Hybrid physics-based/data-based seismic ground motion generator of a site

Accurately estimating the seismic response following an earthquake can save lives. However, limited computational resources and poorly characterized and unknown variability in geology and seismotectonic context pose significant challenges for simulations at the scale of a city or region. This thesis proposes a new approach com- bining adversarial learning methods and physics-based simulations to overcome these limitations, based on the SeismoALICE framework (F. GATTI and D. CLOUTEAU: "Towards blending Physics-Based numerical simulations and seismic databases using Generative Adversarial Network," CMAME 2020). Because of the random fluctuations in the mechanical properties of the geological medium, numerical simulations can only give results for low frequencies (LF) down to 5 or even 10 Hz. The design frequency for civil engineering structures and equipment, on the other hand, reaches 40 Hz. This thesis aims to simulate seismic signals with a higher frequency range [0 - 30 Hz] using knowledge of low-frequency signals and a database of recorded signals. To this end, we are developing an encoder and decoder adapted to seismic signals using a Conformer variant of attention techniques to capture the long-duration correlations present in accelerograms. The discriminator, which ensures that simulated signals resemble recorded signals, has been the subject of extensive development, enabling the encoder and decoder to be optimized using a min-max technique at the heart of adversarialmachine learning methods. To force signal recon- struction, we adapt Focal Frequency Loss (FFL) and Hyper-Spherical Loss (HSL), which are more efficient for this data type, to time series. We then complement the LF signals up to 30 Hz by ex- ploring different generation cases, one-to-one map- ping, and one-to-many mapping to assess the plausibility of the reconstructions in the database. Five methods were developed: Signal-to-Signal Translation, SeismoALICE with shared latent space, SeismoALICE with factorized latent space, BicycleGAN for time series, and Multi-Modal Signal Translation. Their performance was evaluated using Kristeková's Goodness-of-Fit. By manipulating the hidden variables, we proved that it is possible to divide the information into two groups of variables with Gaussian distributions, one for low frequencies and the other for high frequencies. This interpretability made it possible to manipulate the latent space and control the one-to-many mapping. The models, trained on 128,000 seismic signals from the Stanford Earthquake Database (STEAD), demonstrated their performance, with prediction qualities ranging from good to excellent. Finally, their effectiveness was demonstrated by application to the 2019 Le Teil earthquake (in the Ardèche region of Auvergne-Rhone-Alpes, France). This work paves the way for more accurate and efficient prediction of seismic signals by seamlessly integrating physics-based knowledge and machine learning.