Scientific machine learning for speeding up distributed simulations – examples and failures for urban water systems

In this work we illustrate how scientific machine learning algorithms (SciML) can be used to facilitate the development of digital twins for urban drainage systems. Scientific machine learning integrates classical, modelling techniques from scientific computing that are based on first principles, with data-driven machine learning techniques. The main objective is to create models that are robust, fast to run and easier to integrate with data, while largely preserving the level of detail of the widely used hydrodynamic modelling approaches. This concerns both a detailed spatial representation of the drainage system in the models, and an accurate representation of the hydraulics.

We present an initial approach that employs generalized residue networks for the simulation of hydraulics in drainage systems. The main idea is to train neural networks that learn how hydraulic states (level, flow and surcharge volume) at all nodes and pipes in the drainage network evolve from one time step to another, given a set of boundary conditions (surface runoff). The neural networks are trained against simulation results from a hydrodynamic model for a short time series, and achieve Nash-Sutcliffe model efficiency coefficients (NSE) in the order of 0.9 on a test dataset.

The approach achieves simulation times that are in the order of 50 times faster than the corresponding hydrodynamic model. This enables an automated calibration of HiFi model parameters and real-time data assimilation routines, both of which are tuned manually in current practice. We will demonstrate how the runoff parameters in a distributed drainage model can be efficiently calibrated against water level observations, and how an Ensemble Kalman Filter setup can be tuned automatically.

While our SciML setup for simulating drainage networks enables a range of new applications, its disadvantage are the initial training times in the order of 30 to 60 minutes for a system with approximately 100 drainage pipes. Many studies have demonstrated that machine learning approaches can be used to generalize across catchments if they consider physical system properties as an input or as part of the model architecture, and if they are presented with training data from different systems. Graph approaches are an obvious choice for the simulation of drainage systems and can be incorporated in the residue network setup. However, their architecture requires careful design to achieve an accurate simulation of the hydraulics, which is the subject of on-going research.