School of Science Department of Mathematics 42 Geometric Flows Supervisor: FONG Tsz Ho / MATH Student: WU Sen Yuk / MATH-IRE Course: UROP 1100, Summer This is a review of harmonic map between manifolds and the application of the harmonic map heat flow. The harmonic map has crucial application in 2 dimensional manifolds, for example, minimal surfaces and Riemann surfaces. And there is more useful application to the rigidity and vanishing theorem by using the harmonic map heat flow. In this report, we will focus on the application of harmonic map heat flow and the recent results. A Machine Learning Approach to Study the Relationship Between Urban Morphology and Urban Heat Island Supervisor: FUNG Jimmy Chi Hung / MATH Student: MOK Wan Hin / MATH-IRE Course: UROP 4100, Fall In the previous semesters, we explored the usage of random forest (RF) and multilayer perceptron (MLP) in quantifying the urban heat island (UHI) effect by predicting yearly-averaged and daily land surface temperatures (LST) based on static data, including geographical and urban morphological variables. This semester (Fall 2023), in preparation for publishing our previous research work, a literature review was done to explore the research gaps that our previous work had addressed. Then, using a more systematic approach, the previous results were reproduced with minor methodology changes. This report serves as a summary of our previous research results. It will also contribute to the content of the draft of the paper to be published. A Machine Learning Approach to Study the Relationship Between Urban Morphology and Urban Heat Island Supervisor: FUNG Jimmy Chi Hung / MATH Student: PHAM Nguyen Nhat Minh / DSCT Course: UROP 1000, Summer Deep learning models have the ability to effectively forecast air pollution data for individual stations by encoding time series data. In this study, transformer architecture was applied for O3 forecasting by incorporating a deep learning layer with encoder-decoder architecture. The Informer model can efficiently handle long input sequences to get highly accurate predictions. It can be achieved by studying the relevant temporal and spatial patterns of the input data. The novel structure of Informer, such as the encoder, the decoder and the attention mechanism, allow it to capture the complex relationships in long time-series data more effectively compared to standard Transformer models. To elucidate the process of this model, O3 was gained from ground observation data and Community Multiscale Air Quality model (CMAQ) as the inputs to predict for next 5 day. In summary, 2 approaches were implemented: Directly forecasting O3 Concentration and forecasting the model O3 bias. Second approach even showed better performance than CMAQ model, with a higher Index of Agreement (IOA) and a 10% lower root mean square error (RMSE).
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