Core-collapse supernovae (CCSNe) host a large variety of thermodynamic conditions, from cold low-density regions in the external layers of the collapsing star to the hot and very dense nascent proto-neutron star (PNS). Nuclear physics is a key ingredient to determine the evolution of CCSNe. At high densities, the strong interaction governs the equation of state (EOS), which has large impact on the dynamics. Nevertheless, the EOS of dense matter is not fully understood. Numerical simulations are crucial to understand, and explore, the mechanisms involved in the explosion. We use CCSNe simulations as laboratories to study the impact of several nuclear matter properties on the dynamics of the PNS and the explosion. At low densities, nuclear reactions describe the nucleosynthesis that takes place in the events, which play an essential role in the chemical evolution of the universe. We investigate the impact of the composition and the energy released by nuclear reactions on the dynamics of the explosion and the nucleosynthesis.

Classical simulations of quantum many-body systems are essential for both studying and understanding quantum technologies. In recent years, with the improvement and the development of several methods such as tensor networks and neural quantum states, classical simulations can reach outstanding results in both efficiency and accuracy. In this framework, we present a novel approach based on deep learning density functionals for quantum many-body systems. density functional theory can bypass the wavefunction approach for solving the many-body problem increasing the speed up and with good accuracies. By using deep learning, density functional can be easily provided without approximations and with adaptive functional forms. Here, we present the idea based on the deep learning density functional theory applied to continuous systems, with its limits and novel strategies to overcome them. We also show how the theory and the deep learning method can be extended to spin systems. Finally, we show how it is possible to extend the density functional for time dependent spin models and the application of DL-density functionals into that framework.

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