BYU

Abstract by Yajing Zhao

Personal Infomation


Presenter's Name

Yajing Zhao

Degree Level

Masters

Abstract Infomation


Department

Mathematics

Faculty Advisor

Jared Whitehead

Title

Predict Lorenz System Using Bayesian Approaches and Deep Learning

Abstract

Chaos is a common phenomenon in the real world. Examples includes: weather development and electronic circuits, etc. Chaos system is usually sensitive to initial condition. It's of great importance to study chaotic models. In this paper, we use both Bayesian Approaches and Deep Learning to predict the Lorenz system which is the first chaotic model.

Markov Chain Monte Carlo is used to predict the parameters of the Lorenz equations based on observations. Two algorithms Metropolis-Hastings with random walk and Hamiltonian Monte Carlo are implemented.

We also apply the deep learning to forecast the parameters and generate future states given a random initial condition. Specially, we experiment with recurrent neural network, a form of neural network with recurrent feedbacks, which is first proposed for natural language processing. Three algorithms, Elman RNN, Long short-term memory(LSTM), Gated recurrent unit(GRU) are used.

Finally, we'll compare the results from the above methods.