Abstract

In this presentation, I will discuss two recent advancements in my group’s research on Wiener-Hopf modelling and applications. First, we embed Cauchy-Riemann equations into machine learning architectures using so-called mathematics-informed neural networks (MINN). By integrating Cauchy integrals and boundary conditions, the neural network effectively learns to numerically generate 2×2 matrix kernel factorization for Wiener-Hopf analytical models. We validate this approach by comparing machine learning results with existing analytical solutions using a benchmark case of wave scattering from parallel hard-soft plates.  Second, we develop a Wiener-Hopf model to sound radiation from an elliptic duct, which has garnered interest in the context of modern blended-wing-body designs for eco-friendly aviation. We represent the incident and scattered sound fields using Mathieu functions in elliptic cylindrical coordinates and validate the achieved Wiener-Hopf analytic model by comparing with FEM results.  Lastly, I will provide a brief introduction (travel, venue, Visa matters, etc.) of Hangzhou, China, the scenic city Marco Polo once described as “greater than any in the world”, for the upcoming Wiener-Hopf workshop in November. My co-authors, Mr. Sicong Liang and Mr. Ruichen Wang, will attend INI ’s workshop and be available to share more information about these topics.