Download Wave Digital Modeling of Circuits with Multiple One-Port Nonlinearities Based on Lipschitz-Bounded Neural Networks Neural networks have found application within the Wave Digital Filters (WDFs) framework as data-driven input-output blocks for modeling single one-port or multi-port nonlinear devices in circuit systems. However, traditional neural networks lack predictable bounds for their output derivatives, essential to ensure convergence when simulating circuits with multiple nonlinear elements using fixed-point iterative methods, e.g., the Scattering Iterative Method (SIM). In this study, we address such issue by employing Lipschitz-bounded neural networks for regressing nonlinear WD scattering relations of one-port nonlinearities.
Download Training Neural Models of Nonlinear Multi-Port Elements Within Wave Digital Structures Through Discrete-Time Simulation Neural networks have been applied within the Wave Digital Filter
(WDF) framework as data-driven models for nonlinear multi-port
circuit elements. Conventionally, these models are trained on wave
variables obtained by sampling the current-voltage characteristic
of the considered nonlinear element before being incorporated into
the circuit WDF implementation. However, isolating multi-port
elements for this process can be challenging, as their nonlinear
behavior often depends on dynamic effects that emerge from interactions with the surrounding circuit. In this paper, we propose a
novel approach for training neural models of nonlinear multi-port
elements directly within a circuit’s Wave Digital (WD) discretetime implementation, relying solely on circuit input-output voltage
measurements. Exploiting the differentiability of WD simulations,
we embed the neural network into the simulation process and optimize its parameters using gradient-based methods by minimizing
a loss function defined over the circuit output voltage. Experimental results demonstrate the effectiveness of the proposed approach
in accurately capturing the nonlinear circuit behavior, while preserving the interpretability and modularity of WDFs.
Download Fourier Neural Operators for Sample-Rate-Independent Virtual Analog Modeling Neural networks that operate directly on time-domain signals are widely used for virtual analog (VA) modeling. A key limitation of these models is their dependence on the sampling rate used during training, which becomes implicitly encoded in the learned parameters, so that changing it generally alters the realized dynamics. Although architectural modifications to recurrent neural networks have been proposed to enable sample-rate independent operation, these approaches are inherently tailored to upsampling and do not accommodate downsampling scenarios. In this manuscript, we present a VA modeling framework based on Fourier Neural Operators (FNOs) adapted to process fixed-duration audio frames. The proposed formulation defines the learned mapping over a fixed temporal support and evaluates it on uniform grids of different densities, so that a model trained at a single sampling rate can be applied at unseen sampling resolutions. Numerical results on a nonlinear transistor circuit show that the proposed model achieves competitive accuracy in upsampling scenarios while remaining directly applicable to downsampling, unlike a sample-rate independent baseline recurrent architecture.
Download Parameter Estimation via Differentiable Modal Plate Synthesis We present our submission to Task A of the 1st DAFx Parameter Estimation Challenge, which concerns the estimation of the physical parameters of a vibrating plate from a synthetic impulse response. Our approach introduces a differentiable modal plate synthesizer and estimates the plate parameters through inference-time gradient-based optimization of the synthesizer parameters. The six target parameters are recovered by minimizing a multi-scale spectral loss via backpropagation through the differentiable plate model. To handle the non-convexity of the loss landscape, we adopt a two-phase training strategy consisting of multiple short-term probe optimizations, followed by full-scale refinement initialized from the best candidate. We evaluate the approach on eight impulse responses synthesized with the official challenge dataset generator. Compared with a constant-value predictor and the particle swarm optimization baseline provided by the challenge, the proposed method reduces the prediction error by approximately one order of magnitude.
Download Explicit Vector Wave Digital Filter Modeling of Circuits with a Single Bipolar Junction Transistor The recently developed extension of Wave Digital Filters based on vector wave variables has broadened the class of circuits with linear two-port elements that can be modeled in a modular and explicit fashion in the Wave Digital (WD) domain. In this paper, we apply the vector definition of wave variables to nonlinear twoport elements. In particular, we present two vector WD models of a Bipolar Junction Transistor (BJT) using characteristic equations derived from an extended Ebers-Moll model. One, implicit, is based on a modified Newton-Raphson method; the other, explicit, is based on a neural network trained in the WD domain and it is shown to allow fully explicit implementation of circuits with a single BJT, which can be executed in real time.
