提出SPAMoE框架，解决地震反演中多尺度地质结构的频率混叠问题。
SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
- 设计频谱保持编码器与频带路由机制，动态分配不同频率给专家网络
- 在10个OpenFWI子数据集上平均MAE降低44.4%优于基线
- 适合需要高精度速度模型重建的地震成像研究者
全波形反演（FWI）对构建高分辨率地下速度模型至关重要，但计算成本高且病态。尽管深度学习方法提升效率，现有卷积神经网络（CNN）和单范式神经算子（NO）仍面临多尺度地质特征的频率混叠难题。为此，我们提出频谱感知混合专家框架SPAMoE，引入频谱保持的DINO编码器，强制编码表示中高频与低频能量比不低于下界，缓解高频衰减并稳定频域建模。同时设计频谱分解与路由机制，动态将不同频段分配给包含FNO、MNO和LNO的专家集成。在10个OpenFWI子数据集上的实验表明，SPAMoE相较最佳官方报告基线平均MAE降低44.4%，确立了基于学习的全波形反演新架构。代码与数据见https://github.com/zhenyuwang12366/SPAMoE。
原文摘要 · Abstract (English)
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 44.4% relative to the best officially reported OpenFWI baseline, thereby establishing a new architectural framework for learning-based full-waveform inversion. Our code and data are available at https://github.com/zhenyuwang12366/SPAMoE
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