Neural Network Acceleration of the Nonlinear Schrödinger Equation and Its Quantum Implications

The SSFM is a widely used iterative solver for the one-dimensional NLSE, employed in the study of pulse propagation through optical fibers. This video discusses the Nonlinear Schrödinger Neural Network (NLSNN), a convolutional neural network for pulse reconstruction, trained on a ground truth dataset generated using the SSFM. In this study, we match the latency of the NLSNN with that of the SSFM, enabling a fair comparison of their performance. Our results demonstrate that the NLSNN outperforms the SSFM in terms of reconstruction accuracy under certain conditions. Intriguingly, this performance advantage varies with the complexity of the input data, providing valuable insights into the strengths and limitations of each approach. Furthermore, we explore the analytical correspondence between the quantum time-dependent Schrödinger equation (TDSE) and the NLSE. This correspondence bridges the gap between the time evolution of quantum wavefunctions and classical pulse propagation in optical fibers. As a result, our NLSNN approach also offers a path forward for an accelerated solver for the mapped TDSE, potentially opening new avenues for research in both nonlinear optics and quantum mechanics.