In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures.

The real-time control optimization of electrified vehicles is one of the most demanding tasks to be faced in the innovation progress of low-emissions mobility. Intelligent energy management systems represent interesting solutions to solve complex control problems, such as the maximization of the fuel economy of hybrid electric vehicles. In the recent years, reinforcement-learning-based controllers have been shown to outperform well-established real-time strategies for specific applications. Nevertheless, the effects produced by variation in the reward function have not been thoroughly analyzed and the potential of the adoption of a given RL agent under different testing conditions is still to be assessed. In the present paper, the performance of different agents, i.e., Q-learning, deep Q-Network and double deep Q-Network, are investigated considering a full hybrid electric vehicle throughout multiple driving missions and introducing two distinct reward functions. The first function aims at guaranteeing a charge-sustaining policy whilst reducing the fuel consumption (FC) as much as possible; the second function in turn aims at minimizing the fuel consumption whilst ensuring an acceptable battery state of charge (SOC) by the end of the mission. The novelty brought by the results of this paper lies in the demonstration of a non-trivial incapability of DQN and DDQN to outperform traditional Q-learning when a SOC-oriented reward is considered. On the contrary, optimal fuel consumption reductions are attained by DQN and DDQN when more complex FC-oriented minimization is deployed. Such an important outcome is particularly evident when the RL agents are trained on regulatory driving cycles and tested on unknown real-world driving missions.

In cooperative game theory, associated games allow for providing meaningful characterizations of solution concepts. Moreover, generalized values allow computing an influence or power index of each coalition in a game. In this paper, we view associated games through the lens of game maps and we define the novel Shapley-Hodge Game, briefly ``SHoGa''. We characterize SHoGa via an axiomatic approach as a generalized value, and we thoroughly discuss the consistency properties of its associated game. Furthermore, we describe the Hodge decomposition of an oriented graph representing the transitive closure of the Hasse diagram of coalitions in the game. Finally, we show how SHoGa is linked to the solution of the Poisson equation derived from such a decomposition.