Abstract:
Open session.

Chair: Kirstof Cools and Le Van Chien (Ghent University)

Abstract:
The rapidly rising variety of acoustic and electromagnetic applications has demanded the high-precision computing capacity of wave equations in complicated scenarios, for instance, modelling and analyzing systems in the presence of wide bandwidth data, large-scale, multi-scale and multi-physics geometries with complex material properties. This demand has accelerated the critical need for studies of robust, stable and highly efficient computational methods, necessitating more and more efforts from both mathematicians, physicists, computer scientists, and engineers. Within this mini symposium, we aim to bring together international experts in the field of numerical and computational methods for acoustic and electromagnetic wave equations to discuss the latest research and knowledge, explore challenges and new directions, as well as to foster interaction and collaboration between communities. The topics of this mini symposium cover both frequency-domain and time-domain challenges, with a particular focus on finite and boundary element methods.

Chair: Minseok Choi (Pohang University of Science and Technology) and Jooyoung Hahn (Slovak University of Technology in Bratislava)

Abstract:
This symposium addresses recent developments and persistent challenges in using neural network solvers for partial differential equations (PDEs), with a particular focus on the limitations and potential of physics-informed neural networks (PINNs). Despite their innovative approach, PINNs often face significant hurdles such as poor convergence, dependency on large data sets, and difficulties in generalizing across different types of PDEs. The session will examine how integrating classical mathematical concepts and numerical methods has begun to overcome these issues, enhancing the robustness and accuracy of neural network approaches. The discussion will highlight the latest adaptations in neural networks that incorporate advanced sampling strategies, optimization of network architectures, and novel training techniques that reduce the computational burden. Additionally, the symposium will present specific applications where modified PINNs have shown improved performance in solving complex, nonlinear PDEs in real-time scenarios, and in sensor placement strategies that optimize data acquisition in sparse environments. By bringing together diverse perspectives from applied mathematics and engineering, the session aims to provide a comprehensive understanding of how traditional numerical methods can be seamlessly integrated with modern machine learning techniques to address some of the most challenging problems in scientific computing.