In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time‐dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed‐up from the FNO method allows for its combination with the Markov‐chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes.

中文翻译：

---

通过机器学习加速波包传播


在这项工作中，我们讨论了最近引入的称为傅立叶神经算子 (FNO) 的机器学习 (ML) 技术的使用，作为与时间相关的薛定谔方程 (TDSE) 的传统解决方案的有效替代方案。 FNO 是用于偏微分方程近似解的 ML 模型。对于在非简谐势中传播的波包和隧道系统，我们表明 FNO 方法可以通过密度准确、忠实地模拟波包传播。此外，我们还证明，在重复需要量子动力学模拟结果的情况下，例如在参数优化问题（例如控制）的情况下，FNO 可以成为传统 TDSE 求解器的合适替代品。 FNO 方法的加速使其可以与马尔可夫链蒙特卡罗方法相结合，应用于涉及解决逆问题（例如动态过程结果的最优和相干激光控制）的应用中。