Efficient Training of Transfer Mapping in Physics-Infused Machine Learning Models of UAV Acoustic Field

Physics-Infused Machine Learning (PIML) architectures aim at integrating machine learning with computationally-efficient, low-fidelity (partial) physics models, leading to improved generalizability, extrapolability, and robustness to noise, compared to pure data-driven approximation models. End-uses of PIML include, but are not limited to, model-based optimization and model-predictive control. Recently a new PIML architecture was reported by the same authors, known as Opportunistic Physics-mining Transfer Mapping Architecture or OPTMA, which transfers the original inputs into latent features using a transfer neural network; the partial physics model then uses the latent features to generate the final output that is as close as possible to the high-fidelity output. While gradient-free solvers and back-propagation with supervised learning (where optimum labels are pre-generated) have been used to train OPTMA, that approach remains computationally inefficient, and challenging to generalize across different problems or exploit state-of-the-art machine learning architectures. This paper aims to alleviate these issues by infusing the partial physics model inside the neural network, as described via tensors in the popular machine learning framework, PyTorch. Such a description also naturally allows auto-differentiation of the partial physics model, thereby enabling the use of efficient back-propagation methods to train the transfer network. The benefits of the upgraded OPTMA architecture with Automatic Differentiation (OPTMA-Net) is demonstrated by applying it to the problem of modeling the sound pressure field created by a hovering unmanned aerial vehicle (UAV). Ground truth data for this problem has been obtained from an indoor UAV noise measurement setup. Here, the partial physics model is based on the interference of acoustic pressure waves generated by an arbitrary number of acoustic monopole sources. Case studies show that OPTMA-Net provides generalization performance close to, and extrapolation performance that is 4 times better than, those given by a pure data-driven model.