Nonlinear dynamical systems are widely seen in various systems, ranging from climate to biological systems. In several applications, we only have access to the observed time series, and we lack knowledge of the exact governing equations. For practical applications, we are often interested in forecasting the dynamics of these systems. We aim to leverage deep learning models to solve the above mentioned problem.
One interesting work in this line is the Hamiltonian Neural Network, which is applicable to systems where energy is conserved. Another interesting work is the Multistep Neural Network, which is more general than Hamiltonian Neural Networks. In our project, we consider the following benchmark problems: i) spring-mass system, ii) the three-body problem in mechanics and iii) the Lorenz system (chaotic nonlinear dynamical system applicable to weather data). In our project, we compare the performance of LSTM, HNN and multistep neural networks.
