Mesh motion in fluid-structure interaction with deep operator networks

TL;DR

This work tackles mesh motion in ALE-based fluid-structure interaction by learning a mesh-motion operator with DeepONet that maps boundary deformations to interior displacements. The operator enforces Dirichlet boundary conditions via a hard-constraint formulation, and is trained on biharmonic mesh-motion data from the FSI2 benchmark. Evaluations show that the DeepONet mesh motion achieves performance comparable to the biharmonic baseline on FSI test problems and remains robust under severe deformations where biharmonic motion can fail. The findings indicate that data-driven mesh-motion components can augment or replace PDE-based procedures, with future directions including unsupervised training and application to more challenging geometries for improved efficiency and scalability.

Abstract

A mesh motion model based on deep operator networks is presented. The model is trained on and evaluated against a biharmonic mesh motion model on a fluid-structure interaction benchmark problem and further evaluated in a setting where biharmonic mesh motion fails. The performance of the proposed mesh motion model is comparable to the biharmonic mesh motion on the test problems.

Figures (5)

• Figure 1: Partial view of the FSI2 benchmark problem's geometry, centered on the submerged solid. The displacement of the particle $A(t)$ is a reported quantity in the benchmark.
• Figure 2: Minimum cell value of scaled Jacobian mesh quality measure over the dataset with biharmonic extension and best trained DeepONet ($d=7$, $w=512$, $p=32$, seed 1).
• Figure 3: Quantiles of validation loss history DeepONet training (left) and resulting scaled Jacobian mesh quality over FSI2 dataset (right) for 20 random initializations of the best performing hyperparameters found in grid search.
• Figure 4: Drag (top left), lift (top right), $y$-displacement $A_2$ of point on tip of solid (bottom left), and minimum value in $\Omega$ of $J$ (bottom right) in FSI2 benchmark problem with biharmonic and DeepONet mesh motion.
• Figure 5: Histograms of scaled Jacobian mesh quality for biharmonic and DeepONet mesh motion models with solid deformations caused by uniform gravitational load $(0, f_g)$, $f_g \in \{ 1, 2, 2.5 \}$.