arXiv:2505.18565cs.LGcs.CE2025-05被引 1

用物理约束神经网络模拟可动边界流固耦合,精度提升超20%。

Learning Fluid-Structure Interaction with Physics-Informed Machine Learning and Immersed Boundary Methods

  • 分域建模:流体用欧拉网络,结构用拉格朗日网络,通过物理约束耦合
  • 压力误差从12.9%降至2.39%,速度与压力整体精度提升24.1%-91.4%
  • 适合需高精度模拟可动边界问题的研究者,如生物流体力学、柔性结构设计

物理信息神经网络(PINNs)在复杂流体动力学问题中展现出巨大潜力,但在移动边界的流固耦合(FSI)问题中仍鲜有应用。本文针对具有移动界面的FSI系统建模难题,提出一种基于浸入边界法(IBM)原理的欧拉-拉格朗日PINN架构。该方法突破传统统一架构局限,采用领域专用神经网络:欧拉网络处理流体动力学,拉格朗日网络建模结构界面,并通过物理约束实现耦合。同时引入可学习的B样条激活函数与SiLU,以捕捉界面附近的局部高梯度特征与全局流动模式。在二维腔体流动含移动固体结构的问题上,基线统一PINN虽能合理预测速度,但结构区域压力误差高达12.9%。而本提出的欧拉-拉格朗日带可学习激活函数架构(EL-L)在各项指标上表现更优,精度提升24.1%-91.4%,尤其将压力误差降至2.39%。结果表明,基于物理原理的域分解结合局部感知激活函数,是实现高效精确FSI建模的关键。

原文摘要 · Abstract (English)

Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely unexplored. This work addresses the critical challenge of modeling FSI systems with moving interfaces, where traditional unified PINN architectures struggle to capture the distinct physics governing fluid and structural domains simultaneously. We present an innovative Eulerian-Lagrangian PINN architecture that integrates immersed boundary method (IBM) principles to solve FSI problems with moving boundary conditions. Our approach fundamentally departs from conventional unified architectures by introducing domain-specific neural networks: an Eulerian network for fluid dynamics and a Lagrangian network for structural interfaces, coupled through physics-based constraints. Additionally, we incorporate learnable B-spline activation functions with SiLU to capture both localized high-gradient features near interfaces and global flow patterns. Empirical studies on a 2D cavity flow problem involving a moving solid structure show that while baseline unified PINNs achieve reasonable velocity predictions, they suffer from substantial pressure errors (12.9%) in structural regions. Our Eulerian-Lagrangian architecture with learnable activations (EL-L) achieves better performance across all metrics, improving accuracy by 24.1-91.4% and particularly reducing pressure errors from 12.9% to 2.39%. These results demonstrate that domain decomposition aligned with physical principles, combined with locality-aware activation functions, is essential for accurate FSI modeling within the PINN framework.

流固耦合物理信息网络移动边界神经网络

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