Abstract: In this work, we propose a physics-informed Echo State Networks (ESN) to predict the evolution of chaotic systems. Compared to conventional echo state networks, the physics-informed ESN are trained to solve supervised learning tasks while ensuring that their predictions do not violate the given physical laws. This is done by introducing an additional loss during the training of the ESN, which penalizes non-physical predictions by the ESN. The potential of this approach is demonstrated on the Lorenz system where the obtained predictability horizon of the physics-informed ESN was improved by up to nearly 2 Lyapunov times compared to conventional ESN without the need of additional training data. These results illustrate the potential of using machine learning tools combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.

Abstract: Recent use of satellite synthetic aperture radar (SAR) images in flood forecasting has allowed assimilation of spatially dense observations over large rural areas into flood forecasting models. This rich source of observational information has offered a valuable improvement in flood forecasting accuracy as the instruments are able to image day and night, and can see through clouds. However, in urban areas, the use of SAR data is limited due to building shadows and layover effects. Hence, in urban areas it is even more important to use observational data to constrain hydrodynamic flood models, due to the complexity of the landscape and interactions with buildings, sewers, rivers etc. To increase the amount of observation data available in urban areas, and to make use of abundance of technology in cities, our research is concentrating on using novel and easily available data from cities such as CCTV camera images. We have carried out an initial investigation into the impact of assimilating such data on flood forecasts. Our experiments used water level observations extracted from river camera images from four Farson Digital Ltd cameras, for a flood event near Tewkesbury, UK in 2012. We show that these data can improve flood forecast accuracy, especially as they capture the rising limb of the flood when satellite data is usually unavailable. However, in our initial experiments we used manual water level extraction and quality control for the observations, due to complications with the camera settings, image processing, and various digital terrain map resolutions and accuracies. Our next aim is to use machine learning to automatically extract water levels from CCTV images, with associated observation uncertainty. Machine learning will allow us to obtain and use real time water observations from images on a large scale, especially in complex systems such as cities, and we will discuss the potential of this approach.

Abstract: Ensemble Kalman filter (EnKF) has proven successful in assimilating observations of large-scale dynamical systems, such as the atmosphere, into computer simulations for better predictability. Due to the fact that a limited-size ensemble of model states is used, sampling errors accumulate, and manifest themselves as long-range spurious correlations, leading to filter divergence. This effect is alleviated in practice by applying covariance localization. This work investigates the possibility of using machine learning algorithms to automatically tune the parameters of the covariance localization step of ensemble filters. Numerical experiments carried out with the Lorenz96 model reveal the potential of the proposed machine learning approaches.