The main goal of this paper is to show that Bayesian optimization could be regarded as a general framework for the data driven modelling and solution of problems arising in water distribution systems. Hydraulic simulation, both scenario based, and Monte Carlo is a key tool in modelling in water distribution systems. The related optimization problems fall in a simulation/optimization framework in which objectives and constraints are often black-box. Bayesian Optimization (BO) is characterized by a surrogate model, usually a Gaussian process, but also a random forest and increasingly neural networks and an acquisition function which drives the search for new evaluation points. These modelling options make BO nonparametric, robust, flexible and sample efficient particularly suitable for simulation/optimization problems. A defining characteristic of BO is its versatility and flexibility, given for instance by different probabilistic models, in particular different kernels, different acquisition functions. These characteristics of the Bayesian optimization approach are exemplified by the two problems: cost/energy optimization in pump scheduling and optimal sensor placement for early detection on contaminant intrusion. Different surrogate models have been used both in explicit and implicit control schemes. Showing that BO can drive the process of learning control rules directly from operational data. BO can also be extended to multi-objective optimization. Two algorithms have been proposed for multi-objective detection problem using two different acquisition functions.

This paper is focused on two topics very relevant in water distribution networks (WDNs): vulnerability assessment and the optimal placement of water quality sensors. The main novelty element of this paper is to represent the data of the problem, in this case all objects in a graph underlying a water distribution network, as discrete probability distributions. For vulnerability (and the related issue of re-silience) the metrics from network theory, widely studied and largely adopted in the water research community, reflect connectivity expressed as closeness centrality or, betweenness centrality based on the average values of shortest paths between all pairs of nodes. Also network efficiency and the related vulnerability measures are related to average of inverse distances. In this paper we propose a different approach based on the discrete probability distribution, for each node, of the node-to-node distances. For the optimal sensor placement, the elements to be represented as dis-crete probability distributions are sub-graphs given by the locations of water quality sensors. The objective functions, detection time and its variance as a proxy of risk, are accordingly represented as a discrete e probability distribution over contamination events. This problem is usually dealt with by EA algorithm. We’ll show that a probabilistic distance, specifically the Wasserstein (WST) distance, can naturally allow an effective formulation of genetic operators. Usually, each node is associated to a scalar real number, in the optimal sensor placement considered in the literature, average detection time, but in many applications, node labels are more naturally expressed as histograms or probability distributions: the water demand at each node is naturally seen as a histogram over the 24 hours cycle. The main aim of this paper is twofold: first to show how different problems in WDNs can take advantage of the representational flexibility inherent in WST spaces. Second how this flexibility translates into computational procedures.

For the generation of representative volume elements a statistical description of the relevant parameters is necessary. These parameters usually describe the geometric structure of a single grain. Commonly, parameters like area, aspect ratio and slope of the grain relative to the rolling direction are applied. However, usually simple distribution functions like log normal or gamma distribution are used. Yet, these do not take the interdependencies between the microstructural parameters into account. To fully describe any metallic microstructure though, these interdependencies between the singular parameters need to be accounted for. To accomplish this representation, a machine learning approach was applied in this study. By implementing a Wasserstein generative adversarial network, the distribution, as well as the interdependencies could accurately be described. A validation scheme was applied to verify the excellent match between microstructure input data and synthetically generated output data.

Despite numerous studies in statistical downscaling methodology, there remains a lack of methods that can downscale from precipitation modeled in global climate models to regional level high resolution gridded precipitation. This paper reports a novel downscaling method using a Generative Adversarial Network (GAN), CliGAN, which can downscale large-scale annual maximum precipitation given by simulation of multiple atmosphere-ocean global climate models (AOGCM) from Coupled Model Inter-comparison Project 6 (CMIP6) to regional-level gridded annual maximum precipitation data. This framework utilizes a convolution encoder-dense decoder network to create a generative network and a similar network to create a critic network. The model is trained using an adversarial training approach. The critic uses the Wasserstein distance loss function and the generator is trained using a combination of adversarial loss Wasserstein distance, structural loss with the multi-scale structural similarity index (MSSIM), and content loss with the Nash-Sutcliff Model Efficiency (NS). The MSSIM index allowed us to gain insight into the model’s regional characteristics and shows that relying exclusively on point-based error functions, widely used in statistical downscaling, may not be enough to reliably simulate regional precipitation characteristics. Further use of structural loss functions within CNN-based downscaling methods may lead to higher quality downscaled climate model products.

Although the statistical methods of downscaling climate data have progressed significantly, the development of high-resolution precipitation products continues to be a challenge. This is especially true when interest centres on downscaling value over several study sites. In this paper , we report a new downscaling method termed the multi-site Climate Generative Adversarial Network (MSCliGAN), which can simulate annual maximum precipitation to the regional scale during the 1950-2010 period in different cities in Canada by using different AOGCM's from the Coupled Model Inter-Comparison Project 6 (CMIP6) as input. Auxiliary information provided to the downscaling model included topography and land-cover. The downscaling framework uses a convolution encoder-decoder U-net network to create a generative network and a convolution encoder network to create a critic network. An adversarial training strategy is used to train the model. The critic/discriminator used Wasserstein distance as a loss measure and on the other hand the generator is optimized using a summation of content loss on Nash-Shutcliff Model Efficiency (NS), structural loss on structural similarity index (SSIM), and adversarial loss Wasserstein distance. Downscaling results show that downscaling AOGCMs by incorporating topography and land-use/land-cover can produce spatially coherent fields close to observation over multiple-sites. We believe the model has sufficient downscaling potential in data sparse regions where climate change information is often urgently needed.