PHYSICS INFORMED NEURAL NETWORK ON DIFFERENTIAL EQUATIONS - Almira Suheri, Fidya
This final project aims to search for an approximate numerical solution of a differential equation using the Physics Informed Neural Network (PINN) method. This method uses a deep learning approach, namely, an artificial neural network. In the process of building a model, it takes information on initial value problems and boundary conditions in the related differential equations to build an objective function that will be optimized in the model. There are several things to consider when building a model using artificial neural networks, such as nodes, activation functions, and hidden layers. Based on the simulation results, the difference in the use of the number of nodes and the activation function will affect the results of the approximate solution. The model that has been built will be evaluated so that the optimal model is obtained and the numerical approximation solution will be closer to the analytical solution. Furthermore, the most optimal model will be used in numerical continuation simulations to see the bifurcation diagram of the differential equations. The Physics Informed Neural Network (PINN) model is used to find approximate solutions to ”kubik” and ”kubik kuintik” equations. The artificial neural network is built using one hidden layer with 30 nodes and the softplus activation function. Based on the simulation results, the PINN model can approach the ”kubik” and ”kubik kuintik” equation solutions pretty good. In addition, the simulation of numerical continuity on the PINN model can produce a bifurcation phenomenon when using a relatively small value of c.