Auto-differentiable transfer mapping architecture for physics-infused learning of acoustic field

Opportunistic physics-mining transfer mapping architecture (OPTMA) is a hybrid architecture that combines fast simplified physicsmodels 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 pregenerated labels. This article 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 autodifferentiation to be used for training. Sincemanual 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 a priori on the fast simplified physicsmodel (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 noisemonitoring setup in motion capture environment provided the ground truth for target data. Compared to sequential hybrid and pure ML models, OPTMANet/ Dual demonstrate several fold improvement in performing extrapolation, while providing orders of magnitude faster training times compared to the original OPTMA. Impact Statement-The new physics-informed machine learning (PIML) architecture presented in this paper provides in-situ transformation of input or estimation of latent parameters via a neural network, allowing a fast interpretable physics model to make accurate predictions. More specifically, this paper presents two extensions of the original underlying PIML architecture that significantly improves its training efficiency and scope of applicability. The latter is enabled by making OPTMA deployable as an end-To-end neural architecture within PyTorch. Classes of applications where OPTMA is expected to be particularly beneficial include problems where simplified (computationally efficient) physics model(s) are available, and they involve tunable parameters (which are otherwise user-prescribed). Such applications are abound in engineering problems, such as flow/aerodynamic analysis, materials characterization, robot dynamics, and so on. Broadly speaking, the OPTMA architecture can thus be applied to a wide range of prediction problems in engineering, with end-uses being systems analysis, design and control.