Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics

TL;DR

A Fourier neural operator-based fluid-structure interaction solver (FNO-based FSI solver) for efficient simulation of FSI problems, where the solid solver based on the finite difference method is seamlessly integrated with the Fourier neural operator to predict incompressible flow using the immersed boundary method.

Abstract

Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are insufficient to meet the growing requirements for large-scale and long-period simulations. Fortunately, the rapid advancement in neural networks, especially neural operator learning mappings between function spaces, has introduced novel approaches to tackle these challenges via data-driven modeling. In this paper, we propose a Fourier neural operator-based fluid-structure interaction solver (FNO-based FSI solver) for efficient simulation of FSI problems, where the solid solver based on the finite difference method is seamlessly integrated with the Fourier neural operator to predict incompressible flow using the immersed boundary method. We analyze the performance of the FNO-based FSI solver in the following three situations: training data with or without the steady state, training method with one-step label or multi-step labels, and prediction in interpolation or extrapolation. We find that the best performance for interpolation is achieved by training the operator with multi-step labels using steady-state data. Finally, we train the FNO-based FSI solver using this optimal training method and apply it to vesicle dynamics. The results show that the FNO-based FSI solver is capable of capturing the variations in the fluid and the vesicle.

Figures (12)

• Figure 1: The architecture of the FNO-based FSI simulation framework. Top: The architecture of the FNO-based fluid model. The operator maps the solution at the previous $\alpha$ time steps to the next time step. For example, the data from a dashed yellow box is used to predict ${\bf u}^{t_0+\alpha+2}$, with a yellow arrow connecting the feature and label. The FNO is achieved using a combination of 3D-convolutional layers for spatial information processing and recurrent layers for temporal information propagation. Bottom: Structure solver.
• Figure 2: (a) the predicted results and (c) errors of the FNO-4 with inter-set as input. Here, the error refers to the absolute difference between the predicted solution and the IBM solution (b).
• Figure 3: The mean of absolute error between the predicted solution and the IBM solution for the predicted 30-time steps is shown. This figure only demonstrates the x-component of the velocity. The 'ex' in the legend represents the prediction error with extra-set as input.
• Figure 4: The mean of absolute error of experiments (a) without steady state and (b) with steady state. The 'in' in the legend represents the error of the prediction experiment with inter-set as input.
• Figure 5: The mean of absolute error of experiments of (a) interpolation and (b) extrapolation.