Speaker
Description
Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving differential equations by incorporating physical constraints directly into the loss function. In this talk, I explore the potential of PINNs in theoretical physics, ranging from non-linear PDEs to lattice field theory. The main focus of this talk is the application of machine learning to lattice fermions. I present a novel approach where neural networks autonomously construct chiral fermions on the lattice. We show that by imposing physical requirements such as the Ginsparg-Wilson (GW) relation and locality, the network successfully learns the spectral operator of Overlap fermions. We verify the topological properties of the learned operator through the Atiyah-Singer index theorem and spectral flow in $U(1)$ gauge fields. Furthermore, I discuss a remarkable result where the NN "rediscovers" the exact GW relation and its generalized variants from physical constraints, suggesting a new data-driven approach to exploring symmetries in quantum field theory.