  Risk assessment for extreme events requires accurate estimation of high
quantiles that go beyond the range of historical observations. When the risk
depends on the values of observed predictors, regression techniques are used to
interpolate in the predictor space. We propose the EQRN model that combines
tools from neural networks and extreme value theory into a method capable of
extrapolation in the presence of complex predictor dependence. Neural networks
can naturally incorporate additional structure in the data. We develop a
recurrent version of EQRN that is able to capture complex sequential dependence
in time series. We apply this method to forecast flood risk in the Swiss Aare
catchment. It exploits information from multiple covariates in space and time
to provide one-day-ahead predictions of return levels and exceedance
probabilities. This output complements the static return level from a
traditional extreme value analysis, and the predictions are able to adapt to
distributional shifts as experienced in a changing climate. Our model can help
authorities to manage flooding more effectively and to minimize their
disastrous impacts through early warning systems.
