Physics Informed and Recursive Neural Networks for Ordinary Differential Equations

Abstract

The human brain is an amazing organ. This 3-pound mass of fats and proteins is able to take signals from all over the body, process those signals, and determine the best course of action, all instantly. The brain has the ability to learn, remember, and forget information throughout its lifetime. Brains have certain regions that handle certain tasks. This organ is being constantly studied and researchers are constantly finding out new information about this organ. Modern computer scientists have been trying to re-create this organ in a digital form. Computers are being programmed to take signals, in the form of data, process that data, transform the processed data into a new signal, and generate meaningful output. This is done with data processing, training, validating, and testing known sets of signals and desired outputs. Recently, the use of customizable loss functions gave rise to the subfield of Physics Informed Neural Networks (PINN) and using these Informed Neural Networks to estimate parameters of Ordinary Differential Equations (ODE). This paper will investigate and compare different network structures for this task.