Abstract by Yajing Zhao
Predict Chaotic Models with Machine Learning
Chaos theory studies non-linear dynamic systems that are highly sensitive to its initial states, and it has extensive real-world applications. Lorenz system, defined by three ordinary differential equation, is one of the simplest and most well-known chaotic systems. As deep learning arises as the dominating learning scheme in the machine learning and pattern recognition community, we argue that deep learning can be a useful tool to study the Lorenz system. We formulate the above problem as a classical sequence prediction task in machine learning and propose to use Recurrent Neural Network (RNN) to tackle it. We implement several RNN architectures and they attain satisfying results on a large scale dataset we collected. A more interesting research direction is the inverse problem, where we infer the three parameters from the observed states of the Lorenz system. This can be seen as the parameter estimation task in machine learning. We propose two algorithms: Markov chain Monte Carlo (MCMC), a classical Bayesian inference tool for inverse problem (parameter estimation), and a Multi-layer Perceptron (MLP) model.