论文标题
调整储层计算以求解Schrödinger方程
Adapting reservoir computing to solve the Schrödinger equation
论文作者
论文摘要
储层计算是一种机器学习算法，擅长预测时间序列的演变，尤其是动态系统。此外，它还显示出在求解部分微分方程方面出色的性能。在这项工作中，我们适应了这种方法来整合时间依赖性的schrödinger方程，从而在时间上传播初始波函数。由于此类波形是复杂的高维阵列，因此需要扩展储层计算形式主义以应对复杂值数据。此外，我们提出了一种多步学习策略，避免过度适合培训数据。我们通过将适用于分子振动动力学的四个标准问题应用于适应的储层计算方法的性能。
Reservoir computing is a machine learning algorithm that excels at predicting the evolution of time series, in particular, dynamical systems. Moreover, it has also shown superb performance at solving partial differential equations. In this work, we adapt this methodology to integrate the time-dependent Schrödinger equation, propagating an initial wavefunction in time. Since such wavefunctions are complex-valued high-dimensional arrays the reservoir computing formalism needs to be extended to cope with complex-valued data. Furthermore, we propose a multi-step learning strategy that avoids overfitting the training data. We illustrate the performance of our adapted reservoir computing method by application to four standard problems in molecular vibrational dynamics.
