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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=763135
• 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.

这项建议旨在扩大我们在提高有偏抽样方法的适用性、数值精度和计算效率方面的最新进展。这些技术有效地确定了由具有随机波动状态的许多子系统组成的系统的宏观变量(例如能量或错误率)采用很少出现但物理上有意义的值的可能性。这在数值上是通过丢弃一定比例的模拟波动来实现的，这些波动会使系统远离感兴趣的低概率区域。当计算完成时，从有偏差的结果中提取实际的宏观状态概率。为了对罕见事件的性质进行分类，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，但我们将同时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来确保我们的研究继续与应用物理和工程直接相关。显然，在固态物理学中，我们之前已经开发了一种方法来研究伊辛模型中的临界行为，该方法将Wolff簇反转算法与有偏抽样的转移矩阵重新公式相结合。然而，在未来的工作中，我们将用一种类似但更通用的结构来取代Ising特定的Wolff算法，该结构包含的组件变量数量比感兴趣的系统要少得多。这将使相变和极端统计在广泛的复杂线性和非线性系统和网络上的预测和分类成为可能。在流体力学中，我们将应用机器学习技术与有偏采样相结合来估计例如扰动结构的阻力系数，而不需要求解基本的运动方程。最后，我们将根据组合有偏采样/机器学习算法确定的处方，通过对发射信号进行预处理或对检测信号进行后处理，来优化多波长光通信系统中补偿非线性效应的方法。在这里，我们还将设计新的物理和计算改进，其中包括非线性的定性物理模型。