Solving Differential Equations With Deep Neural Networks (DNNs)

Jaysa Grafton

This project utilizes deep neural networks to solve the Poisson and Ginzburg-Landau equations. Results for the Poisson equation show an accurate solution is acquired using a single layer network with no activation function due to linearity. For the Ginzburg-Landau equation, two loss functions are utilized with adjustments being made for boundary conditions and derivatives. Results indicate an accurate approximation for various mesh sizes and allow for comparison of architectures to determine the optimal network parameters.

Major: 
Mathematics
Exhibition Category: 
Physical Sciences
Exhibition Format: 
Poster Presentation
Campus: 
University Park
Faculty Sponsor: 
Leonid Berlyand
Poster Number: 
16658