A Unified Benchmark Study of Shock-Like Problems in Two-Dimensional Steady Electrohydrodynamic Flow Based on LSTM-PINN
Accurately resolving steady electrohydrodynamic (EHD) flows presents a formidable computational challenge due to the strong nonlinear coupling between charged-particle density, velocity fields, and electric potential. These interactions frequently induce sharp transition layers, crossing fronts, and multiscale spatial structures, which notoriously degrade the predictive accuracy of standard mesh-free solvers like Physics-Informed Neural Networks (PINNs). To systematically address this bottleneck, we formulate a unified four-variable operator framework and develop a comprehensive benchmark suite for two-dimensional steady EHD shock-like problems. The benchmark comprises eight rigorously designed cases featuring diverse front geometries, such as oblique, curved, and intersecting layers, alongside complex multiscale patterns. Under strictly identical configurations, including governing equations, source terms, sampling strategies, and loss formulations, we evaluate a Standard MLP-based PINN, a Residual Attention PINN (ResAtt-PINN), and an LSTM-PINN that leverages pseudo-sequential spatial encoding. Extensive numerical experiments demonstrate that the LSTM-PINN consistently achieves the highest predictive accuracy across all eight cases. It successfully reconstructs sharp gradients and intricate multiscale structures where other architectures fail or over-smooth. Furthermore, the LSTM backbone efficiently captures long-range spatial correlations while maintaining an exceptionally low computational overhead and GPU memory footprint. These findings not only establish the LSTM-PINN as a robust and efficient solver for strongly coupled PDEs with shock-like features, but also provide the computational physics community with a standardized, reproducible benchmark for future algorithmic evaluations.