Interpretable SHAP-bounded Bayesian Optimization for Underwater Acoustic Metamaterial Coating Design

We developed an interpretability informed Bayesian optimization framework to optimize underwater acoustic coatings based on polyurethane elastomers with embedded metamaterial features. A data driven model was employed to analyze the relationship between acoustic performance, specifically sound absorption and the corresponding design variables. By leveraging SHapley Additive exPlanations (SHAP), a machine learning interpretability tool, we identified the key parameters influencing the objective function and gained insights into how these parameters affect sound absorption. The insights derived from the SHAP analysis were subsequently used to automatically refine the bounds of the optimization problem automatically, enabling a more targeted and efficient exploration of the design space. The proposed approach was applied to two polyurethane materials with distinct hardness levels, resulting in improved optimal solutions compared to those obtained without SHAP-informed guidance. Notably, these enhancements were achieved without increasing the number of simulation iterations. Our findings demonstrate the potential of SHAP to streamline optimization processes by uncovering hidden parameter relationships and guiding the search toward promising regions of the design space. This work underscores the effectiveness of combining interpretability techniques with Bayesian 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.

A machine learning accelerated inverse design of underwater acoustic polyurethane coatings with cylindrical voids

Here, we report the development of a detailed "Materials Informatics" framework for the design of acoustic coatings for underwater sound attenuation through integrating Machine Learning (ML) and statistical optimization algorithms with a Finite Element Model (FEM). The finite element models were developed to simulate the realistic performance of the acoustic coatings based on polyurethane (PU) elastomers with embedded cylindrical voids. The FEM results revealed that the frequency-dependent viscoelastic behavior of the polyurethane matrix has a significant impact on the magnitude and frequency of the absorption peak associated with the cylinders at low frequencies, which has been commonly ignored in previous studies on similar systems. The data generated from the FEM was used to train a Deep Neural Network (DNN) to accelerate the design process, and subsequently, was integrated with a Genetic Algorithm (GA) to determine the optimal geometric parameters of the cylinders to achieve maximized, broadband, low-frequency waterborne sound attenuation. A significant, broadband, low-frequency attenuation is achieved by optimally configuring the layers of cylindrical voids and using attenuation mechanisms, including Fabry-P\'erot resonance and Bragg scattering of the layers of voids. Integration of the machine learning technique into the optimization algorithm further accelerated the exploration of the high dimensional design space for the targeted performance. The developed DNN exhibited significantly increased speed (by a factor of $4.5\times 10^3$ ) in predicting the absorption coefficient compared to the conventional FEM(s). Therefore, the acceleration brought by the materials informatics framework brings a paradigm shift to the design and development of acoustic coatings compared to the conventional trial-and-error practices.