Abstract: Machine learning and statistical learning is not new in Cosmology and Astronomy. However recently the merge of physics and machine learning has open new avenues for better scientific discoveries. These methods fall under the term Physics Informed Neural Networks or PINNs. In this talk I will review some of the fundamentals and present the advantages and disadvantages.  Then I will go into show two applications in Cosmology that are only possible using PINNS.

The first application involves holography. Using a novel PINN-based approach, we have developed a data-driven algorithm informed by Einstein’s equations to solve complex inverse problems, addressing phase transitions and crossovers.

The second application introduces an enhanced neural network bundle method, significantly reducing computational times for cosmological analysis. We applied this improvement to the Hu-Sawicki and Starobinsky f(R) models, performing statistical analyses on type Ia supernovae data and cosmic chronometers. This new method also offers a refined treatment of the absolute magnitude of supernovae, yielding different distortion parameter estimates compared to previous literature.