Significance This article introduced in 2001 one of the very first successful applications of advanced machine learning techniques to solve complex, multicriteria management problems in water resources dealing with networks of water reservoirs. It applied approximate dynamic programming (here, neuro-dynamic programming - whose approximation of stochastic dynamic programming relies on artificial neural networks) to the integrated water resources management. The methodology is general enough to be potentially useful in other problems of integrated natural resources modelling and management (INRMM). Machine learning in water resources management: why. Efficiently and sustainably managing water resources is a challenging problem due to the variety of criteria to be considered, some of them conflicting (e.g. protecting human lives and economic assets from floods, supplying drinking water, water for agriculture and energy production, preserving ecosystems in lakes, rivers and canals along with their ecosystem services). Furthermore, the climate-driven influences on water systems (such as precipitation, snow accumulation/melt and runoff in river flow and floods, temperature and evapotranspiration in crop fields) are extremely nonlinear phenomena which require robust stochastic approaches. This led advanced machine learning techniques (e.g. stochastic dynamic programming) to become well-established solutions. Failing with complex water systems: the curse of dimensionality. The problem with dynamic programming is that its strong ability to cope with highly nonlinear problems has a limit in the number of dimensions that the modelled system requires. Systems demanding a high number of dimensions cause the computational cost of dynamic programming to explode. For example, water systems with several reservoirs fall within this category of high dimensionality. Renouncing to prohibitive exact solutions for exploring good approximated ones. Approximate dynamic programming greatly mitigates this problem: in this article, the approximation relies on artificial neural networks of a particular class (multilayer perceptron) with proved ability to approximate general, complex functions. Tests on a real-world water system confirmed here, for the first time, the extent of improvement. Abstract The management of a water reservoir can be improved thanks to the use of stochastic dynamic programming (SDP) to generate management policies which are efficient with respect to the management objectives (flood protection, water supply for irrigation and hydropower generation, respect of minimum environmental flows, etc.). The improvement in efficiency is even more remarkable when the problem involves a reservoir network, that is a set of reservoirs which are interconnected. Unfortunately, SDP is affected by the “curse of dimensionality” and computing time and computer memory occupation can quickly become unbearable. Neuro-dynamic programming (NDP) can sensibly reduce the demands on computer time and memory thanks to the approximation of Bellman functions with Artificial Neural Networks (ANNs). In this paper an application of neuro-dynamic programming to the problem of the management of reservoir networks is presented. Cite as: de Rigo, D., Rizzoli, A.E., Soncini-Sessa, R., Weber, E., Zenesi, P. (2001). Neuro-dynamic programming for the efficient management of reservoir networks. Proc. of MODSIM 2001, International Congress on Modelling and Simulation, vol. 4, pp. 1949-1954. DOI: 10.5281/zenodo.7481. ISBN: 0-867405252.

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