The study was conducted by a team led by Xiaofan Li from the University of Hong Kong, China. The researchers designed the framework to address a persistent challenge in fluid-structure interaction: conventional simulations require well-defined governing equations, initial conditions and boundary conditions, while purely data-driven models usually require large training datasets.
The team reported the work in Ocean on June 18, 2026.
“While PINNs have demonstrated remarkable success in single-physics domains, their applications to tightly-coupled multi-physics problems, such as FSI, is still an emerging and challenging area of research. So investigating how to utilize PINNs in FSI problems can play a significant role in addressing more complex issues in practical scenarios, especially when the data required is sparse.” said Xiaofan Li, corresponding author of the study, assistant professor in the department of mechanical engineering at the University of Hong Kong.
The researchers tested the method on a two-dimensional steady flow interacting with a simply supported Euler-Bernoulli beam. “As the physical model has two physical domains, we use two neural networks to represent them respectively. This decoupled training strategy is derived from domain decomposition: dividing the computational domain into several subdomain and each subdomain is represented by a single neural network, which is combined with other neural networks by boundary conditions” Said Xiaofan Li.
The researchers generated approximately 20 million pressure values and 200,000 beam-displacement values using finite-difference simulations, but each training experiment used no more than 1% of the full dataset. In the forward problem that aims to compute the displacement of the beam based on the data from the fluid domain, with 1,000 sampling points in both the fluid and structural domains, the relative L2 errors of the two networks were approximately 0.12% and 0.33%, respectively. Li’s team also found that the model also remained accurate under low levels of Gaussian noise. At noise standard deviations of 1% and 2%, the beam-network errors remained below 1%. Performance declined beyond a clear threshold, with the error increasing to 6.6% at a standard deviation of 15% and to 62% at 20%.
For the uniform-beam inverse problem, the relative error in density identification was merely 0.65% with only 50 sampling points on the structure. In two nonuniform-beam inverse cases, the framework identified spatially varying density with errors of approximately 1.5% and 2.5%. “The experiments we have conducted confirmed that FSI-PINNs could predict the movements of physical fields and infer the unknown parameter of governing equations even if we only had very sparse data, which presented its great potential as a data-efficient method for numerical simulation.” said Xiaofan Li.
Future work will extend the framework to three-dimensional viscous flows and large-deformation structures, improve optimization and loss balancing, and test the method with real sensor data. The ultimate goal is to develop a reliable engineering tool for monitoring coupled fluid-structure systems in data-scarce environments.
Other contributors include Xuanhan Xia, Jinfeng Zhang, Shunxiang Cao and Guangyao Wang from The University of Hong Kong, Tianjin University, Tsinghua Shenzhen International Graduate School, the University of Macau and the Zhuhai UM Science and Technology Research Institute.
This work was supported by the National Natural Science Foundation of China (52301336), the Science and Technology Development Fund of the Macao Special Administrative Region (0048/2025/ITP1), and the University of Macau (SRG2025-00004-FST).
D OI Link:
https://doi.org/10.26599/OCEAN.2026.9470017
Ocean
A physics-informed neural network for fluid–structure coupled simulation of a Euler–Bernoulli beam under steady flow
18-Jun-2026