Comparing Conventional and Physics-Constrained Neural Approaches for Euler Riemann Problems

This work compares the performance of a physics-constrained deep operator network against conventional solvers for the solution of one- and two-dimensional Euler equations. We evaluate trade-offs between solution accuracy, computational efficiency, and scalability across these approaches, with the objective of systematically benchmarking physics-constrained neural operator models against widely used approximate Riemann solvers. The neural operator model leverages the efficiency of operator learning while incorporating physics-informed constraints to enforce conservation laws and entropy conditions, thereby promoting numerical stability and generalization. The model is trained on a dataset of parameterized Euler Riemann problems, with conservation residuals and entropy inequalities embedded in the loss function. Evaluations on canonical 1D shock-tube benchmarks assess the model's ability to capture key flow features (shocks, contacts, and rarefactions), resolve complex interactions, and avoid non-physical solutions, providing a consistent basis for comparison with classical methods.