Taous-Meriem Laleg-Kirati

Sara Nour Sadoun, Giuseppe Alessio D'Inverno, Francois Cottin et al.

Learning-based and physics-informed methods are increasingly used for inverse estimation in controlled nonlinear dynamical systems. However, in many such approaches, the theoretic requirements that make unknown-input reconstruction meaningful, namely well-posedness in the sense of Hadamard, are often disregarded or weakly addressed through generic regularization terms with no explicit guarantees. In this work, we adopt a complementary viewpoint in which these control-theoretic and structural conditions inform the estimator design and constrain its training. We thus develop a physics-informed input-state neural estimator for joint unknown-input and state estimation in nonlinear controlled systems with partial measurements. In the present work, this general framework is instantiated on a model of autonomic cardiac regulation, provides a concrete study case. The estimator is formulated as an inverse neural map conditioned on time and measured outputs, and is trained under data fidelity and dynamical consistency constraints. To ensure it complies with the same structural requirements imposed in robust estimation, we derive left-invertibility conditions by differential-algebraic elimination and embed the resulting constraints directly into the training objective. We further analyze a priori the stability of the inverse mapping to output perturbations and derive a conservative Lipschitz bound that guides the tuning of cost functional hyper-parameters. The framework is evaluated on simulated data, where ground truth data is available, and on two distinct datasets of real cardiovascular recordings. The results show that incorporating control-theoretic solvability constraints into physics-informed learning improves the reliability of inverse inference beyond forward consistency alone.

Da-Yan Liu, Taous-Meriem Laleg-Kirati, Olivier Gibaru et al.

The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti et al.

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises.

Sharefa Asiri, Taous-Meriem Laleg-Kirati

In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of modulating functions-based solution is proven. The wave and the fifth order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.

Fahad Aljehani, Ibrahima N'Doye, Taous-Meriem Laleg-Kirati

Aquaculture systems can benefit from the recent development of advanced control strategies to reduce operating costs and fish loss and increase growth production efficiency, resulting in fish welfare and health. Monitoring the water quality and controlling feeding are fundamental elements of balancing fish productivity and shaping the fish growth process. Currently, most fish-feeding processes are conducted manually in different phases and rely on time-consuming and challenging artificial discrimination. The feeding control approach influences fish growth and breeding through the feed conversion rate; hence, controlling these feeding parameters is crucial for enhancing fish welfare and minimizing general fishery costs. The high concentration of environmental factors, such as a high ammonia concentration and pH, affect the water quality and fish survival. Therefore, there is a critical need to develop control strategies to determine optimal, efficient, and reliable feeding processes and monitor water quality. This paper reviews the main control design techniques for fish growth in aquaculture systems, namely algorithms that optimize the feeding and water quality of a dynamic fish growth process. Specifically, we review model-based control approaches and model-free reinforcement learning strategies to optimize the growth and survival of the fish or track a desired reference live-weight growth trajectory. The model-free framework uses an approximate fish growth dynamic model and does not satisfy constraints. We discuss how model-based approaches can support a reinforcement learning framework to efficiently handle constraint satisfaction and find better trajectories and policies from value-based reinforcement learning.

Da-Yan Liu, Taous-Meriem Laleg-Kirati

Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator to analyze the signal. In this paper, we are interested in a mathematical analysis of this method in discrete case considering noisy signals.

Elham Rostami, Taous-Meriem Laleg-Kirati, Hamidou Tembine

We study training-free flow matching between two Gaussian mixture models (GMMs) using explicit velocity fields that transport one mixture into the other over time. Our baseline approach constructs component-wise Gaussian paths with affine velocity fields satisfying the continuity equation, which yields to a closed-form surrogate for the pairwise kinetic transport cost. In contrast to the exact Gaussian Wasserstein cost, which relies on matrix square-root computations, the surrogate admits a simple analytic expression derived from the kinetic energy of the induced flow. We then analyze how closely this surrogate approximates the exact cost. We prove second-order agreement in a local commuting regime and derive an explicit cubic error bound in the local commuting regime. To handle nonlocal regimes, we introduce a path-splitting strategy that localizes the covariance evolution and enables piecewise application of the bound. We finally compare the surrogate with an exact construction based on the Gaussian Wasserstein geodesic and summarize the results in a practical regime map showing when the surrogate is accurate and the exact method is preferable.

Elham Rostami, Aref Einizade, Taous-Meriem Laleg-Kirati

Accurate localization of the seizure onset zone (SOZ) from intracranial EEG (iEEG) is essential for epilepsy surgery but is challenged by complex spatiotemporal seizure dynamics. We propose SpaTeoGL, a spatiotemporal graph learning framework for interpretable seizure network analysis. SpaTeoGL jointly learns window-level spatial graphs capturing interactions among iEEG electrodes and a temporal graph linking time windows based on similarity of their spatial structure. The method is formulated within a smooth graph signal processing framework and solved via an alternating block coordinate descent algorithm with convergence guarantees. Experiments on a multicenter iEEG dataset with successful surgical outcomes show that SpaTeoGL is competitive with a baseline based on horizontal visibility graphs and logistic regression, while improving non-SOZ identification and providing interpretable insights into seizure onset and propagation dynamics.

