Physics-informed neural networks for multi-material high-accuracy Riemann solver in Eulerian framework

The resolution of interfacial dynamics in multi-material flows critically relies on Riemann solvers, while recent advances in physics-informed neural networks (PINNs) offer transformative potential for solving multi-material Riemann problems. This paper presents a novel PINNs-based multi-material high-accuracy Riemann solver (PINN-MHRS) designed to solve multi-material Riemann problems involving complex equations of state (EOS) without requiring labeled data. PINN-MHRS determines wave system structures through entropy condition analysis and constructs physics-constrained loss functions. A hard constraints strategy enforces continuity conditions, wave speed ordering, and positivity of pressure/density, significantly simplifying optimization and accelerating convergence. The PINN-MHRS is integrated with the modified ghost fluid method via a Fortran-Python hybrid framework, enabling numerical simulations of multi-material interactions. Time advancement is achieved through a cyclic training-prediction alternating strategy that dynamically adapts to evolving interface conditions. Comprehensive validation demonstrates PINN-MHRS's exceptional performance. For one-dimensional shock tube cases with ideal gas EOS, it achieves errors at least five orders of magnitude lower than Harten–Lax–van Leer Contact (HLLC). When handling the complex Jones-Wilkins-Lee (JWL) EOS for explosives, PINN-MHRS exhibits three orders of magnitude higher accuracy (error: 2.90×10−1) compared to HLLC (error: 2.70×102). In two-dimensional air–helium shock–bubble interaction simulations, PINN-MHRS maintains low-error predictions while accurately solving interface evolution details. PINN-MHRS establishes a new paradigm for high-accuracy, stable Riemann solvers in complex multi-material flow simulations. The Fortran-Python hybrid framework successfully bridges machine learning and traditional computational fluid dynamics (CFD). Its ability to handle complex EOS without labeled data and to maintain physical consistency suggests broad applicability to other interfacial dynamics problems.