Download A Quadric Surface Model of Vacuum Tubes for Virtual Analog Applications Despite the prevalence of modern audio technology, vacuum tube amplifiers continue to play a vital role in the music industry. For this reason, over the years, many different digital techniques have been introduced for accomplishing their emulation. In this paper, we propose a novel quadric surface model for tube simulations able to overcome the Cardarilli model in terms of efficiency whilst retaining comparable accuracy when grid current is negligible. After showing the model capability to well outline tubes starting from measurement data, we perform an efficiency comparison by implementing the considered tube models as nonlinear 3-port elements in the Wave Digital domain. We do this by taking into account the typical common-cathode gain stage employed in vacuum tube guitar amplifiers. The proposed model turns out to be characterized by a speedup of 4.6× with respect to the Cardarilli model, proving thus to be promising for real-time Virtual Analog applications.
Download A Clipping Prevention Method for All-Pass Digital Filters with Time-Varying Coefficients A clipping prevention method is proposed for first- and second-order all-pass filters with time-varying coefficients. Unlike conventional anti-clipping or declipping approaches, the method operates directly on the coefficient dynamics and does not rely on assumptions about internal energy evolution, by just asking that the input signal is not already clipping. The core idea is to control the deviation between the output of the time-varying filter and that of an equivalent static all-pass structure with constant coefficients. By adaptively limiting this deviation at runtime, the output is constrained below a prescribed clipping threshold (typically unit magnitude). The method is active only during short transients where clipping would occur, after which the coefficients are released to reach their target values. This preserves the integrity of the input signal and the numerical properties of the all-pass filter. Experimental results confirm the expected behavior even in scenarios where energy-preserving all-pass structures exceed the clipping threshold, suggesting the proposed approach as a practical solution for robust dynamic filter implementations with limited additional computational cost, suitable especially for embedded digital audio processing hardware.
Download Differentiable MIMO Feedback Delay Networks for Multichannel Room Impulse Response Modeling Recently, with the advent of new performing headsets and goggles, the demand for Virtual and Augmented Reality applications has experienced a steep increase. In order to coherently navigate the virtual rooms, the acoustics of the scene must be emulated in the most accurate and efficient way possible. Amongst others, Feedback Delay Networks (FDNs) have proved to be valuable tools for tackling such a task. In this article, we expand and adapt a method recently proposed for the data-driven optimization of single-inputsingle-output FDNs to the multiple-input-multiple-output (MIMO) case for addressing spatial/space-time processing applications. By testing our methodology on items taken from two different datasets, we show that the parameters of MIMO FDNs can be jointly optimized to match some perceptual characteristics of given multichannel room impulse responses, overcoming approaches available in the literature, and paving the way toward increasingly efficient and accurate real-time virtual room acoustics rendering.
Download Differentiable Scattering Delay Networks for Artificial Reverberation Scattering delay networks (SDNs) provide a flexible and efficient
framework for artificial reverberation and room acoustic modeling. In this work, we introduce a differentiable SDN, enabling
gradient-based optimization of its parameters to better approximate the acoustics of real-world environments. By formulating
key parameters such as scattering matrices and absorption filters
as differentiable functions, we employ gradient descent to optimize an SDN based on a target room impulse response. Our approach minimizes discrepancies in perceptually relevant acoustic
features, such as energy decay and frequency-dependent reverberation times. Experimental results demonstrate that the learned SDN
configurations significantly improve the accuracy of synthetic reverberation, highlighting the potential of data-driven room acoustic modeling.
Download A Comparative Study of Kolmogorov-Arnold Networks and Multi-Layer Perceptrons for Virtual Analog Modeling in Wave Digital Filters The design of Virtual Analog (VA) algorithms has traditionally been divided between white-box (physics-based) and black-box (data-driven) approaches. Recent work has shown that hybrid methods, combining physical modeling with neural networks, can effectively leverage the strengths of both paradigms. In particular, Wave Digital Filters (WDFs) can be coupled with Multi-Layer Perceptrons (MLPs) to model circuits with multiple nonlinearities in a fully explicit manner. In this paper, we present a comparative study investigating the use of Kolmogorov-Arnold Networks (KANs) for VA modeling within the WDF framework. Unlike MLPs, KANs shift the learning paradigm by parameterizing activation functions instead of relying exclusively on learned weight matrices, potentially enabling more compact representations. Results show that, for our case study, KANs achieve accuracy comparable to MLPs while requiring approximately 70% fewer parameters at the cost of increased computational complexity. These findings suggest that KANs may represent a promising alternative in scenarios where memory footprint is a primary constraint, such as embedded audio applications, or when target models feature numerous nonlinear elements.