Rose Alaslani, Levina Perzhilla, Muhammad Mahboob Ur Rahman et al.

This work proposes for the first time to utilize the regular smartphone -- a popular assistive gadget -- to design a novel, non-invasive method for self-monitoring of one's hydration level on a scale of 1 to 4. The proposed method involves recording a small video of a fingertip using the smartphone camera. Subsequently, a photoplethysmography (PPG) signal is extracted from the video data, capturing the fluctuations in peripheral blood volume as a reflection of a person's hydration level changes over time. To train and evaluate the artificial intelligence models, a custom multi-session labeled dataset was constructed by collecting video-PPG data from 25 fasting subjects during the month of Ramadan in 2023. With this, we solve two distinct problems: 1) binary classification (whether a person is hydrated or not), 2) four-class classification (whether a person is fully hydrated, mildly dehydrated, moderately dehydrated, or extremely dehydrated). For both classification problems, we feed the pre-processed and augmented PPG data to a number of machine learning, deep learning and transformer models which models provide a very high accuracy, i.e., in the range of 95% to 99%. We also propose an alternate method where we feed high-dimensional PPG time-series data to a DL model for feature extraction, followed by t-SNE method for feature selection and dimensionality reduction, followed by a number of ML classifiers that do dehydration level classification. Finally, we interpret the decisions by the developed deep learning model under the SHAP-based explainable artificial intelligence framework. The proposed method allows rapid, do-it-yourself, at-home testing of one's hydration level, is cost-effective and thus inline with the sustainable development goals 3 & 10 of the United Nations, and a step-forward to patient-centric healthcare systems, smart homes, and smart cities of future.

Juan M. Vargas, Taous-Meriem Laleg-Kirati

In this study, we propose a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schrödinger operator. This projection relies on a design parameter, $γ$, which controls pixel intensity during image reconstruction. The method's performance is evaluated using color images. The selection of $γ$ values is guided by priors based on fuzzy logic and clustering, preserving the spatial adjacency information of the image. Additionally, multi-objective optimization using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to determine the optimal values of $γ$ and the semi-classical parameter, $h$, from the 2D-SCSA. Results demonstrate that the proposed method effectively enhances image contrast while preserving the inherent characteristics of the original image, producing the desired enhancement with minimal artifacts.

Fahad Aljehani, Ibrahima N'Doye, Micaela S. Justo et al.

Successful aquaculture systems can reduce the pressure and help secure the most diverse and productive Red Sea coral reef ecosystem to maintain a healthy and functional ecosystem within a sustainable blue economy. Interestingly, recirculating aquaculture systems are currently emerging in fish farm production practices. On the other hand, monitoring and detecting fish behaviors provide essential information on fish welfare and contribute to an intelligent production in global aquaculture. This work proposes an efficient approach to analyze the spatial distribution status and motion patterns of juvenile clownfish \textit{(Amphiprion bicinctus)} maintained in aquaria at three stocking densities (1, 5, and 10 individuals/aquarium). The estimated displacement is crucial in assessing the dispersion and velocity to express the clownfish's spatial distribution and movement behavior in a recirculating aquaculture system. Indeed, we aim to compute the velocity, magnitude, and turning angle using an optical flow method to assist aquaculturists in efficiently monitoring and identifying fish behavior. We test the system design on a database containing two days of video streams of juvenile clownfish maintained in aquaria. The proposed displacement estimation reveals good performance in measuring clownfish's motion and dispersion characteristics leading to assessing the potential signs of stress behaviors. We demonstrate the effectiveness of the proposed technique for quantifying variation in clownfish activity levels between recordings taken in the morning and afternoon at different stocking densities. It provides practical baseline support for online predicting and monitoring feeding behavior in ornamental fish aquaculture.

Abderrazak Chahid, Fahad Albalawi, Turky Nayef Alotaiby et al.

Epilepsy is a neurological disorder classified as the second most serious neurological disease known to humanity, after stroke. Localization of the epileptogenic zone is an important step for epileptic patient treatment, which starts with epileptic spike detection. The common practice for spike detection of brain signals is via visual scanning of the recordings, which is a subjective and a very time-consuming task. Motivated by that, this paper focuses on using machine learning for automatic detection of epileptic spikes in magnetoencephalography (MEG) signals. First, we used the Position Weight Matrix (PWM) method combined with a uniform quantizer to generate useful features. Second, the extracted features are classified using a Support Vector Machine (SVM) for the purpose of epileptic spikes detection. The proposed technique shows great potential in improving the spike detection accuracy and reducing the feature vector size. Specifically, the proposed technique achieved average accuracy up to 98\% in using 5-folds cross-validation applied to a balanced dataset of 3104 samples. These samples are extracted from 16 subjects where eight are healthy and eight are epileptic subjects using a sliding frame of size of 100 samples-points with a step-size of 2 sample-points