Physics-Informed Long-Short-Term Memory Neural Network for Parameters Estimation of Nonlinear Systems

This article proposes a physics-informed long-short-term memory neural network optimisation method to estimate all parameters of an arbitrary nonlinear system initialised using any initial conditions. Although the technique is applicable for parameters' estimation of any nonlinear system, in this article, two well-known chaotic systems are considered with different initial conditions. The three-dimensional Lorenz chaotic system and the four-dimensional Rössler hyperchaotic system are considered. The Lorenz system exhibits stable, chaotic and periodic behaviours for some sets of parameters. Thus, different sets of parameters of the Lorenz system are individually estimated, leading to stable, periodic and chaotic behaviours. In 10000 epochs, the stable and periodic parameters' estimation accuracy is more than 99%; in 15000 epochs, chaotic parameters' estimation accuracy is more than 99%. Upto same epochs, physics-informed neural network is employed for parameter estimation of stable, periodic and chaotic behaviours of the Lorenz system. The comparison results of estimated parameters are shown with dataset obtained using ode45. Next, Circuit realisation of the Lorenz system is done and the dataset is obtained using multisim circuit simulation for stable, chaotic and periodic behaviour. The proposed physics-informed long-short-term memory neural network is used to obtain parameters from the practical data. Then, the estimation of the Lorenz system with a continuum variation of parameters' sets from stable to chaotic to stable behaviours is successfully achieved using the proposed physics-informed long-short-term memory neural network. Finally, the hyperchaotic Rössler system parameters are successfully estimated using the proposed technique with more than 99% accuracy in 20000 epochs.