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Virtual analog (VA) modeling using neural networks (NNs) has great potential for rapidly producing high-fidelity models. Recurrent neural networks (RNNs) are especially appealing for VA due to their connection with discrete nodal analysis. Furthermore, VA models based on NNs can be trained efficiently by directly exposing them to the circuit states in a gray-box fashion. However, exposure to ground truth information during training can leave the models susceptible to error accumulation in a free-running mode, also known as “exposure bias” in machine learning literature. This paper presents a unified framework for treating the previously proposed state trajectory network (STN) and gated recurrent unit (GRU) networks as special cases of discrete nodal analysis. We propose a novel circuit state-matching mechanism for the GRU and experimentally compare the previously mentioned networks for their performance in state matching, during training, and in exposure bias, during inference. Experimental results from modeling a diode clipper show that all the tested models exhibit some exposure bias, which can be mitigated by truncated backpropagation through time. Furthermore, the proposed state matching mechanism improves the GRU modeling performance of an overdrive pedal and a phaser pedal, especially in the presence of external modulation, apparent in a phaser circuit.

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In this work, we present a data-driven approach to modeling tone stack circuits in guitar amplifiers and distortion pedals. To this aim, the proposed modeling approach uses a feedforward fully connected neural network to predict the parameters of a coupledform state-space filter, ensuring the numerical stability of the resulting time-varying system. The neural network is conditioned on the tone controls of the target tone stack and is optimized jointly with the coupled-form state-space filter to match the target frequency response. To assess the proposed approach, we model three popular tone stack schematics with both matched-order and overparameterized filters and conduct an objective comparison with well-established approaches that use cascaded biquad filters. Results from the conducted experiments demonstrate improved accuracy of the proposed modeling approach, especially in the case of over-parameterized state-space filters while guaranteeing numerical stability. Our method can be deployed, after training, in realtime audio processors.

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