Building Digital Twins of Cities via Urban Theory-Informed Neural Networks

It is argued in this chapter that using purely data-driven approaches to learn and extrapolate city dynamics without any urban theory-imposed constraints could obtain results which may not conform to our theoretical understanding of the urban processes and inspire urban analysis and management. However, by imposing urban theories on neural network trainings, we can make data-driven learnings urban theory-informed and interpretable. Following the spirit of physics-informed neural networks, we can build urban theory-informed neural networks that can solve the forward problem, inverse problem, and equation discovery problem under various circumstances. For the forward problem, we solve the PDEs by constructing a neural network to approximate the solutions that respect the initial and/or boundary conditions of real-life problems. In the inverse problem, we attempt to infer about the inputs and conditions of the urban systems given some observational data about their outputs. For the equation discovery problem, we want to uncover the governing equations of urban dynamical systems from the observational data about the inputs and outputs. For efficient simulation and prediction, we can learn reduced-order models of highly nonlinear complex urban systems within the urban theory-informed framework. Real-life problems such as city traffic flows and urban microclimates are employed for substantiation. The chapter also suggests ways to optimize neural network architectures for urban theory-informed learning.