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：解决由非线性偏微分方程描述的复杂流固耦合（FSI）问题，在众多科学与工程应用中至关重要。传统基于计算流体力学的求解器难以满足大规模、长周期仿真日益增长的需求。日益丰富的数据资源与深度学习的快速发展，为通过数据驱动建模应对这些挑战开辟了新途径。通过可微编程框架将深度学习与经典数值技术无缝融合，可显著提升数据驱动建模性能。本研究提出一种可微混合神经建模框架，用于高效仿真FSI问题：该方法基于浸入边界法对FSI物理过程进行数值离散，并通过可微编程将其与序列神经网络无缝集成。所有模块均在JAX中编程实现，自动微分技术使梯度能够沿整个模型推理轨迹反向传播，从而支持混合神经FSI模型以端到端、序列到序列的方式进行整体训练。通过多个FSI基准案例，我们验证了该方法在刚体和柔性体FSI动力学建模中的优势与能力。该模型在精度、鲁棒性和泛化能力方面，均显著优于纯数据驱动神经模型、弱耦合混合神经模型以及纯数值FSI求解器等基线方法。