Reversible Deep Operator Network for Grid‐Independent, Multi‐Scale Magnetotelluric Inversion and Uncertainty Quantification

Magnetotellurics (MT) is a powerful geophysical technique that leverages natural electromagnetic fields to characterize subsurface electrical conductivity structures. In recent years, deep neural network have shown great potential for MT data inversion. However, existing methods face inherent challenges with sparsely and irregularly sampled data sets: any variation in station layout, frequency range, or survey area extent necessitates full retraining of the network, which severely restricts their applicability to real‐world sparse and multi‐scale data sets. Here, we present a novel deep learning framework—the Reversible Deep Operator Network (RDON)—for the efficient inversion of arbitrarily sparse MT data. RDON integrates a RealNVP‐based invertible neural network into the DeepONet architecture, establishing a bijective mapping between subsurface resistivity distributions and MT responses. This mapping enables grid‐independent forward and inverse modeling within a single network. Without retraining, the architecture flexibly processes arbitrarily sparse MT data and exhibits robust generalization to unseen station distributions, frequency ranges, and model types encountered during the training phase. For scale generalization, we derive an MT‐specific scale‐invariance theorem that not only provides theoretical justification for cross‐scale generalization but also enables rigorous quantification of associated generalization errors. This allows the trained network to perform zero‐shot inference across distinct survey scales, and we further mitigate scale‐related errors via transfer learning with lightweight fine‐tuning. In addition, RDON incorporates a bootstrap resampling‐based uncertainty quantification scheme, which achieves substantial computational efficiency gains over conventional approaches. Field data application from the West Junggar region validates the reliability and practical utility of RDON under complex geological conditions.