Coupling Fourier Neural Operators with Diffusion Models for Broadband Elastodynamic Wavefields

  • Perrone, Niccolò (Politecnico di Milano)
  • Lehmann, Fanny (ETH AI Center)
  • Fresca, Stefania (University of Washington)
  • Gatti, Filippo (Université Paris-Saclay CentraleSupélec)

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High-fidelity simulation of elastodynamic wave propagation in heterogeneous media is a cornerstone of many applications in computational mechanics, yet remains computationally prohibitive when broadband accuracy and large-scale domains are required. Recent progress in neural-operator learning has enabled efficient surrogate modeling of such systems, providing fast and physically informed approximations of wavefields from material and source parameters. In this work, we present a hybrid operator–generative framework that combines a Multiple-Input Fourier Neural Operator (MIFNO) with a conditional diffusion-based generative model to achieve broadband reconstruction of three-dimensional elastodynamic velocity fields. Building on preliminary site-wise generative refinements introduced in , we extend the approach to the full spatio-temporal domain, enabling spatially coherent and physically consistent wavefield generation. The neural operator provides a low-frequency, geometry-accurate prior consistent with the governing elastodynamic behavior, while the generative model stochastically reconstructs unresolved fine-scale and high-frequency content. The methodology is evaluated on large-scale 3D simulations from the HEMEWS-3D dataset , which comprises spectral-element solutions of seismic wave propagation in heterogeneous geological settings. Quantitative assessments based on spatial and spectral error metrics demonstrate that the proposed coupling significantly improves broadband fidelity compared to operator-based predictions alone, while preserving correct wave arrival times and global field structure. By integrating deterministic operator learning with probabilistic generative modeling, this work contributes a scalable and flexible paradigm for physics-aware, data-driven simulation in computational wave mechanics, with potential impact on uncertainty-aware analysis and large-scale virtual testing.