Modelling, Computing and Data Applications for Real World Problems

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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.