论文标题
贝叶斯对时间依赖性量子动态的反问题优化
Bayesian optimization for inverse problems in time-dependent quantum dynamics
论文作者
论文摘要
我们基于汉密尔顿参数和schrödinger方程的解决方案之间的反馈回路，证明了时间依赖性量子动力学反向问题的有效算法。我们的方法将反问题作为目标向量估计问题提出了反向问题，并使用Schrödinger方程解决方案的贝叶斯替代模型来指导反馈循环的优化。对于替代模型，我们将高斯流程与矢量输出和由带有贝叶斯信息标准（BIC）构建的矢量输出和复合内核作为内核选择度量。高斯工艺的输出旨在在不同时间实例中同时对可观察的模型进行建模。我们表明，使用矢量输出的高斯过程和BIC指导的内核结构的使用将反馈回路中的迭代次数减少至少3倍。我们还证明了贝叶斯对噪声数据的反相反问题的优化应用。为了证明算法，我们考虑了多原子分子的方向和比对，因此$ _2 $和手性丙烷氧化物（PPO）是由强激光脉冲引起的。我们使用取向或对齐信号的模拟时间演变来确定分子极化量张量的相关组件至1％的精度。我们表明，对于PPO的极化性张量的五个独立组件，可以使用30个量子动力学计算来实现这一目标。
We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schrödinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schrödinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduce the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO$_2$ and chiral propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors to within 1% accuracy. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.
