Cornelis W. Oosterlee (Utrecht University, the Netherlands)

Prof. Dr. Ir. Cornelis ("Kees") Oosterlee holds the Chair of Financial Mathematics at the Mathematical Institute of Utrecht University and currently serves as Head of the Institute.

He has been actively engaged in computational finance since 2000, contributing extensively to research on numerical methods for financial mathematics.

He is the co-author of two widely recognized textbooks, "Multigrid" (2001) and "Mathematical Modeling and Computation in Finance" (2019).

His research contributions include the development of several innovative numerical techniques in financial derivative pricing and risk management, such as the COS method for Fourier cosine expansions, the SWIFT method based on the Shannon Wavelet Inverse Fourier Transform, the Stochastic Grid Bundling Method (SGBM), the Stochastic Collocation Monte Carlo Method (SCMC), and the Seven-League (7L) scheme for efficient pricing and risk evaluation. Beyond numerical finance, his research group is actively involved in applying machine learning to finance, with a focus on optimal portfolio selection, time series analysis, and anomaly detection.

Prof. Oosterlee has led EU-funded projects on risk management in finance and insurance, working closely with industry partners. Additionally, he has contributed to several Dutch national research initiatives. He has also been a guest lecturer at renowned institutions, including Oxford University in the UK, Hitotsubashi University in Japan, and the University of A Coruña in Spain.

Prof. dr. ir. C.W. (Kees) Oosterlee - Utrecht University

King Abdullah University of Science and Technology, KSA.

Website: Jinchao Xu | Computer, Electrical and Mathematical Sciences and Engineering

Title: Finite element and finite neuron methods

Abstract: In this talk, I discuss recent progress in understanding neural networks from the perspective of finite element methods, multigrid methods, and approximation theory. Specifically, I show that ReLU neural networks are mathematically equivalent to continuous, piecewise linear finite element functions, and that by introducing ReLU² activations, one can exactly represent higher-order finite element spaces on arbitrary polyhedral meshes. Moreover, inspired by multigrid methods, we developed MgNet, a convolutional neural network architecture demonstrating high computational efficiency. Additionally, from the viewpoint of approximation theory, I introduce recent work on Barron spaces and metric entropy, providing new perspectives on the expressive power and approximation capabilities of neural networks.

Khalifa University, UAE

Website: Prof. Hadi Susanto - Khalifa University

Bifurcation analysis and dynamics forecasting are fundamental to understanding complex systems, but traditional numerical methods can be computationally expensive and inefficient for high-dimensional or nonlinear problems. In this talk, I will present how neural networks offer a powerful alternative by significantly improving computational efficiency in detecting bifurcation points, characterizing stability changes, and forecasting system behavior. By leveraging data-driven models, neural networks can reduce computational costs while maintaining accuracy, making them a valuable tool for analyzing complex dynamical systems. I will discuss key methodologies, challenges, and applications, highlighting their potential to enhance bifurcation analysis and predictive modeling.