AI 中文总结
该研究开发了学习记忆依赖型相关泛函的神经网络框架，经二维两电子体系测试，其性能优于标准泛函，为突破绝热近似提供了新策略。
AI 中文摘要
含时密度泛函理论虽在理论上是精确的，但实际应用中采用仅具有局部时间依赖性的交换-相关泛函的绝热近似。同时，精确的相关势在形式上依赖于包括电子密度时间序列在内的诸多量。本文开发了一种学习具有显式记忆依赖性的相关泛函神经网络模型的框架，该框架包含两种不同方法，均通过伴随优化关联。一种方法将泛函学习与反演解耦以获取相关势的真值；另一种方法直接学习泛函而无需反演。我们将这些方法应用于二维两电子体系的电子动力学建模，两种情况下均得到测试集传播误差较低的相关泛函，其性能比标准的局域密度近似和广义梯度近似泛函高出1至2个数量级。总体而言，该框架为突破绝热近似、开发能精确传播激发态和/或非平衡动力学的记忆依赖相关泛函提供了一种策略。
英文摘要
Time-dependent density functional theory, though exact in theory, is in practice applied in an adiabatic approximation using exchange-correlation functionals with only local temporal dependence. Simultaneously, the exact correlation potential formally depends on, among other quantities, the time-history of electron densities. Here we develop a framework to learn neural network models of correlation functionals that feature explicit memory-dependence. Our framework includes two different approaches, both linked through their use of adjoint-based optimization. One approach decouples the learning of the functional from inversion to find ground truth values of the correlation potential. The other approach learns the functional directly without requiring inversion. We apply these methods to modeling the electron dynamics of two-electron systems in two spatial dimensions. In both cases, our methods yield correlation functionals with low test set propagation error, outperforming standard local density and generalized gradient approximation functionals by one to two orders of magnitude. Overall, our framework points at one strategy to move beyond the adiabatic approximation and develop memory-dependent correlation functionals that yield accurate propagation for excited state and/or non-equilibrium dynamics.
Comments16 pages, 8 figures
