Nogueira, XesúsRamos, LucíaSeijo Conchado, SoniaCouceiro, IvánKhelladi, SofianeRamírez, Luis2026-02-132026-02-132025Nogueira, X., Ramos, L., Seijo, S., Couceiro, I., Khelladi, S., & Ramírez, L. (2025). Data-driven Riemann solvers: A neural network approach and a hybrid solver. Physics of Fluids, 37(9). https://doi.org/10.1063/5.0288995https://hdl.handle.net/2183/47422[Abstract] The accurate and efficient numerical solution of the Riemann problem is the basis of Godunov-type schemes. Approximate Riemann solvers are widely used for their efficiency, although they exhibit inaccuracies and instabilities in challenging regimes such as strong rarefactions or near-vacuum conditions. This work explores the use of deep neural networks (NNs) to address these limitations. We present two distinct data-driven frameworks: first, a NN-based solver trained to predict the exact solution of the Riemann problem, and second, a high-performance hybrid scheme. The hybrid approach uses the standard Harten–Lax–van Leer-contact (HLLC) Riemann solver as the main solver, enhanced with a computationally inexpensive, physics-based detector that identifies interfaces where the HLLC solution is likely to be inaccurate or to fail. At these interfaces, the scheme selectively uses the pretrained NN to ensure a more accurate solution. Through a series of benchmark tests, we show that the NN solver accurately reproduces the exact solution of the Riemann problem, but at a significant computational cost. In contrast, the proposed hybrid solver achieves a comparable level of accuracy to the NN solver, while it requires nearly the same computational cost as the standard HLLC solver.engArtificial neural networksNumerical algorithmsFinite volume methodsComputational fluid dynamicsFluid flowsjournal articleopen access10.1063/5.0288995