Wong Hong Shen, Chan Wei Xuan, Li Bing Huan, Yap Choon Hwai
Department of Bioengineering, Imperial College London, Exhibition Road, London, SW7 2AZ, UK.
Department of Chemical Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, UK.
Sci Rep. 2024 May 21;14(1):11577. doi: 10.1038/s41598-024-62117-9.
Fluid dynamics computations for tube-like geometries are crucial in biomedical evaluations of vascular and airways fluid dynamics. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional computational fluid dynamics (CFD) methods. However, vanilla PINNs often demand longer training times than conventional CFD methods for each specific flow scenario, limiting their widespread use. To address this, multi-case PINN approach has been proposed, where varied geometry cases are parameterized and pre-trained on the PINN. This allows for quick generation of flow results in unseen geometries. In this study, we compare three network architectures to optimize the multi-case PINN through experiments on a series of idealized 2D stenotic tube flows. The evaluated architectures include the 'Mixed Network', treating case parameters as additional dimensions in the vanilla PINN architecture; the "Hypernetwork", incorporating case parameters into a side network that computes weights in the main PINN network; and the "Modes" network, where case parameters input into a side network contribute to the final output via an inner product, similar to DeepONet. Results confirm the viability of the multi-case parametric PINN approach, with the Modes network exhibiting superior performance in terms of accuracy, convergence efficiency, and computational speed. To further enhance the multi-case PINN, we explored two strategies. First, incorporating coordinate parameters relevant to tube geometry, such as distance to wall and centerline distance, as inputs to PINN, significantly enhanced accuracy and reduced computational burden. Second, the addition of extra loss terms, enforcing zero derivatives of existing physics constraints in the PINN (similar to gPINN), improved the performance of the Mixed Network and Hypernetwork, but not that of the Modes network. In conclusion, our work identified strategies crucial for future scaling up to 3D, wider geometry ranges, and additional flow conditions, ultimately aiming towards clinical utility.
管状几何结构的流体动力学计算在血管和气道流体动力学的生物医学评估中至关重要。物理信息神经网络（PINNs）已成为传统计算流体动力学（CFD）方法的一种有前途的替代方法。然而，对于每个特定的流动场景，普通PINNs通常比传统CFD方法需要更长的训练时间，这限制了它们的广泛应用。为了解决这个问题，人们提出了多案例PINN方法，其中对各种几何案例进行参数化，并在PINN上进行预训练。这使得能够快速生成未知几何结构中的流动结果。在本研究中，我们通过对一系列理想化的二维狭窄管流进行实验，比较了三种网络架构，以优化多案例PINN。评估的架构包括“混合网络”，将案例参数视为普通PINN架构中的附加维度；“超网络”，将案例参数纳入一个在主PINN网络中计算权重的侧网络；以及“模式”网络，其中输入到侧网络的案例参数通过内积对最终输出做出贡献，类似于深度算子网络（DeepONet）。结果证实了多案例参数化PINN方法的可行性，“模式”网络在准确性、收敛效率和计算速度方面表现出卓越的性能。为了进一步增强多案例PINN，我们探索了两种策略。首先，将与管几何结构相关的坐标参数，如到壁的距离和中心线距离作为PINN的输入，显著提高了准确性并减轻了计算负担。其次，添加额外的损失项，在PINN中强制现有物理约束的零导数（类似于广义PINN（gPINN）），提高了混合网络和超网络的性能，但对模式网络没有效果。总之，我们的工作确定了对于未来扩展到三维、更广泛的几何范围和更多流动条件至关重要的策略，最终目标是实现临床应用。
