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.

目前的提案包括两个项目： 1. 为高频波传播问题开发有效的数值方案。高频波传播的计算模拟在地震波、声波、电磁波和光波产生的许多应用中非常重要。该问题通常通过亥姆霍兹方程来建模。关于求解具有恒定波数的线性亥姆霍兹方程已经发表了许多工作。相比之下，对于包含不连续性的变波数亥姆霍兹方程和非线性亥姆霍兹方程，可用的结果较少。在克尔介质和地球物理学中的电磁波传播建模中会出现非线性问题和变化的波数。我们的工作将集中于开发有效的计算算法来解决这些难题。 2.针对现实世界问题集成模型、计算和数据现在，商业、科学、工程、医疗保健和医学研究等领域的各种来源都会定期生成和记录海量数据，我们计划探索如何将可用数据用于解决复杂问题。采用机器学习算法的数据驱动方法已成为某些应用的强大工具，但许多问题仍未解决。为了解决这个困难，我们考虑另一种方法，通过整合数学模型、科学计算和数据来解决现实世界的问题。这种新方法的解决方案将用于验证数据驱动方法的结果。为了证明这种方法的有效性，我们研究了源自两个实际应用的两个问题：（1）毒性评估中的化合物分类； (2)气动弹性响应异常的检测和预测。 该提案需要强有力的 HQP 培训，学术界和工业界对具有应用数学、科学计算和数据科学及其对现实世界问题的应用方面的工作经验的学员有很高的需求。