Physics-informed neural networks as surrogate models of hydrodynamic simulators

In response to growing concerns surrounding the relationship between climate change and escalating flood risk, there is an increasing urgency to develop precise and rapid flood prediction models. Although high-resolution flood simulations have made notable advancements, they remain computationally expensive, underscoring the need for efficient machine learning surrogate models. As a result of sparse empirical observation and expensive data collection, there is a growing need for the models to perform effectively in 'small-data' contexts, a characteristic typical of many scientific problems. This research combines the latest developments in surrogate modelling and physics-informed machine learning to propose a novel Physics-Informed Neural Network-based surrogate model for hydrodynamic simulators governed by Shallow Water Equations. The proposed method incorporates physics-based prior information into the neural network structure by encoding the conservation of mass into the model without relying on calculating continuous derivatives in the loss function. The method is demonstrated for a high-resolution inland flood simulation model and a large-scale regional tidal model. The proposed method outperforms the existing state-of-the-art data-driven approaches by up to 25 %. This research demonstrates the benefits and robustness of physics-informed approaches in surrogate modelling for flood and hydroclimatic modelling problems.