arXiv subjects

Uros Sutulovic

Publications and source records attributed to Uros Sutulovic.

4 recordsLinked to original sources

arXiv2026

Automatic denoising and differentiation based on Savitzky-Golay filtering and Homogeneous Differentiators for attractor reconstruction via differential embedding

Differential embedding methods aim to reconstruct attractors of dynamical systems from noisy measured time series, but require accurate estimates of signal derivatives. We introduce SHADED (Savitzky-Golay and Homogeneous-differentiator based Automatic DEnoising and Differentiation), a novel methodology for denoising and estimation of derivatives up to an arbitrary order, which enables attractor reconstruction via differential embedding from noisy time series data. Homogeneous Differentiators (HD) guarantee finite-time derivative estimates in the presence of noise, while subsequent Savitzky-Golay (SG) filtering attenuates chattering. Crucially, SHADED extracts all parameters required for application of both HD and SG automatically from the data, without requiring manual tuning that may lead to inaccurate reconstruction, and can also incorporate prior knowledge, if available, thereby yielding a flexible tool for data-driven numerical differentiation of noisy signals. The obtained differential embeddings can reveal features of the underlying dynamics that are useful, e.g., for system identification, pattern recognition and discrimination between dynamic regimes; the latter application is particularly important in biomedical settings, to help distinguish between different physiological and pathological states. We demonstrate the efficacy of SHADED by testing it on computational neuroscience models, LTspice-simulated chaotic electronic circuits, and photoplethysmography and arterial blood pressure experimental recordings: across all these case studies, SHADED produces accurate derivative estimates and accurate attractor reconstructions via differential embedding (whenever a ground truth is available) or geometrically coherent and reproducible reconstructions consistent with the expected dynamics (in the absence of a ground truth), without the need for manual parameter tuning.

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arXiv2026

gPC-based robustness analysis of neural systems through probabilistic recurrence metrics

Neuronal systems often preserve their characteristic functions and signalling patterns, also referred to as regimes, despite parametric uncertainties and variations. For neural models having uncertain parameters with a known probability distribution, probabilistic robustness analysis (PRA) allows us to understand and quantify under which uncertainty conditions a regime is preserved in expectation. We introduce a new computational framework for the efficient and systematic PRA of dynamical systems in neuroscience and we show its efficacy in analysing well-known neural models that exhibit multiple dynamical regimes: the Hindmarsh-Rose model for single neurons and the Jansen-Rit model for cortical columns. Given a model subject to parametric uncertainty, we employ generalised polynomial chaos to derive mean neural activity signals, which are then used to assess the amount of parametric uncertainty that the system can withstand while preserving the current regime, thereby quantifying the regime's robustness to such uncertainty. To assess persistence of regimes, we propose new metrics, which we apply to recurrence plots obtained from the mean neural activity signals. The overall result is a novel, general computational methodology that combines recurrence plot analysis and systematic persistence analysis to assess how much the uncertain model parameters can vary, with respect to their nominal value, while preserving the nominal regimes in expectation. We summarise the PRA results through probabilistic regime preservation (PRP) plots, which capture the effect of parametric uncertainties on the robustness of dynamical regimes in the considered models.

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arXiv2025

Efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators

Reconstructing the attractors of complex nonlinear dynamical systems from available measurements is key to analyse and predict their time evolution. Existing attractor reconstruction methods typically rely on topological embedding and may produce poor reconstructions, which differ significantly from the actual attractor, because measurements are corrupted by noise and often available only for some of the state variables and/or their combinations, and the time series are often relatively short. Here, we propose the use of Homogeneous Differentiators (HD) to effectively de-noise measurements and more faithfully reconstruct attractors of nonlinear systems. Homogeneous Differentiators are supported by rigorous theoretical guarantees about their de-noising capabilities, and their results can be fruitfully combined with time-delay embedding, differential embedding and functional observability. We apply our proposed HD-based methodology to simulated dynamical models of increasing complexity, from the Lorenz system to the Hindmarsh-Rose model and the Epileptor model for neural dynamics, as well as to empirical data of EEG recordings. In the presence of corrupting noise of various types, we obtain drastically improved quality and resolution of the reconstructed attractors, as well as significantly reduced computational time, which can be orders of magnitude lower than that of alternative methods. Our tests show the flexibility and effectiveness of Homogeneous Differentiators and suggest that they can become the tool of choice for preprocessing noisy signals and reconstructing attractors of highly nonlinear dynamical systems from both theoretical models and real data.

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arXiv2025

Efficient gPC-based quantification of probabilistic robustness for systems in neuroscience

Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable when addressing complex models in neuroscience, we propose an alternative to computationally expensive Monte Carlo (MC) methods by introducing and analysing the generalised polynomial chaos (gPC) framework for uncertainty quantification. We consider both intrusive and non-intrusive gPC approaches, which turn out to be scalable and allow for a fast comprehensive exploration of parameter spaces. Focusing on widely used models of neural dynamics as case studies, we explore the trade-off between efficiency and accuracy of gPC methods, and we adopt the proposed methodology to investigate parametric uncertainties in models that feature multiple dynamic regimes.

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