Studying the Propagation of Errors in a Lorenz System with a Global Prediction Algorithm

In this study, we investigate the increase in errors of a global prediction algorithm as it tries to predict values, in a chaotic system, that lie increasingly larger timestamps ahead in the future. Our approach involves training a neural network (global prediction algorithm) on the data points of a Lorenz Attractor, which is a deterministic yet chaotic system. We then give inputs to the trained neural network and try to make predictions about the state of the Lorenz Attractor, for future timestamps. It is found that the predicted error increases as the model makes predictions further into the future. The errors are visualized through a line graph to inspect the trend in the propagation of error. Our findings provide insights into the potential and limitations of using global prediction algorithms like neural networks for predicting the behavior of phenomena that are chaotic in nature.