Deep Learning-Based Wave Digital Modeling of Rate-Dependent Hysteretic Nonlinearities for Virtual Analog Applications

Electromagnetic components greatly contribute to the peculiar timbre of analog audio gear. Indeed, distortion effects due to the nonlinear behavior of magnetic materials are known to play an important role in enriching the harmonic content of an audio signal. However, despite the abundant research that has been devoted to the characterization of nonlinearities in the context of virtual analog modeling over the years, the discrete-time simulation of circuits exhibiting rate-dependent hysteretic phenomena remains an open challenge. In this article, we present a novel data-driven approach for the wave digital modeling of rate-dependent hysteresis using recurrent neural networks (RNNs). Thanks to the modularity of wave digital filters, we are able to locally characterize the wave scattering relations of a hysteretic reluctance by encapsulating an RNN-based model into a single one-port wave digital block. Hence, we successfully apply the proposed methodology to the emulation of the output stage of a vacuum-tube guitar amplifier featuring a nonlinear transformer.