Biased sampling algorithms for scientific and engineering applications

本提案旨在扩展我们最近在提高偏差抽样方法的适用性，数值精度和计算效率方面的进展。这些技术有效地确定宏观变量，如能量或错误率，由许多具有随机波动状态的子系统组成的系统采用很少发生但物理上显著值的可能性。这是通过丢弃一定比例的模拟波动来实现的，这些波动使系统远离低概率区域。计算完成后，从有偏差的结果中提取出实际的宏观状态概率。为了对罕见事件的属性进行分类，并进一步估计给定的输入变量配置是否会产生不寻常的系统响应，我们将把有偏抽样与适当的机器学习和相关方法相结合。虽然所得到的算法将以磁性自旋系统的理想模型为基准，但我们将同时确保我们的研究继续与应用物理和工程直接相关，通过检查流体中极端事件的统计和行为，多通道相干光学系统和网络中的非线性补偿。明确地说，在固态物理中，我们之前已经开发了一种方法来研究Ising模型中的临界行为，该方法将Wolff聚类反转算法与有偏差采样的转移矩阵重新表述相结合。然而，在未来的工作中，我们将用一个类似但更一般的结构取代特定于ising的Wolff算法，该结构包含的组件变量数量明显少于感兴趣的系统。这将使相变的预测和分类以及大范围复杂线性和非线性系统和网络的极端统计成为可能。在流体力学中，我们将把机器学习技术与有偏抽样相结合，在不求解运动方程的情况下估计扰动结构的阻力系数。最后，我们将优化补偿多波长光通信系统中非线性效应的方法，通过根据组合偏置采样/机器学习算法确定的处方对传输信号进行预处理或对检测信号进行后处理。在这里，我们也将设计新的物理和计算改进，纳入非线性的定性物理模型。

This proposal seeks to extend our recent progress in enhancing the applicability, numerical accuracy and computational efficiency of biased sampling methods. These techniques efficiently determine the likelihood that macroscopic variables, such as the energy or error rate, of a system comprised of many subsystems with randomly fluctuating states adopt rarely occurring but physically significant values. This is achieved numerically by discarding a certain fraction of simulated fluctuations that displace the system away from the low probability region of interest. When the calculation is complete, the actual macroscopic state probabilities are extracted from the biased result. To classify the properties of rare events and further estimate if a given configuration of input variables will produce an unusual system response, we will integrate biased sampling with appropriate machine learning and related methods. While the resulting algorithms will be benchmarked against idealized models of magnetic spin systems, we will simultaneously insure that our research continues to be directly relevant to applied physics and engineering by examining the statistics and behavior of extreme events in fluids, nonlinearity compensation in multichannel coherent optical systems and networks. Explicitly, in solid-state physics we have previously developed a method for investigating critical behavior in the Ising model that combined the Wolff cluster reversal algorithm with a transition matrix reformulation of biased sampling. In future work, we will however replace the Ising-specific Wolff algorithm by an analogous but more general construct containing a significantly smaller number of component variables than the system of interest. This will enable the prediction and classification of phase transitions and extreme statistics over a wide range of complex linear and nonlinear systems and networks. In fluid mechanics, we will apply machine-learning techniques in combination with biased sampling to estimate e.g. the drag coefficient of a perturbed structure without solving the underlying equations of motion. Finally, we will optimize methods for compensating nonlinear effects in multi-wavelength optical communication systems by preprocessing the transmitted or post processing the detected signals according to a prescription determined by a combined biased sampling / machine-learning algorithm. Here we will as well devise novel physical and computational refinements that incorporate qualitative physical models of the nonlinearities.