Summary

Physics informed neural networks (PINN) are introduced in 2017 to solve classical applied mathematics problems, such as partial differential equations (PDE), using machine learning and artificial intelligence approaches. Modern methods based on PINN techniques have advantages in optimization and automatic differentiation. On the other hand, machine learning has the potential to address the following two challenges in a relatively simple and fast way: 1). Processing huge databases of numerical and observational data, and 2). Solving highly complex nonlinear systems of hyperbolic equations on warped space-time manifolds.

The main goal of this project is to use the possibility of physically informed neural networks to solve inverse problems, i.e. differential equations with unknown parameters that can be determined from observational data. At the same time, applying machine learning algorithms, known for their capabilities as universal function approximators and in symbiosis with physical laws and symmetries, are expected to be the perfect tools for solving the hyperbolic equations describing gravitational waves. The obtained results will be innovative, original and significant in the field of mathematics, informatics, machine learning and gravitational-wave astrophysics.

The project is interdisciplinary as machine learning will be combined with the fundamental laws of physics, in particular the modeling of gravitational waves. This process requires extreme precision in order not to miss events and physical effects when compared with observational data. On the other hand, wave models need to be fast to estimate, as searches and parameter estimation require tens to hundreds of millions of gravity waveform estimates, which can be achieved with machine learning of physically informed neural networks.

The final product of scientific research is a package of innovative knowledge, scientific research software and interpretation of the obtained new effects in the proposed models. The obtained results have the potential to reveal fundamental secrets of nature such as dark matter and dark energy, the existence of new fundamental fields and new exotic compact objects.