Multi-fidelity optimization of a soft nozzle–propeller system

We optimized a soft nozzle inspired by a squid's funnel that generates greater thrust than a rigid nozzle under the same propeller-driven inflow. To exploit nonlinear deformations driven by wave propagation, we used a multi-fidelity Bayesian optimization (MFBO) approach that minimizes experimental costs while maximizing thrust gain. For this, we built an efficient experimental framework—including thrust measurement systems and soft-material 3D printing—and developed a CFD solver integrating OpenFOAM, preCICE, and Calculix (OPC) to achieve strong fluid–structure coupling with adjustable fidelity for rapid design exploration. The nozzle geometry was defined by nine parameters, such as height, mean radius, spline-based axial contour, and thickness distribution. We experimentally tested 20% of the designs using a load cell for thrust measurement, while the remaining 80% were evaluated computationally with the OPC solver at multiple fidelity levels. The MFBO method, using Gaussian process regression with a radial basis kernel, adaptively selected promising candidates and assessed data fidelity. Through iterative testing and refinement, the optimized nozzle achieved a 7% thrust increase over the baseline design. Using 3D Digital Image Correlation (DIC) and 3D Particle Image Velocimetry (PIV), we revealed the fluid–structure interaction mechanisms behind this improvement. The final design not only outperformed rigid nozzles but also reproduced key characteristics of biological soft nozzles, offering insight into how natural systems may have evolved to handle similar flow conditions.