Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. This study introduces NeuroSEM, a hybrid framework integrating PINNs with the high-fidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh–Bénard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU–CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

中文翻译：

---

NeuroSEM：通过耦合 PINN 和光谱元件来模拟多物理场问题的混合框架


多物理场问题的特点是流体动力学、传热学、结构力学和电磁学之间复杂的相互作用，由于其耦合性质，其本身就具有挑战性。虽然可能有关于某些状态变量的实验数据，但将这些数据与数值求解器集成仍然是一个重大挑战。物理信息神经网络 （PINN） 在各种工程学科中都显示出有希望的成果，特别是在处理嘈杂数据和求解偏微分方程 （PDE） 中的逆问题方面。然而，它们在预测多物理场状态下的非线性现象（特别是涉及湍流）的有效性尚未完全确定。本研究介绍了 NeuroSEM，这是一个将 PINN 与高保真光谱元法 （SEM） 求解器 Nektar++ 集成的混合框架。NeuroSEM 利用 PINN 和 SEM 的优势，为多物理场问题提供强大的解决方案。PINN 经过训练，可以吸收特定子域中的数据并对物理现象进行建模，然后将其集成到 Nektar++ 求解器中。我们展示了 NeuroSEM 在腔流和流经圆柱体的流中热对流的效率和准确性。该框架通过对数据可用的子域和状态变量进行寻址来有效地处理数据同化。我们将 NeuroSEM 应用于 Rayleigh-Bénard 对流系统，包括缺少热边界条件和噪声数据集的情况。最后，我们将提出的 NeuroSEM 框架应用于真实粒子图像测速 （PIV） 数据，以捕获以马蹄形涡度结构为特征的流型。 我们的结果表明，NeuroSEM 准确地模拟了物理现象并同化了指定子域内的数据。该框架的即插即用特性有助于将其扩展到其他多物理场或多尺度问题。此外，NeuroSEM 还针对在新兴的集成 GPU-CPU 架构上高效执行进行了优化。这种混合方法提高了仿真的准确性和效率，使其成为应对各个科学领域复杂工程挑战的强大工具。