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.
News
Conferences
Tenth International Conference
New Trends in the Applications of Differential Equations in Sciences (NTADES 2023)
17-20 July 2023, St. Constantine and Helena, Varna (Bulgaria)
Seminars
Seminar on Applications of Differential Applications in Sciences