Turbulence prediction is essential in engineering disciplines such as aerospace and energy, where precise modelling of anisotropic boundary layers and multiscale vortex structures improves design efficiency and safety. Conventional neural networks typically employ data-driven methods, which lack physical interpretability and perform poorly in complex flows. This paper presents Anisotropic and Multiscale Cross-Attention Physics-Inspired Neural Networks(AMSPINN), a novel architecture that incorporates turbulence physics as prior knowledge to enhance accuracy and scalability. The architecture integrates domain-specific features, including spatial partitioning for computational efficiency, anisotropic multi-head attention to capture directional dependencies, and a multiscale information block for hierarchical feature fusion, thereby bridging data-driven machine learning with fundamental turbulence physics. In evaluations on standard benchmarks and Johns Hopkins Turbulence Database(JHTDB), AMSPINN consistently outperforms state-of-the-art models such as Transolver. Across four benchmark datasets, it achieves error reductions ranging from 3.8% to 64%. On the JHTDB, AMSPINN demonstrates relative error reductions of 27.8%, 18.8%, and 37.2% for boundary-layer flow prediction, multiscale vortex prediction, and realistic turbulent flow prediction, respectively. This physics-inspired approach bridges data-driven and theoretical methods, offering promising advancements in turbulent flow simulations.
Lu et al. (Wed,) studied this question.