Modelling, Computing and Data Applications for Real World Problems

现实世界问题的建模、计算和数据应用

• 批准号: RGPIN-2019-04556
• 负责人: Wong, YauShu
• 金额: $ 1.24万
• 依托单位: University of Alberta
• 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=758368
• 关键词: Modelling; Computing; Data; Applications; Real

The present proposal consists of two projects: 1.Developing efficient numerical schemes for high frequency wave propagation problems. Computational simulation for high frequency wave propagation is important in many applications arising from seismic, acoustic, electromagnetic and optical waves. The problem is usually modelled by the Helmholtz equations. Many work has been published on solving linear Helmholtz equation with constant wave number. In contrast, there are fewer results available for Helmholtz equation with varying wave numbers containing discontinuities and the nonlinear Helmohtz equation. Nonlinear problems and varying wave numbers arise in modelling propagation of electromagnetic waves in Kerr media and geophysics. Our work will focus on developing efficient computational algorithms to solve these difficult problems. 2.Integrating model, computing and data for real world problems With massive data are now routinely generated and recorded from a wide range of sources in business, sciences, engineering, health care and medical research, we plan to explore how the available data can be utilized to solve complex problems. Data-driven method with the machine learning algorithm has emerged as a powerful tool for certain applications, but many questions remain unsolved. To address the difficulty, we consider another approach by integrating mathematical model, scientific computing and data to solve real world problems. The solution from this new approach will be used to validate the result from the data-driven method. To demonstrate the effectiveness of this approach, we examine two problems originated from two real applications: (1) chemical compounds classifications in toxicity assessment; (2) detection and prediction for anomaly in aeroelastic response. The proposal entails a strong HQP training, and trainees with working experience in applied mathematics, scientific computing and data sciences and its application for real world problems are in high demand in academic and industry sector.

本提案由两个项目组成：1。为高频波传播问题开发有效的数值方案。在地震，声学，电磁波和光波引起的许多应用中，高频传播的计算模拟很重要。该问题通常由Helmholtz方程建模。关于求解具有恒定波数的线性Helmholtz方程的许多工作。相比之下，对于Helmholtz方程的可用结果较少，其中包含不连续性和非线性Helmohtz方程的波浪数。非线性问题和不同的波数在建模Kerr培养基和地球物理中电磁波的传播时会出现。我们的工作将着重于开发有效的计算算法来解决这些困难问题。 2.现在常规生成和记录来自商业，科学，工程，医疗保健和医学研究的广泛来源的现实世界问题的整合模型，计算和数据，我们计划如何利用可用数据来解决复杂的问题。具有机器学习算法的数据驱动方法已成为某些应用程序的强大工具，但许多问题仍未解决。为了解决难度，我们通过整合数学模型，科学计算和数据来解决现实世界问题，从而考虑另一种方法。这种新方法的解决方案将用于验证数据驱动方法的结果。为了证明这种方法的有效性，我们研究了两个实际应用的问题：（1）化合物在毒性评估中分类； （2）气弹性反应中异常的检测和预测。 该提案需要进行强大的HQP培训，并且在应用数学，科学计算和数据科学方面具有工作经验及其在现实世界中的应用方面具有工作经验，在学术和行业领域的需求量很高。