Machine learning non-reciprocity of a passive linear waveguide with a local nonlinear, asymmetric gate

Abstract

In this work, we propose a new, simple, and highly effective passive phononic waveguide with controllable global non-reciprocity by means of local nonlinear and asymmetric elements. The nonlinearity and asymmetry in the waveguide are realized by means of a local nonlinear gate with a cubic stiffness nonlinearity that couples two detuned, dissipative gate oscillators. A wave transmits across the nonlinear gate by applying a harmonic excitation. The transmitted wave is either monochromatic or strongly modulated (SMR) and triggers the global non-reciprocity. The objectives of this work are to study the effect of local nonlinearity and asymmetry on the global non-reciprocal acoustics and to optimize the non-reciprocal performance of the waveguide. We employ the complexification averaging method (CX-A) in the acoustics to predict the bifurcations that govern the non-reciprocal acoustics. However, a limitation of the single-frequency CX-A method is its failure to predict the SMRs. Alternatively, we train machine learning simulators in order to optimize the two performance measures, i.e., energy transmissibility and non-reciprocity. The trained machine learning model drastically saves the simulation time and allows the optimization of performances. Our results show how powerful machine learning approaches can be employed for designing and optimizing practical waveguides with tailored non-reciprocity features.