UC Berkeley

The large-scale structures (LSS) of the Universe contain significant information about the cosmos, providing insights into its composition and the underlying physical laws. Current and upcoming cosmological surveys aim to measure the LSS and the evolution of the universe with multiple probes, allowing us to constrain cosmological parameters to high precision and search for deviations from the standard cosmological model. To realize the full potential of these datasets, it is crucial to develop robust analysis methods capable of extracting the maximum amount of information.

Simulation-based inference (SBI) leverages high-fidelity cosmological simulations for inference and holds promise for extracting rich non-Gaussian information from these data. However, its application is limited by several challenges. This dissertation focuses on addressing these challenges to facilitate the deployment of SBI approaches in upcoming survey analyses.

On the simulation side, running a large number of high-resolution, large-volume cosmological simulations for training the SBI model is computationally challenging. We develop effective machine learning models to improve the modeling of non-linear gravity and baryonic physics in low-resolution fast simulations. By combining these models with fast N-body simulations, we can predict various baryonic observables and accurate weak lensing signals at a low computational cost.

On the inference side, we integrate physical constraints (symmetries) and domain knowledge (the hierarchical structure of the data) into the SBI models, and apply them to learn the field-level data likelihood function for optimal cosmological analysis. Inaccurate modeling of physical processes and systematic effects could bias the SBI constraints. To address this, we use field-level data likelihood and multiscale analysis for anomaly detection of model misspecification, enabling robust SBI analysis. Additionally, we perform a large-scale comparative study to identify the best hyperparameter and loss function choices for optimal SBI performance.

These developments mark a substantial step toward the full deployment of SBI approaches into cosmological survey analysis pipelines, offering the promise of a deeper understanding of our Universe and the potential discovery of new physics beyond the current model.