Multidimensional integration using machine learning and Monte Carlo methods for acoustic predictions

To predict underwater noise radiated by a ship, various numerical methods are available. In underwater acoustics, the most effective prediction methods consist in solving an acoustic analogy using an integral formulation. In this study, we propose a machine learning surrogate-based method, combined with Monte Carlo integration, to efficiently estimate volume integrals that arise in acoustic analogies. We use three machine learning surrogate models: multi-layer perceptrons, Gaussian processes and gradient-boosted decision trees. For each model, a theoretical background is presented. We conduct numerical experiments to compare the state-of-the-art classical Monte Carlo quadrature method with our new machine learning based method. We first apply our method to simple canonical functions, which are analytically integrable, to evaluate the accuracy of our method. We then use a multi-layer perceptron-based surrogate model to approximate a fabricated function that mimics the characteristics of noise sources found in acoustic prediction models, such as those related to turbulent flows near geometrical singularities. Numerical experiments demonstrate that the proposed machine learning-based approach achieves performance levels comparable to state-of-the-art Monte Carlo quadrature methods, demonstrating the potential of ML techniques in this domain.