Biased sampling algorithms for scientific and engineering applications

用于科学和工程应用的偏置采样算法

• 批准号: RGPIN-2020-03907
• 负责人: Yevick, David
• 金额: $ 1.75万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=716716
• 关键词: Biased; sampling; algorithms; scientific; engineering

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.

这一建议旨在扩大我们最近的进展，提高适用性，数值精度和计算效率的偏置抽样方法。 这些技术有效地确定宏观变量的可能性，如能量或错误率，由许多子系统随机波动状态的系统采用很少发生，但物理上有意义的值。 这是通过丢弃一定比例的模拟波动，使系统远离感兴趣的低概率区域的数字实现的。 当计算完成时，从有偏结果中提取实际宏观状态概率。 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，我们将把有偏采样与适当的机器学习和相关方法相结合。 虽然由此产生的算法将以磁自旋系统的理想化模型为基准，但我们同时将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，确保我们的研究继续与应用物理和工程直接相关。 解释，在固态物理学中，我们以前已经开发出一种方法，用于调查的关键行为的伊辛模型，结合沃尔夫集群反转算法与过渡矩阵重构的偏置采样。 然而，在未来的工作中，我们将用一个类似的但更一般的结构取代伊辛特定的沃尔夫算法，该结构包含比感兴趣的系统少得多的分量变量。 这将使预测和分类的相变和极端的统计在广泛的复杂的线性和非线性系统和网络。 在流体力学中，我们将应用机器学习技术结合有偏采样来估计例如扰动结构的阻力系数，而无需求解基本的运动方程。 最后，我们将优化方法，用于补偿多波长光通信系统中的非线性效应，通过预处理传输或后处理检测到的信号，根据处方确定的组合偏置采样/机器学习算法。 在这里，我们也将设计新的物理和计算的改进，将定性的非线性物理模型。