Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable programming framework can significantly improve data-driven modeling performance. In this study, we propose a differentiable hybrid neural modeling framework for efficient simulation of FSI problems, where the numerically discretized FSI physics based on the immersed boundary method is seamlessly integrated with sequential neural networks using differentiable programming. All modules are programmed in JAX, where automatic differentiation enables gradient back-propagation over the entire model rollout trajectory, allowing the hybrid neural FSI model to be trained as a whole in an end-to-end, sequence-to-sequence manner. Through several FSI benchmark cases, we demonstrate the merit and capability of the proposed method in modeling FSI dynamics for both rigid and flexible bodies. The proposed model has also demonstrated its superiority over baseline purely data-driven neural models, weakly-coupled hybrid neural models, and purely numerical FSI solvers in terms of accuracy, robustness, and generalizability.
翻译:解决非线性偏微分方程描述的复杂流体-结构相互作用(FSI)问题在各种科学和工程应用中至关重要。传统的基于计算流体力学的求解器无法处理对大规模和长周期模拟的不断增长的需求。数据的不断增加和深度学习(DL)的快速发展通过数据启用建模打开了新的途径来解决这些挑战。通过可微分编程框架无缝集成DL和经典数值技术可以显著提高数据驱动建模性能。在本研究中,我们提出了一种不同iable的混合神经建模框架,用于有效模拟FSI问题,其中基于浸没边界法的数值离散化FSI物理与顺序神经网络无缝集成,使用可微分编程。所有模块都在JAX中编程,其中自动微分使梯度向后传播超过整个模型回滚轨迹,允许整个混合神经FSI模型以端到端,序列到序列的方式进行训练。通过几个FSI基准案例,我们展示了所提出的方法在建模刚体和柔性物体的FSI动力学方面的价值和能力。所提出的模型还证明了其在准确性,鲁棒性和一般化方面优于基线纯数据驱动的神经模型,弱耦合混合神经模型和纯数值FSI求解器。