State-of-the-art implementations of PINNs for the lid-driven cavity problem – a critical review with future perspectives

Journal article, 2026

The lid-driven cavity (LDC) problem is a canonical benchmark for incompressible flow. Owing to the corner boundary discontinuities, multiscale vortical structures, possible multiplicity of steady solutions, and the change of flow properties at different Reynolds numbers, LDC provides a stringent test for numerical methods. This review surveys the application of physics-informed neural networks (PINNs) to LDC. The literature is organized around four main classes of design choices, namely LDC formulation for PINNs, PINNs architecture, optimization and training strategy, and loss function, evaluation, and some selected results. Within each class, the review examines the literature, then presents insights drawn from the reviewed studies and introduces the open questions and suggestions for future research associated with each design aspect. The review indicates that transfer learning, domain decomposition, special training strategies, discretization-based residual evaluation, and optimization modifications can be interpreted as a spectrum of approaches that differ in implementation difficulty and resource requirements when improving PINNs performance on LDC. Furthermore, the review shows that comparisons across studies remain difficult because architectures, boundary treatments, and evaluation metrics vary widely, while ablation studies are often lacking.