Adaptive Multi-Fidelity Structural Optimization under Fluid-Structure Interaction.

The design of structures and vehicles subject to fluid-structure interaction (FSI) often requires high-fidelity coupled analysis. While the design variables pertain to the structure, the computational cost is usually dominated by the fluid solver, making iterative optimization prohibitively expensive. This paper presents an adaptive multi-fidelity optimization method that combines high-fidelity FSI analysis with a lightweight surrogate for fluid-induced loads and a decision model that selects between surrogate and high-fidelity fluid evaluations. During optimization, results from completed FSI analyses are used to incrementally update a non-intrusive surrogate model based on nearest-neighbor search and radial interpolation. To maintain accuracy across varying geometries, a hybrid Lagrangian-Eulerian mapping function is developed to transfer fluid loads between structural designs. The evolution in surface orientation is handled through decomposition of the traction vectors in local orthonormal bases. An adaptive Gaussian process regression model is employed to predict surrogate error and quantify uncertainty, allowing risk-aware selection of when coupled analysis is required. As design evaluations cluster near the optimal solution, the accuracy of the surrogate model naturally improves, thereby reducing the reliance on high-fidelity fluid evaluations. This optimization framework treats the high-fidelity FSI model as the ground truth, instead of a pre-computed dataset. It requires no offline training, preserves the high-fidelity structural model in all design evaluations, and ensures that the final design is evaluated by high-fidelity FSI analysis. The fundamental idea is justified theoretically using a simplified model problem, which shows that the leading-order error is a monotonically increasing, concave, and bounded function of the fluid added mass. The framework is implemented using open-source software and demonstrated numerically through two benchmark examples. For shape optimization of a flexible panel under shock loading, results show an 80% reduction in computational cost while maintaining accuracy within 2.3% of fully high-fidelity FSI optimization.