物理信息神经网络：流体力学计算的新范式

Physics-Informed Neural Networks: A New Paradigm in Computational Fluid Dynamics

摘要: 流体动力学以Navier-Stokes方程为核心，在航空航天、生物医学及环境科学等领域发挥关键作用。传统计算流体动力学(CFD)通过离散化方法求解复杂流动问题，然而在高维、高雷诺数场景下，网格依赖导致计算成本剧增，且在噪声数据或逆问题中精度受限。物理信息神经网络(PINNs)通过将物理定律嵌入深度学习框架，开辟了流体力学计算的新范式。其无网格特性与高数据效率突破了传统方法的局限，为正向预测与逆向推断提供了统一工具。本文综述了PINNs在流体力学中的最新进展，聚焦其在稀疏数据流场重构、多尺度特征捕捉及复杂几何问题中的应用，如三维尾流模拟、超声速激波捕获及血流动力学分析。域分解、自适应采样与损失函数优化等技术显著提升了计算效率与鲁棒性，使PINNs在多物理场耦合及非牛顿流体模拟中展现潜力。然而，高雷诺数湍流的训练稳定性、计算资源需求及模型可解释性仍为瓶颈。未来通过算法优化、不确定性量化及与实验数据的深度融合，PINNs有望超越传统CFD，成为流体力学计算的高效新范式，推动该领域向智能化、精确化迈进。

Abstract: Fluid dynamics, anchored in the Navier-Stokes equations, is pivotal to aerospace, biomedical engineering, and environmental science. Traditional computational fluid dynamics (CFD) relies on discretization techniques to address complex flows, yet struggles with escalating computational costs in high-dimensional, high-Reynolds-number scenarios, where mesh dependency limits efficiency, and accuracy falters with noisy data or inverse problems. Physics-Informed Neural Networks (PINNs) introduce a new paradigm by embedding physical laws into deep learning frameworks, offering a mesh-free, data-efficient approach that unifies forward predictions and inverse inference. This review synthesizes recent advances in PINNs for fluid dynamics, spotlighting their prowess in reconstructing flow fields from sparse data, capturing multiscale features, and tackling complex geometries—exemplified by applications in three-dimensional wake simulations, supersonic shock capturing, and blood hemodynamics. Innovations such as domain decomposition, adaptive sampling, and loss function optimization enhance computational efficiency and robustness, extending PINNs’ potential to multi-physics coupling and non-Newtonian flow modeling. Nevertheless, challenges persist, including training instability in high-Reynolds-number turbulence, computational resource demands, and limited interpretability. Future progress, driven by algorithmic refinements, uncertainty quantification, and integration with experimental data, positions PINNs to surpass traditional CFD, heralding a new era of intelligent, precise computational fluid dynamics.