Many relationships in physics, biology, chemistry, economics, engineering, etc., are defined by differential equations. In general, a differential equation (DE) describes how variables are affected by the rate of change of other variables. For instance, a DE explains how the position of a mass vibrating on spring changes with time in relation to the mass’s velocity and acceleration. A physics-informed neural network (PINN) produces responses that adhere to the relationship described by a DE (whether the subject is physics, engineering, economics, etc.). In contrast, an inverse physics-informed neural network (iPINN) acts on a response and determines the parameters of the DE that produced it. PINNs and iPINNs are trained by including a constraint during training that forces the relationship between the input and output of the neural network to conform to the DE being modeled.
