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Nonlinear dynamical systems such as Lorenz63 equations are known to bechaotic in nature and sensitive to initial conditions. As a result, a smallperturbation in the initial conditions results in deviation in state trajectoryafter a few time steps. The algorithms and computational resources needed toaccurately identify the system states vary depending on whether the solution isin transition region or not. We refer to the transition and non-transitionregions as unstable and stable regions respectively. We label a system state tobe stable if it's immediate past and future states reside in the same regime.However, at a given time step we don't have the prior knowledge about whethersystem is in stable or unstable region. In this paper, we develop and train afeed forward (multi-layer perceptron) Neural Network to classify the systemstates of a Lorenz system as stable and unstable. We pose this task as asupervised learning problem where we train the neural network on Lorenz systemwhich have states labeled as stable or unstable. We then test the ability ofthe neural network models to identify the stable and unstable states on adifferent Lorenz system that is generated using different initial conditions.We also evaluate the classification performance in the mismatched case i.e.,when the initial conditions for training and validation data are sampled fromdifferent intervals. We show that certain normalization schemes can greatlyimprove the performance of neural networks in especially these mismatchedscenarios. The classification framework developed in the paper can be apreprocessor for a larger context of sequential decision making framework wherethe decision making is performed based on observed stable or unstable states.

Lorenz System State Stability Identification using Neural Networks