Reducing the impact of earthquakes requires reliable estimates of ground shaking for engineering design and seismic risk mitigation. Probabilistic seismic hazard analysis (PSHA) has traditionally relied on empirical ground-motion models (GMMs), calibrated using recordings from past earthquakes, to provide efficient site-specific ground shaking estimates. However, major advances in computational resources, the rapid expansion of earthquake data collection, and improved representations of subsurface structure have made physics based ground-motion simulations a more realistic and a practical alternative. This dissertation aims to improve both simulation based and traditional GMM based hazard approaches by using machine learning to develop more realistic earthquake source descrip-tions, strengthen the treatment of uncertainty, and better represent the spatial complexity of ground motions.To enable scalable simulation-based hazard calculations, it is essential to generate large ensembles of earthquake rupture scenarios that are physically realistic while capturing the key source complexity. To achieve this, I develop a machine-learning based pseudo dynamic rupture generator calibrated against full dynamic rupture simulations that produces heterogeneous slip, rupture velocity, and rise time in a spatio-temporal consistency, allowing efficient sampling of realistic rupture scenarios. Applications to hypothetical scenarios and a well recorded earthquake demonstrate that the proposed approach reproduces accurate ground-motion estimates. To propagate the variability of rupture models produced by the rupture generator into hazard in a transparent and systematic way, it is also necessary to separate differences due to modeling choices from random rupture-to-rupture fluctuations. To address this, I identify dominant source parameters controlling variability and develop a logic-tree based workflow that treats variability in alternative rupture parameterizations. The framework is tested through simulation-based hazard calculations, showing stable exceedance curves while reducing computational cost, thereby providing a practical pathway for incorporating rupture variability into probabilistic ground-motion predictions. Physics-based ground-motion simulations are currently limited to low frequencies due to high computational cost and the lack of sufficiently detailed Earth structure models, while engineering applications require high frequency ground motions predictions. To overcome this, I develop a hybrid simulation and machine-learning framework that augments low-frequency synthetic seismograms with data-driven high-frequency content to generate broadband ground-motion time histories. The approach is trained and validated using dense strong-motion datasets from Japan, demonstrating that it can recover high-frequency spectral behavior while preserving the physically consistent low-frequency components. In many regions, limited computational resources and the lack of dense observations to validate simulations still require the use of GMMs for hazard assessment. However, because GMMs are formulated for single sites, regional hazard and risk calculations must rely on additional assumptions to represent the spatial dependence of shaking across a portfolio. To improve these representations, I quantify the spatial correlation structure of different ground-motion residuals using a large strong-motion dataset from Japan, and develop a graph-based generative machine-learning framework that produces spatially correlated residual fields conditioned on event and site attributes, providing a scalable way to simulate realistic shaking fields for joint exceedance applications.

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