Neural network river forecasting with multi-objective fully informed particle swarm optimization

In this work, we suggest that the poorer results obtained with particle swarm optimization (PSO) in some previous studies should be attributed to the cross-validation scheme commonly employed to improve generalization of PSO-trained neural network river forecasting (NNRF) models. Cross-validation entails splitting the training dataset into two, and accepting particle position updates only if fitness improvements are concurrently measured on both subsets. The NNRF calibration process thus becomes a multi-objective (MO) optimization problem which is still addressed as a single-objective one. In our opinion, PSO cross-validated training should be carried out under an MO optimization framework instead. Therefore, in this work, we introduce a novel MO variant of the swarm optimization algorithm to train NNRF models for the prediction of future streamflow discharges in the Shenandoah River watershed, Virginia (USA). The case study comprises over 9,000 observations of both streamflow and rainfall observations, spanning a period of almost 25 years. The newly introduced MO fully informed particle swarm (MOFIPS) optimization algorithm is found to provide better performing models with respect to those developed using the standard PSO, as well as advanced gradient-based optimization techniques. These findings encourage the use of an MO approach to NNRF cross-validated training with swarm optimization.

Legitimising neural network river forecasting models: a new data-driven mechanistic modelling framework

In this paper we address the difficult problem of gaining an internal, mechanistic understanding of a neural network river forecasting (NNRF) model. Neural network models in hydrology have long been criticised for their black-box character, which prohibits adequate understanding of their modelling mechanisms and has limited their broad acceptance by hydrologists. In response, we here present a new, data-driven mechanistic modelling (DDMM) framework that incorporates an evaluation of the legitimacy of a neural network's internal modelling mechanism as a core element in the model development process. The framework is exemplified for two NNRF modelling scenarios, and uses a novel adaptation of first order, partial derivate, relative sensitivity analysis methods as the means by which each model's mechanistic legitimacy is explored. The results demonstrate the limitations of standard, goodness-of-fit validation procedures applied by NNRF modellers, by highlighting how the internal mechanisms of complex models that produce the best fit scores can have much lower legitimacy than simpler counterparts whose scores are only slightly inferior. The study emphasises the urgent need for better mechanistic understanding of neural network-based hydrological models and the further development of methods for elucidating their mechanisms.