physics-informed neural-field inversion is not the network architecture but the regularizer. The full pipeline reproduces in under one hour on consumer hardware.