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: 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=714557
• 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.

本提案包括两个项目： 1.开发高频波传播问题的有效数值方案。 高频波传播的计算机模拟在地震、声波、电磁波和光波等许多应用中具有重要意义。这个问题通常用亥姆霍兹方程来模拟。关于常波数线性Helmholtz方程的求解，已有许多工作发表。相对而言，对于含有间断的变波数Helmholtz方程和非线性Helmohtz方程，可得到的结果较少。非线性问题和变化的波数出现在模拟克尔介质和电磁物理中的电磁波传播。我们的工作将集中在开发有效的计算算法来解决这些困难的问题。 2.为真实的世界问题集成模型、计算和数据 随着大量数据现在从商业，科学，工程，医疗保健和医学研究的广泛来源中定期生成和记录，我们计划探索如何利用现有数据来解决复杂问题。数据驱动方法与机器学习算法的结合已经成为某些应用的有力工具，但仍有许多问题没有解决。为了解决这一难题，我们考虑了另一种方法，即通过整合数学模型、科学计算和数据来解决真实的世界问题。这种新方法的解决方案将用于验证数据驱动方法的结果。为了证明该方法的有效性，我们研究了两个问题源于两个真实的应用：（1）化学品的毒性评估分类;（2）检测和预测异常的气动弹性响应。 该提案需要强大的HQP培训，在应用数学，科学计算和数据科学及其应用于真实的世界问题方面具有工作经验的学员在学术和工业部门的需求很高。