Dr. Faruk Özger

Igdir University, Turkiye

Title: Polynomial-Augmented Hybrid Neural Networks for Solving Fractional Differential Equations 

Abstract: Fractional differential equations (FDEs) pose significant computational challenges due to their complex dynamics. While spectral methods and polynomial-based approximations have shown promise in solving integral and differential equations, their integration with modern machine learning frameworks remains underexplored. In this talk, we present a polynomial-augmented hybrid neural network architecture that uses operational matrices of orthogonal polynomials to solve FDEs. By embedding spectral techniques into neural network training, our approach combines the approximation power of polynomials with the adaptive learning capabilities of deep networks, enabling efficient and accurate solutions for fractional operators. We demonstrate the method’s advantages over traditional solvers in terms of convergence rates and scalability, offering a unified framework for both linear and nonlinear FDE problems.

Dr. Radosław Kycia

Cracow University of Technology, Kraków, Poland

Title: Geometric decomposition method in solving equations of physics and geometry

Abstract: I will show how to solve the parallel transport equation (locally) on an associated vector bundle using only the Poincare lemma and related linear homotopy operator. The solution only sometimes exists, and I will show where there is a problem. Moreover, using the homotopy operator and its Hodge star dual on the Riemannian manifold, I will show how to solve many other differential equations that contain exterior derivative and coderivative (from equations on Clifford bundle to the inverse problem of variational calculus), which we called geometry-based differential equations. This also includes the algebraic equation for the kernel of curvature operator, where the curvature is treated as the square of the exterior covariant derivative. Our method provides a quick, easy, and algorithmic way of solving such problems that even students can grasp. This method is all you need to do local differential geometry. The talk is based on [1], [2], and [3].

Literature:

[1] R.A. Kycia, J. Šilhan, “Inverting covariant exterior derivative”, arXiv:2210.03663 [math.DG]

[2] E.A. Kycia, “The Poincare Lemma for Codifferential, Anticoexact Forms, and Applications to Physics”. Results Math 77, 182 (2022). https://doi.org/10.1007/s00025-022-01646-z

[3] R.A. Kycia, “The Poincare Lemma, Antiexact Forms, and Fermionic Quantum Harmonic Oscillator”. Results Math 75, 122 (2020). https://doi.org/10.1007/s00025-020-01247-8

Presentation

Dr. Sarbaz Khoshnaw

University of Raparin, Kurdistan Region, Iraq

Title: The Role of Mathematical Modelling in Understanding HIV infectious disease

Abstract: The HIV infectious disease has been considered a worldwide issue, and many global efforts have been suggested. Mathematical models play an important role with computational simulations to minimize the impact of this disease in the community. In this talk, I will present an HIV infectious disease model. The model describes the interaction between the HIV viruses, CD4+ T cells, infected cells, and the CTL immune response. Firstly, this infectious disease can be modeled as a system of differential equations with transmission parameters. Secondly, identifying model critical transmissions are also key elements to study this disease further. In addition, the basic reproduction number, R_0, and its parameter elasticity can be calculated at the equilibrium points. Another mathematical tool here is local sensitivities for each model state with respect to the model parameters, these sensitivities can be computed using three different techniques: non-normalizations, half-normalizations and full-normalizations. Finally, some numerical results are computed for the different initial states and parameters.

Dr. Agnieszka Niemczynowicz

Cracow University of Technology, Poland

Title: Hypercomplex Neural Networks: Current State of Knowledge and Future Perspectives

Abstract: Hypercomplex neural networks (HNNs) represent a rapidly evolving field that extends traditional artificial neural networks into higher-dimensional number systems, such as complex numbers, quaternions, and octonions. These architectures offer unique advantages in handling multidimensional data, preserving phase and amplitude information, and reducing network complexity through parameter sharing.

This lecture provides a comprehensive overview of the current knowledge in hypercomplex neural networks, covering their mathematical foundations, architectural designs, and key application areas. We also examine the main challenges facing researchers in this domain, including optimization difficulties, limited interpretability, and the lack of standardized benchmarks.

Furthermore, the lecture explores promising directions for future research, highlighting the growing potential of HNNs as a powerful tool in modern machine learning while emphasizing the need for continued theoretical and practical advancements. 

Presentation

Dr. Rizgar Haji Salih 

University of Raparin, Kurdistan Region, Iraq 

Title: Centre Bifurcation of 3D Systems

Abstract: The center-focus problem is a key issue in the qualitative theory of planar differential equations, also known as the Poincaré center-focus problem. It involves determining whether an equilibrium point at the origin is a weak focus or a center. If all orbits in a neighborhood of the origin are periodic, the origin is classified as a center; otherwise, it acts as a saddle focus, with orbits spiraling around it. The distinction between center and focus is central to this problem. Solutions to the center problem at Hopf points can be approached using two main methods: the classical Lyapunov Center Theorem, which requires the existence of a real analytic local first integral, and the modern method involving the inverse Jacobi multiplier. Current research in bifurcation theory focuses on the bifurcation of limit cycles from critical points, typically initiated by perturbing a focus or center, with center bifurcation being a common technique for estimating cyclicity and studying these limit cycles.

Presentation

Dr. Seyyed Ali Mohammadiyeh

University of Kashan, Kashan, I. R. Iran

Title: Using AI to Model Real-World Systems: From Weather to Economics

Abstract:    Many real-world systems—such as the weather, financial markets, and ecosystems—change over time in ways that are difficult to predict. Traditionally, we have used mathematical tools like differential equations and dynamical systems theory to understand them. However, with the rise of AI, we now have new ways to model and make sense of these complex patterns. In this talk, I will explore how machine learning and neural networks can be used to build models of real-world dynamical systems. I will share examples from weather forecasting or economic trends where AI shines, where it struggles, and how it can complement traditional models. We’ll look at modern techniques like LSTMs, and discuss why blending AI with domain knowledge often leads to better, more reliable results. Whether you're coming from a math, computer science, or applied research background, this talk will offer practical insights into how AI and dynamical systems can work together to solve real-world problems.

Dr. Zahraa Ch. Oleiwi

University of AlQadisiya, Iraq

Title: Imbalanced Dataset And Its Impact on Performance of Learning Techniques

Abstract: The class imbalance problem in machine learning occurs when the distribution of classes in a dataset is uneven, making it challenging to detect and classify minority classes accurately. This is common in applications like fraud detection, rare medical diagnoses, and identifying oil spills, where the minority class is underrepresented. Imbalanced datasets can lead to models that focus on the majority class, resulting in poor performance and misdiagnosis of important cases. This is particularly critical in situations like cancer detection, where accurately identifying the minority class is essential. To address the issues associated with training models on imbalanced datasets, various techniques have been developed to enhance classification performance. These strategies can be categorized into three broad groups: algorithm-level methods that modify the learning process, data-level methods that involve techniques such as resampling or synthetic data generation, and cost-sensitive methods that incorporate different costs associated with misclassification of various classes. Through the application of these methods, it is possible to achieve more balanced and effective predictive outcomes, particularly for minority class instances.