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

2026-05-14

AI Summary

This study addresses the unclear convergence mechanisms and slow convergence of neural reparameterized full-waveform inversion (NeurFWI) at high resolutions. For the first time, it establishes a theoretical framework based on Neural Sensitivity Kernels (NSK) and Wavelet Tangent Kernels (WTK), integrated with Neural Tangent Kernel (NTK) theory, to elucidate NeurFWI’s convergence behavior from both model and data perspectives. The analysis reveals how neural representations adaptively modulate the original kernel functions via NTK, thereby controlling spectral filtering, gradient wavenumber content, and frequency bias. Leveraging these insights, the authors design an enhanced NeurFWI method with tailored feature structures that significantly improves inversion accuracy and computational efficiency. Notably, this work also marks the first successful extension of NeurFWI into medical imaging applications.

Abstract

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.

Problem

• Neural Reparameterized FWI
• convergence behavior
• theoretical mechanism
• neural sensitivity kernel
• wave tangent kernel

Innovation

• Neural Sensitivity Kernel
• Wave Tangent Kernel
• Neural Reparameterized FWI
• Neural Tangent Kernel
• Full-Waveform Inversion