  Recent research in deep learning has shown that neural networks can learn
differential equations governing dynamical systems. In this paper, we adapt
this concept to Virtual Analog (VA) modeling to learn the ordinary differential
equations (ODEs) governing the first-order and the second-order diode clipper.
The proposed models achieve performance comparable to state-of-the-art
recurrent neural networks (RNNs) albeit using fewer parameters. We show that
this approach does not require oversampling and allows to increase the sampling
rate after the training has completed, which results in increased accuracy.
Using a sophisticated numerical solver allows to increase the accuracy at the
cost of slower processing. ODEs learned this way do not require closed forms
but are still physically interpretable.
