Maximum-entropy principle in knowledge-enhanced machine learning in acoustics

Abstract

Recent acoustics investigations increasingly apply model-based methods, they purposely empower learning machines to analyze intrinsic parameters encapsulated in well-established models from experimental data. These data-driven analyses incorporate the well-understood /established models to the machine learning process as an important part of prior information, in addition to another part of prior information on the model parameters of interest. A data-driven machine learning method represents a learning process from data to update our knowledge, namely, learning from the data. This consistently represents the core of probabilistic inference within Bayesian framework on how one's prior knowledge is improved upon the experimental data. This paper discusses the data-driven machine learning methods in a way of thinking like a Bayesian. It emphasizes that knowledge-enhanced incorporation of the well-understood models in many learning processes can rigorously resort to the principle of maximum entropy, including Gaussian process due to their Bayesian nature. Benefits of the data-driven machine learning methods are highlighted when incorporating well understood/established models. This paper discusses physics-informed, knowledge-enhanced methods based on recent acoustic investigations, such as estimation of acoustic boundary conditions in wave-based numerical simulations and diffusion-equation-informed reverberation analysis.