Abstract:
A neural network (or artificial neural network) is a powerful tool that is being applied to more and more fields. Many of the end users, however, are more attracted by the algorithm terms such as neurons, hidden layers, backpropagation, etc., and failed to see the mathematics inside. This report is devoted to explaining the mathematical foundations of neural networks – the universal approximation theorem. And a step further, by introducing a practical example of the application of a physics-informed neural network in flow field measurement, I will discuss a slightly different application of it in solving a PDE.
Biography:
Zhuang Su got his bachelor's degree in mathematics from Sichuan University, China, and got his doctoral degree in fluid mechanics from Peking University specializing in experimental fluid mechanics. His research interests are vortical flows, turbulent mixing, and flow field measurement techniques. Zhuang Su joined NYU Shanghai in 2021 and now he is working in the applied mathematics lab.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai