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

Hansani Weeratunge, Dominic Robe, Elnaz Hajizadeh

TL;DR

This work presents a SHAP-bounded Bayesian Optimization framework to efficiently design underwater acoustic metamaterial coatings in polyurethane matrices with embedded voids. A DNN surrogate maps ten design variables to the frequency-weighted sound absorption objective, while SHAP explains variable importance to guide iterative refinement of the design bounds, reducing the search space without extra simulations. Applied to PU80 and PU90 materials, the approach achieves up to 11% improvement over standard BO within 400 evaluations and demonstrates enhanced data efficiency under computational constraints. The method combines interpretability with optimization to accelerate discovery and is generalizable to other materials and engineering design problems.

Abstract

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.

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

TL;DR

This work presents a SHAP-bounded Bayesian Optimization framework to efficiently design underwater acoustic metamaterial coatings in polyurethane matrices with embedded voids. A DNN surrogate maps ten design variables to the frequency-weighted sound absorption objective, while SHAP explains variable importance to guide iterative refinement of the design bounds, reducing the search space without extra simulations. Applied to PU80 and PU90 materials, the approach achieves up to 11% improvement over standard BO within 400 evaluations and demonstrates enhanced data efficiency under computational constraints. The method combines interpretability with optimization to accelerate discovery and is generalizable to other materials and engineering design problems.

Abstract

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.
Paper Structure (13 sections, 1 equation, 4 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 1 equation, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Model Problem
  4. Objective Function
  5. SHAP-Bounded Bayesian Optimization
  6. Deep Neural Networks for Mapping Design Variables to Acoustic Performance
  7. Interpretable Machine Learning with SHAP
  8. SHAP-Guided Parameter Space Refinement
  9. Results and Discussion
  10. SHAP Analysis for PU90
  11. SHAP Analysis for PU80
  12. Discussion
  13. Conclusion

Figures (4)

  • Figure 1: Illustration of the complementary information provided by SHAP and BO. A) An objective function with many local optima and a large-scale trend. Black points represent function evaluations during an optimization. The vertical black line indicates the global maximum. B) The SHAP values for the two parameters X and Y at the evaluated points. C) A Gaussian Process Regression (GPR) model fit to the evaluated points. D) The Expected Improvement (EI) calculated from the GPR model.
  • Figure 2: The design of the current study. A) the structural parameters for the metamaterial design being optimized. $r_1$ and $r_2$ are the radii of the first and second layer of voids. $D_1$ and $D_2$ are the horizontal distances of the layers from their respective edges. $B_1,B_2,B_3$, and $B_4$ are the vertical distances of each void from their respective edges. B) The proposed optimization methodology. GPR and DNN models are trained on a cumulative data set. SHAP analysis is applied to the model DNN. If the sampling budget is not exhausted, boundaries are refined. The argmax of EI for the GPR model within the refined bounds is then added to the data set.
  • Figure 3: Results of PU90 (a) Variation of the SHAP value for each feature. Lighter colors emphasize higher SHAP values. Red vertical dashed lines indicate the parameter values for the best-so-far layout. Black vertical dashed lines indicate the crossover from regions with negative to positive SHAP values. (b) Mean SHAP values, ranking features by their overall impact. (c) Convergence plot illustrating the mean and standard deviation of the best objective function value at each iteration. The black point and broken line indicate the number of iterations at which SHAP-informed BO surpassed standard BO's optimal solution after 400 iterations.
  • Figure 4: Results of PU80 (a) Variation of the SHAP value for each feature. Lighter colors emphasize higher SHAP values. Red vertical dashed lines indicate the parameter values for the best-so-far layout. Black vertical dashed lines indicate the crossover from regions with negative to positive SHAP values. (b) Mean SHAP values, ranking features by their overall impact. (c) Convergence plot illustrating the mean and standard deviation of the best objective function value at each iteration. The black point and broken line indicate the number of iterations at which SHAP-informed BO surpassed standard BO's optimal solution after 400 iterations.