This paper presents a completely data-driven and machine-learning-based approach, in two stages, to first characterize and then forecast hourly water demand in the short term with applications of two different data sources: urban water demand (SCADA data) and individual customer water consumption (AMR data). In the first case, reliable forecasting can be used to optimize operations, particularly the pumping schedule, in order to reduce energy-related costs, while in the second case, the comparison between forecast and actual values may support the online detection of anomalies, such as smart meter faults, fraud or possible cyber-physical attacks. Results are presented for a real case: the water distribution network in Milan.

Bayesian optimization has become a widely used tool in the optimization and machine learning communities. It is suitable to problems as simulation/optimization and/or with an objective function computationally expensive to evaluate. Bayesian optimization is based on a surrogate probabilistic model of the objective whose mean and variance are sequentially updated using the observations and an “acquisition” function based on the model, which sets the next observation at the most “promising” point. The most used surrogate model is the Gaussian Process which is the basis of well-known Kriging algorithms. In this paper, the authors consider the pump scheduling optimization problem in a Water Distribution Network with both ON/OFF and variable speed pumps. In a global optimization model, accounting for time patterns of demand and energy price allows significant cost savings. Nonlinearities, and binary decisions in the case of ON/OFF pumps, make pump scheduling optimization computationally challenging, even for small Water Distribution Networks. The well-known EPANET simulator is used to compute the energy cost associated to a pump schedule and to verify that hydraulic constraints are not violated and demand is met. Two Bayesian Optimization approaches are proposed in this paper, where the surrogate model is based on a Gaussian Process and a Random Forest, respectively. Both approaches are tested with different acquisition functions on a set of test functions, a benchmark Water Distribution Network from the literature and a large-scale real-life Water Distribution Network in Milan, Italy.

Visual pursuit marks substantial recuperation from a vegetative state and evolution into a minimally-conscious state, but its incidence in different studies suggests some unreliability in contrast with its established prognostic relevance. Subjects in vegetative ( n =9) or minimally-conscious ( n =13) states were tested for visual pursuit 6 times/day (9:30, 10:30, and 11:30 am , and 2:00, 3:00, and 4.00 pm , for a total of 132 determinations). Visual pursuit was observed at all testing times in 8 minimally-conscious patients, and never in 5 subjects in a vegetative state. Its incidence per subject ranged from 50–100% of testing times in the minimally-conscious state (83±23%), and 0–33% in a vegetative state (7%±12), with spontaneous fluctuations during the day and maximal levels at 10.30 am and 3.00 pm , and was never observed at the post-prandial time point (2:00 pm ). The overall chance of observing visual tracking at least once during the day was ∼33% in the vegetative state, whereas that of not observing it in the minimally-conscious state was ∼38%. These percentages are congruent with the reported misdiagnosis rate between the two conditions, and document spontaneous variability possibly related to circadian rhythms.

This paper presents a sequential model based optimization framework for optimizing a black-box, multi-extremal and expensive objective function, which is also partially defined, that is it is undefined outside the feasible region. Furthermore, the constraints defining the feasible region within the search space are unknown. The approach proposed in this paper, namely SVM-CBO, is organized in two consecutive phases, the first uses a Support Vector Machine classifier to approximate the boundary of the unknown feasible region, the second uses Bayesian Optimization to find a globally optimal solution within the feasible region. In the first phase the next point to evaluate is chosen by dealing with the trade-off between improving the current estimate of the feasible region and discovering possible disconnected feasible sub-regions. In the second phase, the next point to evaluate is selected as the minimizer of the Lower Confidence Bound acquisition function but constrained to the current estimate of the feasible region. The main of the paper is a comparison with a Bayesian Optimization process which uses a fixed penalty value for infeasible function evaluations, under a limited budget (i.e., maximum number of function evaluations). Results are related to five 2D test functions from literature and 80 test functions, with increasing dimensionality and complexity, generated through the Emmental-type GKLS software. SVM-CBO proved to be significantly more effective as well as computationally efficient.

Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt concerning a certain performance metric. Prompt optimization can be considered as a combinatorial optimization problem, with the number of possible prompts (i.e., the combinatorial search space) given by the size of the vocabulary (i.e., all the possible n-grams) raised to the power of the length of the prompt. Exhaustive search is impractical; thus, an efficient search strategy is needed. We propose a Bayesian Optimization method performed over a continuous relaxation of the combinatorial search space. Bayesian Optimization is the dominant approach in black-box optimization for its sample efficiency, along with its modular structure and versatility. We use BoTorch, a library for Bayesian Optimization research built on top of PyTorch. Specifically, we focus on Hard Prompt Tuning, which directly searches for an optimal prompt to be added to the text input without requiring access to the Large Language Model, using it as a black-box (such as for GPT-4 which is available as a Model as a Service). Albeit preliminary and based on “vanilla” Bayesian Optimization algorithms, our experiments with RoBERTa as a large language model, on six benchmark datasets, show good performances when compared against other state-of-the-art black-box prompt optimization methods and enable an analysis of the trade-off between the size of the search space, accuracy, and wall-clock time.