Solving PDEs with Neural Networks: A Case Study in the Slit-well Microfluidic Device

Speaker: Andrew Nagel (MCSC)

Room: SHA 356

Abstract: Partial differential equations (PDES) are mathematical models that can describe complex phenomena in many scientific disciplines. A new method for solving PDEs, known as the neural network method, is used to approximate solutions with deep neural networks (DNNs) by learning directly from the PDE problem statement. One of the appeals of this method is the ease with which it can obtain the solution to highly parameterized PDEs.

In this talk, I will highlight how the NNM is implemented by focusing on a case study that is representative of problems in biophysics research. Specifically, the method is used to obtain the solution to a PDE modelling nanoparticle passage through a microfluidic device known for its sorting capabilities. Typically, these types of problems are studied using particle simulations. However, to evaluate how the system changes when problem parameters like molecular size are modified, the particle simulations must be repeated many times. Instead, this talk overviews how the NNM can naturally be extended to express solutions to these problems as differentiable functions of their problem parameters.