This project investigates how abstract Fourier expansions involving rational function systems can model linear time-invariant dynamical systems and generalize these results to kernel expansions to develop novel modeling schemes for machine learning methods and nonlinear maps. We thereby develop mathematically justified, data-driven approximation algorithms applicable across a diverse range of disciplines.
This project develops new mathematical tools to understand and model complex systems, from engineering to machine learning. Many real-world systems—like electrical circuits or mechanical devices—can be described using equations that link their inputs to their outputs. Often, we do not know the exact rules governing a system, so instead we try to learn a model directly from measured data. This project proposes new ways to break down these system descriptions into simpler building blocks, using tools from harmonic analysis, making the resulting models more robust and reliable, even when the system's complexity is unknown in advance.
Beyond these classical dynamical systems, the project extends similar ideas to modeling general nonlinear relationships in data, which is central to many machine learning methods. We show how these harmonic analysis techniques, originally developed for describing dynamical systems, can be adapted to build more efficient machine learning models, particularly ones based on "kernel methods," which currently struggle with large datasets due to high computational costs. Our approach makes these techniques more scalable and practical for real-world use.
Another goal is to simplify complex models without sacrificing accuracy, a process known as model order reduction. We propose new methods to shrink complicated system descriptions into much simpler ones while preserving important properties like stability. These methods are also applicable to more general nonlinear models, including neural networks and complex physical processes.
Finally, we address a major challenge in modern artificial intelligence: many powerful machine learning models, such as deep neural networks, act as unpredictable "black boxes," making them unsuitable for safety-critical use. To address this, we design new types of neural network components that are both efficient and more interpretable, giving insight into how the model makes decisions.
Journal Articles
- Detection of brake disc deformation with adaptive wavelet neural networks, T. Dózsa, P. Őri, G. Ungvári, Z. Szabó, A. Soumelidis, I. Lakatos, and P. Kovács, IEEE Trans. Instrum. Meas., Mar. 2026, https://doi.org/10.1109/TIM.2026.3674239
Conference Papers
- Second-order optimization of variable projection SVM models and road abnormality detection, A. Angino, M. Voigt, R. Krause, and T. Dózsa, ICASSP 2026 – 2026 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 1641–1645, Barcelona, Spain, 2026, https://doi.org/10.1109/ICASSP55912.2026.11463454
- Acoustic overload detection with rational Gaussian wavelet based convolutional neural networks, A. M. Ámon, T. Dózsa, and P. Kovács, International Conference on Noise and Vibration Engineering, Leuven, Belgium, Jul. 2026, Accepted for publication
Preprints / Submitted Papers
- Generalized rational Prony and Bernoulli methods, T. Dózsa, M. Voigt, Z. Szabó, J. Bokor, and P. Kovács, arXiv preprint arXiv:2510.03510, Oct. 2025, https://doi.org/10.48550/arXiv.2510.03510
- Tube-based model predictive control with random Fourier features for nonlinear systems, Á. M. Bokor, T. Dózsa, F. Biertümpfel, and Á. Szabó, arXiv preprint arXiv:2511.16425, Nov. 2025, Submitted for publication, https://doi.org/10.48550/arXiv.2511.16425
- Adaptive kernel methods, T. Dózsa, A. Angino, Z. Szabó, J. Bokor, and M. Voigt, arXiv preprint arXiv:2601.21707, Jan. 2026, Submitted for publication, https://doi.org/10.48550/arXiv.2601.21707
- H2-optimal model order reduction using hyperbolic geometry, A. Angino, T. Dózsa, and M. Voigt, Mar. 2026, Submitted for publication
- Classification and detection of multiple UAVs using rational Gaussian wavelet neural networks, G. Ungvári, F. Braun, A. Ámon, P. Kackstädter, J. Volk, P. Kovács, and T. Dózsa, arXiv preprint arXiv:2605.26310, May 2026, Submitted for publication, https://doi.org/10.48550/arXiv.2605.26310
- System identification using real rational orthogonal expansions and variable projection, M. Szabari, T. Dózsa, A. Soumelidis, and P. Kovács, Jul. 2026, Submitted for publication
