Enhancing Urban Flood Prediction Accuracy with Physics-Informed Neural Networks: A Case Study in Real-Time Rainfall Data Integration&#160;
Authors: Raeisi Sina , Piadeh Farzad , Behzadian Kourosh 
Published: March 2024

Urban flooding presents significant socio-economic challenges in cities, emphasising the need for effective flood forecasting [1]. Traditional flood prediction methods are data-intensive and time-consuming for calibration and computation. However, due to data scarcity and the necessity to account for real-time variable factors, Machine/Deep Learning (ML/DL) techniques are emerging as preferred solutions. These methods offer an advantage over slow, yet accurate, calibrated numerical models by handling limitations more efficiently [2]. More recently, a notable DL technique, called the Physics-Informed Neural Network (PINN), integrates physics understanding into the modeling process. This approach enables the model to incorporate physical principles into its inputs, enhancing its predictive capabilities despite limited data availability. Similar to other DL models, PINNs consist of an input layer, several hidden layers, and an output layer. However, as added value, the structure of these layers in PINN models varies based on the problem's nature and hyperparameters such as weights and biases are adjusted based on physical equations/roles/formula during the training phase to minimise the loss function [3]. Application of PINN models have been tasted widely in other contexts such as groundwater systems, climate prediction, energy systems, and waste management [4]. However, in the context of real-time flood early warning systems, this issue remains relatively novel.This study aims to develop a PINN model to detect flood events at specific points in an urban drainage system at the earlier timesteps of rainfall. The model employs the Horton equation applied to the rainfall hyetograph (both time-dependent) to process real-time data. This input allows the model to predict water level rises at certain points in the channel, identifying potential flooding. This new data is used as both input data and roles of bias adjusting during training model. The results show that by integrating physics-based rainfall inputs, accuracy of prediction have been significantly enhanced especially for longer timesteps in comparison to well-developed ML models.&#160;References:[1] Piadeh, F., Behzadian, K., Chen A., Campos L., Rizzuto J., Kapelan Z. (2023). Event-based decision support algorithm for real-time flood forecasting in urban drainage systems using machine learning modelling. Environmental Modelling &amp; Software, 167, p.105772.[2] Piadeh, F., Behzadian, K., Chen A., Kapelan, Z., Rizzuto, J., Campos, L. (2023). Enhancing urban flood forecasting in drainage systems using dynamic ensemble-based data mining. Water Research, 247, p.120791.[3] Raissi, M., Perdikaris, P., Karniadakis, G. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, pp. 686-707.[4] Li, H., Zhang, Z., Li, T., Si, X. (2024). A review on physics-informed data-driven remaining useful life prediction: Challenges and opportunities, Mechanical Systems and Signal Processing, 209, p.111120.