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

TL;DR

This paper introduces a Fourier neural operator-based fluid-structure interaction solver that efficiently predicts vesicle dynamics by integrating neural operator learning with traditional fluid-structure simulation methods.

Contribution

The paper presents a novel FNO-based FSI solver that combines neural operator learning with finite difference methods for efficient and accurate fluid-structure interaction simulations.

Findings

FNO-based FSI solver accurately captures vesicle dynamics.

Multi-step label training with steady-state data yields best interpolation performance.

The method effectively predicts fluid and vesicle variations in complex interactions.

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.