Physics-Informed Token Transformer for Nonlinear Balance Laws: Schwarzschild-Burgers Fluid Flows

This paper introduces a Physics-Informed Token Transformer (PITT) methodology for solving nonlinear hyperbolic balance laws in one spatial dimension. The approach combines symbolic equation tokenization, a Fourier neural operator encoder, and an explicit Rankine-Hugoniot law for shock motion with a learned correction term. The method is demonstrated on the relativistic Schwarzschild-Burgers equation as a scalar model for fluid flows with discontinuities.