# Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel

arXiv: https://arxiv.org/abs/2605.14370 · HTML: https://mlsanity.com/paper/2605.14370/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 75 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 25 of 25)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)
- [The Recurrent Neural Tangent Kernel](https://mlsanity.com/paper/2006.10246/) (2020)
- [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs](https://mlsanity.com/paper/1811.07875/) (2018)
- [A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics](https://mlsanity.com/paper/1904.04326/) (2019)
- [The Shaped Transformer: Attention Models in the Infinite Depth-and-Width Limit](https://mlsanity.com/paper/2306.17759/) (2023)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [A prior regularized full waveform inversion using generative diffusion models](https://mlsanity.com/paper/2306.12776/) (2023)
- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [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)
- [On the exact computation of linear frequency principle dynamics and its generalization](https://mlsanity.com/paper/2010.08153/) (2020)
- [Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping](https://mlsanity.com/paper/2002.00031/) (2020)
- [Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?](https://mlsanity.com/paper/2412.06158/) (2024)
- [Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows](https://mlsanity.com/paper/2412.00486/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Full waveform inversion guided by travel time tomography](https://mlsanity.com/paper/1607.00968/) (2016)
- [Compound Regularization of Full-waveform Inversion for Imaging Piecewise Media](https://mlsanity.com/paper/1903.04405/) (2019)
- [How Learnable Grids Recover Fine Detail in Low Dimensions: A Neural Tangent Kernel Analysis of Multigrid Parametric Encodings](https://mlsanity.com/paper/2504.13412/) (2025)
- [Initial Model Incorporation for Deep Learning FWI: Pretraining or Denormalization?](https://mlsanity.com/paper/2506.05484/) (2025)
- [Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Framework](https://mlsanity.com/paper/2603.22362/) (2026)

## Abstract (arXiv)

Full-waveform inversion (FWI) estimates unknown parameters in the wave equation from limited boundary measurements. Recent advances in neural reparameterized FWI (NeurFWI) demonstrate that representing the parameters using a neural network can reduce the reliance on the high-quality initial model and wavefield data, at the cost of slow high-resolution convergence. However, its underlying theoretical mechanism remains unclear. In this study, we establish the neural sensitivity kernel (NSK) and the wave tangent kernel (WTK) to analyze their convergence behavior from both model and data domains. These theoretical frameworks show that the neural tangent kernel (NTK) induced by neural representation adaptively modulates the original sensitivity and wave tangent kernels. This modulation leads to several key outcomes, i.e., the spectral filtering effect, the gradient wavenumber modulation, and the wave frequency bias, connecting the convergence behavior of NeurFWI with the eigen-structures of NSK and WTK. Building on these insights, we propose several enhanced NeurFWI methods with tailored eigen-structures in NSK and WTK to improve inversion performances and efficiency. We numerically validate these theoretical claims and the proposed methods in seismic exploration, and firstly extend their application to medical imaging.