# A Review of Neural Network-Based Emulation of Guitar Amplifiers
## 1 Introduction  
The use of vacuum tubes in electronics has largely diminished since the advent of semiconductor technologies, leading to their replacement in almost all fields except that of music technology, where a return to and rise of vacuum tubes can be observed [1]. Musicians tend to prefer the sonic characteristics of vacuum tube amplifiers over those of solid-state ones. Nevertheless, the shortcomings of vacuum tubes in the realm of guitar amplification are numerous and include elevated cost and weight, poor durability, and high power consumption. Their solid-state counterparts remedy some of the disadvantages of vacuum tube amplifiers but remain less popular among musicians who often seek the particular tone of the tube amplifiers used in iconic albums and guitar rigs. Researchers have turned to Digital Signal Processing (DSP) methods for the emulation of vacuum tube amplifiers in order to circumvent some of the downsides of this technology. These DSP methods are not limited to guitar amplification or distortion and can consist of a wide range of audio effects such as reverberation, delay, and pitch-shifting [2]. The existing DSP methods for tube amplifier emulation can be divided into three categories depending on the degree of prior knowledge of the target device used. The \"white-box\" approach is historically the first and emulates each electronic component. The \"black-box\" approach tries to match the output of the target device given a specific input using mathematical functions uncorrelated with the internal components. Gray-box methods are similar to black-box but utilize some information about the target device in order to fine-tune the model. They comprise a block-oriented structure inspired by internal information of the device but the simulation disregards the behaviour of each of the individual components. These three modelling approaches will be discussed in further detail in Section 2. These three \"traditional\" methods do, however, present some drawbacks. On one end of the spectrum, obtaining the internal knowledge of the target device needed for white-box approaches is both a costly and labour-intensive task and can provide inaccuracies in the emulation. They can also be computationally expensive. On the other side of the spectrum, black-box methods can also be computationally costly or cannot accurately approximate the nonlinear mapping of the amplifier. These methods will be discussed further in a future section. The computational cost of these methods is also prohibitive for real-time use, which is a fundamental factor to be considered in Virtual Analog (VA) modelling. Amplifier emulations need to be fast enough to run in real-time in order to be used by musicians. If the latency of an emulation exceeds around 10 ms, it can be perceived by the musician and hinder their playing [3]. The use of machine learning, in particular neural networks, has seen a significant increase in all data-related fields in recent years due to, in part, the increased computational capabilities of modern-day computers and the possibility of parallelizing computations on their GPU. The field of audio processing is no exception and the application of neural networks to the task of tube amplifier emulation seems to be appropriate. Indeed, neural networks are made up of the basic building blocks necessary for this type of problem including the presence of nonlinear activation functions which are well suited to model the nonlinearities created by vacuum tubes. Moreover, certain neural network architectures are able to capture and replicate the dynamic nature of a system. For example, autoregressive models retain information from previous time steps for their computations. Thus, the memory effect of amplifiers can be modeled using the appropriate type of neural network. Additionally, neural networks reduce the time necessary to create the emulation of a given analog device.