STATISTICAL MACHINE LEARNING AND PHYSICS INFORMED NEURAL NETWORKS IN ASTRONOMICAL SIMULATIONS

The emergence of machine learning has revolutionized many fields of science and engineering, and in the last decade, it has become increasingly popular due to the availability of large datasets and powerful computational resources. One recent development in the field is the application of physics-informed neural networks (PINNs), which have shown significant potential in solving complex systems, partial differential equations, and hydrodynamic simulations in cosmology. Firstly, we implemented kernel density estimation, a traditional machine learning method, to provide a novel constraint on the high-temperature nuclear equation of state (EOS) and determine which EOS candidates are favorable based on an information-theoretic metric. This approach provided a valuable tool for testing and refining nuclear models and predicting the properties of dense matter. Next, we have explored the applications of PINNs in various contexts. We investigated the bias and variance trade-off of PINNs for solving Burgers' equation under noisy data. We discovered that the variance of the predictions increases monotonically with the noise level, highlighting the need for careful consideration of the noise level in PINN applications. Finally, we developed a new PINN model embedding physics knowledge to predict baryonic properties from dark matter halos. We introduced a new loss function that includes a mean squared error, Kullback-Leibler divergence (KLD), and a stellar-to-halo mass relation to recovering the scatter properties of baryonic matter, which has been an unsolved problem in other machine learning approaches to hydrodynamic simulations.