Application of Scientific Machine Learning Methods in Epidemical Modeling: Undetected COVID-19 Population Ratio Prediction
Date
2023-08-31
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Combining deep learning techniques with mathematical models can compensate for the drawbacks of each method. Deep learning methods can help increase accuracy, while mathematical models can save computational costs by constraining the neural network (NN) structure. The combined method is efficient for capturing the dynamics of real-life data with a small sample size. In addition, the trained model can be sparsely regressed to a concise parametric model using data-driven methods for learning the mechanics, and used for prediction. In this thesis we focus on the application to epidemic modelling. Some theoretical background is introduced in Chapter 1. In Chapter 2, the methodology for developing scientific learning model on epidemic population data is explained. Discrete time-shifting is considered because of the latent detection of infected population. The undetected rate is modelled in two ways: using a constant detection rate, and by involving the detection rate as an output of the NN. The trained models are regressed to the dynamic systems via SINDy for learning the terms, and for prediction. In Chapter 3, we apply the model to the first wave of COVID-19 in Calgary where the data only contains 12 points of weekly detected infected population. In Chapter 4, the model is extended to the first wave of COVID-19 in Canada, where there is training data containing 18 weeks of the detected infected population and the deceased population. In Chapter 5, some conclusions are drawn and the future potential of this method is discussed.
Description
Keywords
Epidemical Modeling, Universal Differential Equations, Deep Learning, Data-driven Methods
Citation
Liu, X. (2023). Application of scientific machine learning methods in epidemical modeling: undetected COVID-19 population ratio prediction (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.