ESSPINNs: Entropy-Stable Finite-Volume Solvers Embedded in Physics-Informed Neural Networks
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We present a hybrid finite-volume and physics-informed neural network framework for learning solutions of nonlinear systems of conservation laws. The method, termed ESSPINNs (Entropy- Stable Scheme PINNs), embeds high-resolution entropy-conservative fluxes together with entropy- stable numerical dissipation directly into the PINN training loop. The use of entropy-stable operators is motivated by the fact that nonlinear hyperbolic systems admit multiple weak solutions, and the physically relevant one is selected by an entropy condition.
