Revisiting the double-well problem by deep learning with a hybrid network

Solving physical problems by deep learning is accurate and efficient mainly accounting for the use of an elaborate neural network. We propose a novel hybrid network which integrates two different kinds of neural networks: LSTM and ResNet, in order to overcome the difficulty met in solving strongly-oscillating dynamics of the system's time evolution. By taking the double-well model as an example we show that our new method can benefit from a pre-learning and verification of the periodicity of frequency by using the LSTM network, simultaneously making a high-fidelity prediction about the whole dynamics of system with ResNet, which is impossibly achieved in the case of single network. Such a hybrid network can be applied for solving cooperative dynamics in a system with fast spatial or temporal modulations, promising for realistic oscillation calculations under experimental conditions.