arXiv subjects

Achraf El Messaoudi

Publications and source records attributed to Achraf El Messaoudi.

3 recordsLinked to original sources

arXiv2026

Nonlinear port-Hamiltonian system identification from input-state-output data (ISO-pHNN)

In this paper, we introduce a framework called ISO-pHNN for identifying nonlinear port-Hamiltonian systems using input-state-output data. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured way. We explore different architectures based on MLPs, KANs, and using prior information. The identification technique is validated through examples featuring nonlinearities in either the skew-symmetric terms, the dissipative terms, or the Hamiltonian. We show that incorporating a port-Hamiltonian structure does not lower the accuracy and that using additional prior information improves long-term predictions.

eess.SY↗

arXiv2026

Target Parameterization in Diffusion Models for Nonlinear Spatiotemporal System Identification

Machine learning is becoming increasingly important for nonlinear system identification, including dynamical systems with spatially distributed outputs. However, classical identification and forecasting approaches become markedly less reliable in turbulent-flow regimes, where the dynamics are high-dimensional, strongly nonlinear, and highly sensitive to compounding rollout errors. Diffusion-based models have recently shown improved robustness in this setting and offer probabilistic inference capabilities, but many current implementations inherit target parameterizations from image generation, most commonly noise or velocity prediction. In this work, we revisit this design choice in the context of nonlinear spatiotemporal system identification. We consider a simple, self-contained patch-based transformer that operates directly on physical fields and use turbulent flow simulation as a representative testbed. Our results show that clean-state prediction consistently improves rollout stability and reduces long-horizon error relative to velocity- and noise-based objectives, with the advantage becoming more pronounced as the per-token dimensionality increases. These findings identify target parameterization as a key modeling choice in diffusion-based identification of nonlinear systems with spatial outputs in turbulent regimes.

eess.SY↗

arXiv2026

PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network

Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available. In this context, port-Hamiltonian (pH) models provide a natural physics-informed representation. However, when these models are parameterized with standard multilayer perceptrons (MLPs), the learned constitutive components often remain poorly interpretable. In this paper, we propose a structure-preserving identification framework for nonlinear port-Hamiltonian systems based on Kolmogorov-Arnold Networks (KANs). The proposed PH-KAN model parameterizes the interconnection matrix, dissipation matrix, Hamiltonian, and input mapping using dedicated KAN blocks, while enforcing the port-Hamiltonian constraints by construction. This yields constitutive representations in which the nonlinear functions defining the identified pH components can be explicitly inspected, leading to a more interpretable model than with standard MLP-based parameterizations.

math.OC↗