Alec Wright

Jan Wilczek, Alec Wright, Vesa Välimäki et al.

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.

Alec Wright, Alistair Carson, Lauri Juvela

This paper introduces Open-Amp, a synthetic data framework for generating large-scale and diverse audio effects data. Audio effects are relevant to many musical audio processing and Music Information Retrieval (MIR) tasks, such as modelling of analog audio effects, automatic mixing, tone matching and transcription. Existing audio effects datasets are limited in scope, usually including relatively few audio effects processors and a limited amount of input audio signals. Our proposed framework overcomes these issues, by crowdsourcing neural network emulations of guitar amplifiers and effects, created by users of open-source audio effects emulation software. This allows users of Open-Amp complete control over the input signals to be processed by the effects models, as well as providing high-quality emulations of hundreds of devices. Open-Amp can render audio online during training, allowing great flexibility in data augmentation. Our experiments show that using Open-Amp to train a guitar effects encoder achieves new state-of-the-art results on multiple guitar effects classification tasks. Furthermore, we train a one-to-many guitar effects model using Open-Amp, and use it to emulate unseen analog effects via manipulation of its learned latent space, indicating transferability to analog guitar effects data.

Alistair Carson, Alec Wright, Stefan Bilbao

Modulation effects such as phasers, flangers and chorus effects are heavily used in conjunction with the electric guitar. Machine learning based emulation of analog modulation units has been investigated in recent years, but most methods have either been limited to one class of effect or suffer from a high computational cost or latency compared to canonical digital implementations. Here, we build on previous work and present a framework for modelling flanger, chorus and phaser effects based on differentiable digital signal processing. The model is trained in the time-frequency domain, but at inference operates in the time-domain, requiring zero latency. We investigate the challenges associated with gradient-based optimisation of such effects, and show that low-frequency weighting of loss functions avoids convergence to local minima when learning delay times. We show that when trained against analog effects units, sound output from the model is in some cases perceptually indistinguishable from the reference, but challenges still remain for effects with long delay times and feedback.

Victor Zheleznov, Stefan Bilbao, Alec Wright et al.

Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable techniques has enabled construction of explicit and stable numerical solvers for such systems. On the other hand, neural ordinary differential equations have been successful in modelling nonlinear systems from data. In this work, we examine how scalar auxiliary variable techniques can be combined with neural ordinary differential equations to yield a stable differentiable model capable of learning nonlinear dynamics. The proposed approach leverages the analytical solution for linear vibration of the system's modes so that physical parameters of a system remain easily accessible after the training without the need for a parameter encoder in the model architecture. Compared to our previous work that used multilayer perceptrons to parametrise nonlinear dynamics, we employ gradient networks that allow an interpretation in terms of a closed-form and non-negative potential required by scalar auxiliary variable techniques. As a proof of concept, we generate synthetic data for the nonlinear transverse vibration of a string and show that the model can be trained to reproduce the nonlinear dynamics of the system. Sound examples are presented.

Eloi Moliner, Michal Švento, Alec Wright et al.

Accurately estimating nonlinear audio effects without access to paired input-output signals remains a challenging problem. This work studies unsupervised probabilistic approaches for solving this task. We introduce a method, novel for this application, based on diffusion generative models for blind system identification, enabling the estimation of unknown nonlinear effects using black- and gray-box models. This study compares this method with a previously proposed adversarial approach, analyzing the performance of both methods under different parameterizations of the effect operator and varying lengths of available effected recordings. Through experiments on guitar distortion effects, we show that the diffusion-based approach provides more stable results and is less sensitive to data availability, while the adversarial approach is superior at estimating more pronounced distortion effects. Our findings contribute to the robust unsupervised blind estimation of audio effects, demonstrating the potential of diffusion models for system identification in music technology.

Alistair Carson, Vesa Välimäki, Alec Wright et al.

Neural networks have become ubiquitous in audio effects modelling, especially for guitar amplifiers and distortion pedals. One limitation of such models is that the sample rate of the training data is implicitly encoded in the model weights and therefore not readily adjustable at inference. Recent work explored modifications to recurrent neural network architecture to approximate a sample rate independent system, enabling audio processing at a rate that differs from the original training rate. This method works well for integer oversampling and can reduce aliasing caused by nonlinear activation functions. For small fractional changes in sample rate, fractional delay filters can be used to approximate sample rate independence, but in some cases this method fails entirely. Here, we explore the use of real-time signal resampling at the input and output of the neural network as an alternative solution. We investigate several resampling filter designs and show that a two-stage design consisting of a half-band IIR filter cascaded with a Kaiser window FIR filter can give similar or better results to the previously proposed model adjustment method with many fewer filtering operations per sample and less than one millisecond of latency at typical audio rates. Furthermore, we investigate interpolation and decimation filters for the task of integer oversampling and show that cascaded half-band IIR and FIR designs can be used in conjunction with the model adjustment method to reduce aliasing in a range of distortion effect models.

Victor Zheleznov, Stefan Bilbao, Alec Wright et al.

Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string, where geometric nonlinear effects lead to perceptually important effects including pitch glides and a dependence of brightness on striking amplitude. A modal decomposition leads to a coupled nonlinear system of ordinary differential equations. Recent work in applied machine learning approaches (in particular neural ordinary differential equations) has been used to model lumped dynamic systems such as electronic circuits automatically from data. In this work, we examine how modal decomposition can be combined with neural ordinary differential equations for modelling distributed musical systems. The proposed model leverages the analytical solution for linear vibration of system's modes and employs a neural network to account for nonlinear dynamic behaviour. Physical parameters of a system remain easily accessible after the training without the need for a parameter encoder in the network architecture. As an initial proof of concept, we generate synthetic data for a nonlinear transverse string and show that the model can be trained to reproduce the nonlinear dynamics of the system. Sound examples are presented.

Otto Mikkonen, Alec Wright, Eloi Moliner et al.

The sound of magnetic recording media, such as open-reel and cassette tape recorders, is still sought after by today's sound practitioners due to the imperfections embedded in the physics of the magnetic recording process. This paper proposes a method for digitally emulating this character using neural networks. The signal chain of the proposed system consists of three main components: the hysteretic nonlinearity and filtering jointly produced by the magnetic recording process as well as the record and playback amplifiers, the fluctuating delay originating from the tape transport, and the combined additive noise component from various electromagnetic origins. In our approach, the hysteretic nonlinear block is modeled using a recurrent neural network, while the delay trajectories and the noise component are generated using separate diffusion models, which employ U-net deep convolutional neural networks. According to the conducted objective evaluation, the proposed architecture faithfully captures the character of the magnetic tape recorder. The results of this study can be used to construct virtual replicas of vintage sound recording devices with applications in music production and audio antiquing tasks.

Alec Wright, Vesa Välimäki

This work investigates alternate pre-emphasis filters used as part of the loss function during neural network training for nonlinear audio processing. In our previous work, the error-to-signal ratio loss function was used during network training, with a first-order highpass pre-emphasis filter applied to both the target signal and neural network output. This work considers more perceptually relevant pre-emphasis filters, which include lowpass filtering at high frequencies. We conducted listening tests to determine whether they offer an improvement to the quality of a neural network model of a guitar tube amplifier. Listening test results indicate that the use of an A-weighting pre-emphasis filter offers the best improvement among the tested filters. The proposed perceptual loss function improves the sound quality of neural network models in audio processing without affecting the computational cost.