Auto-Differentiable Transfer Mapping Architecture for Physics-Infused Learning of Acoustic Field

Abstract

Opportunistic Physics-mining Transfer Mapping Architecture (OPTMA) is a hybrid architecture that combines fast simplified physics models with neural networks in order to provide significantly improved generalizability and explainability compared to pure data-driven machine learning (ML) models. However, training OPTMA remains computationally inefficient due to its dependence on gradient-free solvers or back-propagation with supervised learning over expensively pre-generated labels. This paper presents two extensions of OPTMA that are not only more efficient to train through standard back-propagation but are readily deployable through the state-of-the-art library, PyTorch. The first extension, OPTMA-Net, presents novel manual reprogramming of the simplified physics model, expressing it in Torch tensor compatible form, thus naturally enabling PyTorch's in-built Auto-Differentiation to be used for training. Since manual reprogramming can be tedious for some physics models, a second extension called OPTMA-Dual is presented, where a highly accurate internal neural net is trained apriori on the fast simplified physics model (which can be generously sampled), and integrated with the transfer model. Both new architectures are tested on analytical test problems and the problem of predicting the acoustic field of an unmanned aerial vehicle. The interference of the acoustic pressure waves produced by multiple monopoles form the basis of the simplified physics for this problem statement. An indoor noise monitoring setup in motion capture environment provided the ground truth for target data. Compared to sequential hybrid and pure ML models, OPTMA-Net/Dual demonstrate several fold improvement in performing extrapolation, while providing orders of magnitude faster training times compared to the original OPTMA.