arXiv:2505.18565v5 Announce Type: replace 
Abstract: 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.

تقدم دراسة جديدة بنية مبتكرة من نوع Euler-Lagrange لشبكات الأعصاب المستندة إلى الفيزياء (PINNs) التي تعالج بشكل فعال مشاكل التفاعل بين السوائل والهياكل (FSI) ذات الحدود المتحركة. تدمج هذه الطريقة أساليب الحدود المغمورة لتحسين نمذجة الفيزياء المتميزة لمجالات السوائل والهياكل، متجاوزةً القيود التي تواجهها الهياكل الموحدة التقليدية.

Un nuevo estudio presenta una arquitectura innovadora Euler-Lagrange para las Redes Neuronales Informadas por la Física (PINNs) que aborda de manera efectiva los problemas de interacción fluido-estructura (IFS) con fronteras móviles. Este enfoque integra métodos de frontera sumergida para modelar mejor la física distinta de los dominios fluidos y estructurales, superando las limitaciones de las arquitecturas unificadas tradicionales.

Une nouvelle étude présente une architecture innovante Euler-Lagrange pour les réseaux de neurones informés par la physique (PINNs) qui aborde efficacement les problèmes d'interaction fluide-structure (IFS) avec des frontières mobiles. Cette approche intègre des méthodes de frontière immergée pour mieux modéliser la physique distincte des domaines fluides et structurels, surmontant les limitations des architectures unifiées traditionnelles.

A new study introduces an innovative Eulerian-Lagrangian architecture for Physics-Informed Neural Networks (PINNs) that effectively addresses fluid-structure interaction (FSI) problems with moving boundaries. This approach integrates immersed boundary methods to better model the distinct physics of fluid and structural domains, overcoming limitations of traditional unified architectures.

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

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