Research Symposium

BIO

Joey Fishback is second year math major from West Palm Beach Florida. He is drawn to the aesthetics, rigor and relationships that math and FSU's math department offer "the people are the best part of math department". In his free time he enjoys, playing piano -both classical and jazz- and practicing with FSU club ultimate team. In the future he hopes to one day become a professor, to learn what it means to become a part of the living breathing body which is modern mathematics and to share that with others.

Comparing PINN to classical methods

Abstract

Physics Informed Neural Networks “PINN” developed by Maziar Raissi, Paris Perdikaris, George Em Karniadakis is a neural network architecture which includes physical laws - often in the form of an ordinary differential equation (ODE) or partial differential equation (PDE)- in the loss function. This research compares solutions of ordinary differential equations using PINN to classical methods such as RK4, RK6, forward Euler, backward Euler. The benefits and significance of PINN, lies in its mesh free nature and its effectiveness with limited training data as opposed to purely data driven approaches. To demonstrate using the ODE y’ = y with initial conditions y(0) = 1 we 1: find/create classical methods 2: create a PINN 3: compare them based on ease of implementation, accuracy and efficiency. Previous research on PINN suggests that in higher dimensional cases PINN will have an advantage over classical methods.

Keywords: math, Pinn, neural networks, computers