Physics-based super-resolved simulation of 3D elastic wave propagation adopting scalable Diffusion Transformer

Abstract: In this study, we develop a Diffusion Transformer (referred as to DiT1D) for synthesizing realistic earthquake time histories. The DiT1D generates realistic broadband accelerograms (0-30 Hz resolution), constrained at low frequency by 3-dimensional (3D) elastodynamics numerical simulations, ensuring the fulfillment of the minimum observable physics. The DiT1D architecture, successfully adopted in super-resolution image generation, is trained on recorded single-station 3-components (3C) accelerograms. Thanks to Multi-Head Cross-Attention (MHCA) layers, we guide the DiT1D inference by enforcing the low-frequency part of the accelerogram spectrum into it. The DiT1D learns the low-to-high frequency map from the recorded accelerograms, duly normalized, and successfully transfer it to synthetic time histories. The latter are low-frequency by nature, because of the lack of knowledge on the underground structure of the Earth, demanded to fully calibrate the numerical model. We developed a CNN-LSTM lightweight network in conjunction with the DiT1D, so to predict the peak amplitude of the broadband signal from its low-pass-filtered counterpart, and rescale the normalized accelerograms rendered by the DiT1D. Despite the DiT1D being agnostic to any earthquake event peculiarities (magnitude, site conditions, etc.), it showcases remarkable zero-shot prediction realism when applied to the output of validated earthquake simulations. The generated time histories are viable input accelerograms for earthquake-resistant structural design and the pre-trained DiT1D holds a huge potential to integrate full-scale fault-to-structure digital twins of earthquake-prone regions.