A differentiable hybrid neural-finite element framework for fluid-solid interaction with large deformation moving boundaries

Fluid–solid interaction (FSI) is ubiquitous in natural and engineering systems, but its multiphysics nature and nonlinear boundary dynamics pose significant challenges for efficient and accurate modeling. This study proposes a differentiable hybrid neural–physical framework for large-deformation FSI, combining a long-short term memory (LSTM)-based fluid closure with a nonlinear finite element (FE) solver for the solid components of the system. The implementation in JAX enables gradient-based, solver-in-the-loop training using fluid-solid interface forces estimated using a Smoothed Particle Hydrodynamics (SPH) solver. Force-injected solid simulations are conducted together with conditioning and frequency-domain analyses of the equations of motion (EOM) to examine error amplification and rollout behavior in hybrid FSI. The results show that frequency-dependent ill-conditioning can amplify interface-force inconsistencies near resonance, which helps explain the reduced accuracy and robustness of weakly coupled hybrid variants and motivates physically consistent data assimilation through differentiable training. The FSI framework is then evaluated and cross-validated against an independent Arbitrary Lagrangian-Eulerian (ALE) solver on a vortex-induced vibration (VIV) benchmark. Under temporal extrapolation and one-shot parameter extrapolation, the strongly coupled model proposed in this framework achieves the best overall accuracy and robustness. Nonetheless, the cross-validation highlighted value in data-training from multiple solvers. After offline training, the hybrid framework enables inference approximately 30,000 × faster than SPH and ALE solvers, demonstrating its potential for many-query applications, such as design exploration, control and uncertainty quantification.