Predicting Stellar Mass Accretion: An Optimized Echo State Network Approach in Time Series Modeling

Modeling the dynamics of the formation and evolution of protostellar disks as well as the history of stellar mass accretion typically involve the numerical solution of complex systems of coupled differential equations. The resulting mass accretion history of protostars is known to be highly episodic due to recurrent instabilities and also exhibits short timescale flickering. By leveraging the strong predictive abilities of neural networks, we extract some of the critical temporal dynamics experienced during the mass accretion including periods of instability. Particularly, we utilize a novel form of the Echo-State Neural Network (ESN), which has been shown to efficiently deal with data having inherent nonlinearity. We introduce the use of Optimized-ESN (Opt-ESN) to make model-independent time series forecasting of mass accretion rate in the evolution of protostellar disks. We apply the network to multiple hydrodynamic simulations with different initial conditions and exhibiting a variety of temporal dynamics to demonstrate the predictability of the Opt-ESN model. The model is trained on simulation data of $\sim 1-2$ Myr, and achieves predictions with a low normalized mean square error ($\sim 10^{-5}$ to $10^{-3}$) for forecasts ranging between 100 and 3800 yr. This result shows the promise of the application of machine learning based models to time-domain astronomy.