To improve the dynamic performance, this paper proposes a dual-mode digital controller with a high accuracy load current estimator and Gaussian adaptive duty cycle switching for DC-DC buck converters with an auxiliary power stage. The proposed digital controller has two operating modes: steady state and transient. In steady-state mode, a conventional PID control module is used to regulate the main power stage and the output voltage. In transient mode, a charge balance control module is responsible for controlling the auxiliary power stage to improve the dynamic performance. A long short-term memory (LSTM)-based load current estimator is proposed to obtain high accuracy load current. It employs a multiple-to-one structure and estimates the load current based on time series data (a sequence of data points indexed in time order). A Gaussian adaptive duty cycle switching is proposed to suppress the output voltage chattering when transitioning between the auxiliary and the main power stages. Simulation and experimental results demonstrate that the proposed controller has a superior dynamic performance when compared to controllers using linear-based load current estimator and direct duty cycle switching. The overshoot/undershoot and settling time can be reduced by over 50 % for a 1.9 A load transient in a 5 to 1.8 V buck converter operating switching at 2 MHz..