SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion

2026-04-08

AI Summary

Full-waveform inversion (FWI) suffers from high computational cost, ill-posedness, and challenges in handling frequency aliasing and high-frequency collapse across multiscale geological structures. To address these issues, this work proposes SPAMoE, a spectrum-aware hybrid neural operator framework that innovatively integrates a spectrum-preserving DINO encoder, a spectral decomposition-based dynamic routing mechanism, and a mixture of Fourier, Moment, and Legendre Neural Operators (FNO/MNO/LNO) within a Mixture-of-Experts architecture. This spectrum-adaptive design enables more accurate and robust modeling of multiscale subsurface features. Evaluated on ten OpenFWI benchmark subsets, SPAMoE achieves an average mean absolute error (MAE) reduction of 54.1% compared to the best-performing baseline, demonstrating significantly improved inversion accuracy and multiscale representation capability.

Abstract

Full-waveform inversion (FWI) is pivotal for reconstructing high-resolution subsurface velocity models but remains computationally intensive and ill-posed. While deep learning approaches promise efficiency, existing Convolutional Neural Networks (CNNs) and single-paradigm Neural Operators (NOs) struggle with one fundamental issue: frequency entanglement of multi-scale geological features. To address this challenge, we propose Spectral-Preserving Adaptive MoE (SPAMoE), a novel spectrum-aware framework for solving inverse problems with complex multi-scale structures. Our approach introduces a Spectral-Preserving DINO Encoder that enforces a lower bound on the high-to-low frequency energy ratio of the encoded representation, mitigating high-frequency collapse and stabilizing subsequent frequency-domain modeling. Furthermore, we design a novel Spectral Decomposition and Routing mechanism that dynamically assigns frequency bands to a Mixture-of-Experts (MoE) ensemble comprising FNO, MNO, and LNO. On the ten OpenFWI sub-datasets, experiments show that SPAMoE reduces the average MAE by 54.1% relative to the best officially reported OpenFWI baseline, thereby establishing a new architectural framework for learning-based full-waveform inversion.

Problem

• Full-waveform inversion
• Frequency entanglement
• Multi-scale geological features
• Neural Operators
• Spectrum-aware

Innovation

• Spectrum-Aware
• Mixture-of-Experts
• Neural Operators
• Full-Waveform Inversion
• Frequency Decomposition