Paper Archive

This paper presents an examination of State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Through experiments with datasets generated under different initial conditions and sample rates, we assess the capacity of these models to accurately model the complex behaviours observed in string dynamics. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in nonlinear cases for long-sequence modelling. We inform the design of these architectures with the structure of the problems at hand. Although challenges remain in extending model predictions beyond the training horizon (i.e., extrapolation), the focus of our investigation lies in the models’ ability to generalise across different initial conditions within the training time interval. This research contributes insights into the physical modelling of dynamical systems (in particular those addressing musical acoustics) by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement. Our results highlight the efficacy of these models in simulating non-linear dynamics and emphasise their wide-ranging applicability in accurately modelling dynamical systems over extended sequences.

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Modal methods for simulating vibrations of strings, membranes, and plates are widely used in acoustics and physically informed audio synthesis. However, traditional implementations, particularly for non-linear models like the von Kármán plate, are computationally demanding and lack differentiability, limiting inverse modelling and real-time applications. We introduce a fast, differentiable, GPU-accelerated modal framework built with the JAX library, providing efficient simulations and enabling gradientbased inverse modelling. Benchmarks show that our approach significantly outperforms CPU and GPU-based implementations, particularly for simulations with many modes. Inverse modelling experiments demonstrate that our approach can recover physical parameters, including tension, stiffness, and geometry, from both synthetic and experimental data. Although fitting physical parameters is more sensitive to initialisation compared to methods that fit abstract spectral parameters, it provides greater interpretability and more compact parameterisation. The code is released as open source to support future research and applications in differentiable physical modelling and sound synthesis.

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We present two Transformer-based methods for Task A of the 1st DAFx Parameter Estimation Challenge, which requires estimating six effective physical parameters of a synthetic plate-reverb model from its impulse response (IR). Method A1 combines an Audio Spectrogram Transformer encoder and Transformer regressor with differentiable IR refinement. Method A2 uses the same encoder to condition a continuous normalizing flow and refines sampled candidates using particle swarm optimisation (PSO) and gradient polishing. Both methods preserve the absolute IR scale to recover surface density. On a synthetic holdout set of 100 IRs, both refinement procedures reduce waveform and parameter errors by more than three orders of magnitude relative to the unrefined neural outputs. The PSO-based pipeline achieves the lowest errors, indicating near-perfect recovery in this matched synthetic setting.

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We describe two submissions to Task B of the 1st DAFx Parameter Estimation Challenge, which estimates an unknown number of modal frequency, decay, and gain triples from a synthetic plate-reverb impulse response. The first method combines pooled spectral features with time-domain and absolute-scale conditioning in a real-valued convolutional count-density network, while the second uses a complex-valued Transformer count-density network. Both methods jointly infer the modal count and per-mode attributes directly from the IR. On an independently generated 100-IR comparison set, the two neural estimators achieve lower overall challenge error than the evaluated classical baselines, with frequency and decay estimation substantially more accurate than gain estimation.

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