Interpretable SHAP-bounded Bayesian optimization for underwater acoustic metamaterial coating design

Abstract We present an interpretability-informed Bayesian optimization framework for the inverse design of underwater acoustic coatings composed of polyurethane elastomers with embedded metamaterial features. A data-driven model was used to capture the relationship between acoustic performance, specifically, sound absorption and the corresponding geometrical design variables. To interpret these relationships, we applied SHapley Additive exPlanations (SHAP), enabling the identification of key parameters influencing the objective function and providing both global and local insights into their effects. The insights from the SHAP analysis were used to automatically refine the bounds of the design space, guiding the optimization process toward more promising regions. This approach was tested on two polyurethane materials with different hardness levels and yielded improved optimal designs compared to standard Bayesian optimization without increasing the number of simulations. This work underscores the effectiveness of combining interpretability techniques with optimization for the efficient and cost-effective design of underwater acoustic metamaterials under strict computational constraints and can be generalized towards other materials and engineering optimization problems.