Predictive Modeling of Light–Matter Interaction in One Dimension: A Dynamic Deep Learning Approach

Abstract

The mathematical modeling and the associated numerical simulation of the light–matter interaction (LMI) process are well-known to be quite complicated, particularly for media where several electronic transitions take place under electromagnetic excitation. As a result, numerical simulations of typical LMI processes usually require a high computational cost due to the involvement of a large number of coupled differential equations modeling electron and photon behavior. In this paper, we model the general LMI process involving an electromagnetic interaction medium and optical (light) excitation in one dimension (1D) via the use of a dynamic deep learning algorithm where the neural network coefficients can precisely adapt themselves based on the past values of the coefficients of adjacent layers even under the availability of very limited data. Due to the high computational cost of LMI simulations, simulation data are usually only available for short durations. Our aim here is to implement an adaptive deep learning-based model of the LMI process in 1D based on available temporal data so that the electromagnetic features of LMI simulations can be quickly decrypted by the evolving network coefficients, facilitating self-learning. This enables accurate prediction and acceleration of LMI simulations that can run for much longer durations via the reduction in the cost of computation through the elimination of the requirement for the simultaneous computation and discretization of a large set of coupled differential equations at each simulation step. Our analyses show that the LMI process can be efficiently decrypted using dynamic deep learning with less than 1% relative error (RE), enabling the extension of LMI simulations using simple artificial neural networks.