A benchmark-based method for evaluating hyperparameter optimization techniques of neural networks for surface water quality prediction

Highlights

● Manually adjustment of hyperparameters is highly random and computational expensive.

● Five HPO techniques were implemented in surface water quality prediction NN models.

● The proposed benchmark-based method for HPO evaluation is feasible and robust.

● TPE-based BO was the recommended HPO method for its satisfactory performance.

Abstract

Neural networks (NNs) have been used extensively in surface water prediction tasks due to computing algorithm improvements and data accumulation. An essential step in developing an NN is the hyperparameter selection. In practice, it is common to manually determine hyperparameters in the studies of NNs in water resources tasks. This may result in considerable randomness and require significant computation time; therefore, hyperparameter optimization (HPO) is essential. This study adopted five representatives of the HPO techniques in the surface water quality prediction tasks, including the grid sampling (GS), random search (RS), genetic algorithm (GA), Bayesian optimization (BO) based on the Gaussian process (GP), and the tree Parzen estimator (TPE). For the evaluation of these techniques, this study proposed a method: first, the optimal hyperparameter value sets achieved by GS were regarded as the benchmark; then, the other HPO techniques were evaluated and compared with the benchmark in convergence, optimization orientation, and consistency of the optimized values. The results indicated that the TPE-based BO algorithm was recommended because it yielded stable convergence, reasonable optimization orientation, and the highest consistency rates with the benchmark values. The optimization consistency rates via TPE for the hyperparameters hidden layers, hidden dimension, learning rate, and batch size were 86.7%, 73.3%, 73.3%, and 80.0%, respectively. Unlike the evaluation of HPO techniques directly based on the prediction performance of the optimized NN in a single HPO test, the proposed benchmark-based HPO evaluation approach is feasible and robust.

Graphical abstract

Keywords

Neural networks / Hyperparameter optimization / Surface water quality prediction / Bayes optimization / Genetic algorithm

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Acknowledgements

This study was financially supported by the National Key R&D Project (No. 2022YFC3203203) and the Shaanxi Province Science Fund for Distinguished Young Scholars (No. S2023-JC-JQ-0036).

Conflict of Interests

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11783-024-1814-5 and is accessible for authorized users.

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