Koopman Operator Enhanced 3D Voxcel Auto-Encoder to Predict 3D Seismic Waves Propagation

Neural surrogates for seismic simulation are typically either transformer-heavy or depend on hand-crafted physics losses. We introduce VoxelKoop, a lightweight alternative that pairs a 3-D voxel auto-encoder with a single complex Koopman matrix. The encoder compresses a $64^3$ S-wave–velocity voxel data and seismic source parameter, the Koopman operator advances the latent state linearly in Fourier space, and the decoder reconstructs the three ground-motion components. This strictly linear core yields a numerically stable, eigen-interpretable model that is an order of magnitude smaller than transformer-based neural operators. Trained on 30 k SEM3D scenarios, VoxelKoop matches or exceeds baseline accuracy on peak-velocity metrics and executes $2.1\times$ faster on one GPU, demonstrating its potential for real-time, site-specific hazard prediction.