Machine and Deep Learning methods are gradually being integrated into industrial operations, although at different speeds for different types of industries. The aerospace and aeronautical industries have been recently pushing to develop a roadmap for concepts of design assurance and integration of neural network-related technologies in the aeronautical sector. Within such a roadmap, there is currently no clear definition of what would constitute a certifiable validation protocol for an industrial surrogate model. This paper aims to bridge this gap and contribute to the paradigm of AI-based certification in the context of supervised learning, by proposing a practical and comprehensible validation pipeline of a surrogate model that integrates concepts and methods from deep learning, mathematical optimization and statistical data science. This pipeline is represented as a directed graph of ten logical steps/nodes, incorporating both linear-sequential procedures and feedback loops to iteratively refine the surrogate model. Each of these logical steps solves specific machine learning problems by merging previously scattered key statistical methods with some novel algorithmic solutions. We provide details and best practices for each of the steps and we illustrate the application of this pipeline in a realistic supervised problem arising in aerostructural design: predicting the likelihood of different stress-related failure modes during different flight maneuvers based on a (large) set of features characterizing the aircraft internal loads and geometric parameters. • Novel 10-step validation pipeline for AI certification in aerospace. • Integration of ML, optimization & statistics for industrial application. • Computationally efficient algorithms for each pipeline step. • Applied to stress-related failure mode prediction in aircraft design.

The family of image visibility graphs (IVG/IHVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such\an operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibility graphs encapsulates relevant information on the structure of the images and we explore their potential as image filters. We introduce several graph features, including the novel concept of Visibility Patches, and show through several examples that these features are highly informative, computationally efficient and universally applicable for general pattern recognition and image classification tasks.

Although in the literature several Air Transportation Networks have been modeled through the mathematical framework of Complex Networks, less attention has been devoted to their evolution: specifically, topology is studied as static, excluding any schedule information. Simulating the growth of an air network is not an easy task, due to the great amount and heterogeneity of agents interacting (aircrafts, controllers and more). In this work we use a recently developed tool, called Scheduled Network, to define an algorithm to simulate such a growth; the basic assumption is that the cost for passengers should be minimized, which is approximated with the time needed to go from one airport to another one. Some results are presented, and the role and importance of hubs (that is, central airports where great part of the flights are concentrated) is discussed. INTRODUCTION The Air Transportation Network has been rapidly evolving in the last decades, mainly due to the many technological changes introduced: more efficient aircraft have modified any previous business perspective, giving birth for instance to low-cost airlines. The increment in the number of operations, and the consequent need for optimal investment strategy, is a significant challenge for regulation and control authorities: for example, Eurocontrol is forecasting a growth of up to 220% in the number of flights inside Europe in the time window 2005 − 2030 (STATFOR, 2008). Intuitively, the study of the structure of this network and the forecast of its evolution are extremely valuable tools for policy makers: but indeed are not easy tasks, due to the great number of agents interacting and to the complex interactions between them. Inside the Complex Science paradigm, we have chosen an instrument which simplifies that task, and we have adapted it to this context: that is, Complex Network theory. Complex Networks are mathematical objects with a simple definition (Boccaletti et al., 2006; Newman, 2003): nodes (which represent any kind of physical or virtual entities) connected through links (once again, any kind of relations) following a given topology. Exploiting this generality, many studies of the structure of real and virtual systems (Costa et al., 2008), and properties of such topologies (Costa et al., 2007) have been proposed. Although powerful, this network framework has an important drawback: the structure is considered as static, and does not include any time evolution. Let us show an example of how this can lead to some problematic consequences. In a previous work, Guimera (Guimera et al., 2005) constructed the network of worldwide flights by connecting two cities if there were a direct flight connecting them; no information regarding flights duration or allowed concatenations is therefore taken into account. For instance suppose that a customer has a flight at 12:00 from Stockholm to Paris, and another flight the same day from Paris to Toulouse at 13:00; clearly we cannot claim that Stockholm and Toulouse are connected in that time window by a path of length 2, as the passenger would be flying at 13:00 and would miss the second plane: he/she will have to wait until the next flight, maybe the following day. To overcome this class of problems, an extension of Complex Network which includes the time scheduling has been developed by the authors (Zanin et al., 2009). This Scheduled Networks approach allows dynamically activating links according to an external source of information: as a consequence, it is possible to directly study its topology and extract useful information, as mean rotation times and system efficiency. In this work, we have applied Scheduled Networks to several virtual air networks with the aim of forecasting their evolution. Initial conditions are defined as airport positions and flux of passengers between them: after that, links (that is, flights) are sequentially added to minimize an objective function which represents the cost for customers to travel across the network. The remainder of the work is organized as follows: first, an introduction to the mathematics of Scheduled Networks is presented; after that, several virtual networks are constructed, and some conclusions about the behavior of such systems is discussed. SCHEDULED NETWORKS The first step to construct an algorithm for simulating the growth of air traffic networks is to define an extension of Complex Networks which includes a time schedule. So, we start with the definition of a static directed network, Proceedings 23rd European Conference on Modelling and Simulation ©ECMS Javier Otamendi, Andrzej Bargiela, Jose Luis Montes, Luis Miguel Doncel Pedrera (Editors) ISBN: 978-0-9553018-8-9 / ISBN: 978-0-9553018-9-6 (CD) Figure 1: (Left) Representation of a simple directed network, which has been expanded (Center) to include a representation of time (i.e. the time needed to travel along a link). At the Right, both connections of the network are deactivated, by deleting the first link of each path. where n nodes are connected through links; those connections are represented in an adjacency matrix An×n, where the element aij has a value of 1 if there exists a link between nodes i and j, and zero otherwise (Bollobas, 2002). This structure is now transformed to include the time needed to travel a connection, as shown in Fig. 1. To the primary nodes, which correspond to the original nodes of the graph, some secondary nodes are added, that are used to delay movements according to the scheduling information. Those secondary nodes are virtual, as they do not exist in the real system under study, and represent the time length of each link. The new adjacency matrix is now the combination of a differential adjacency matrix dA, which is constant and represents one time step, and an Activation Matrix, which holds the scheduling information. The global adjacency matrix, and therefore dA, is a square matrix of n× n elements, where n is the sum of primary and secondary nodes (n = np + ns). To simplify the notation, S is constructed so that the primary nodes are represented first, followed by secondary ones. This new adjacency matrix is divided into four parts, as in Eq. 1. A = [ P R Act T ] (1) Within Graph theory, the adjacency matrix fully characterizes the set of allowed movements that a given agent can perform inside a network. In a similar way, each one of the four sub-networks has a specific function: • Persistence matrix (P): is a np × np identity matrix, which allows agents in a primary node to stay there indefinitely. • Activation Matrix (Act): this matrix represents the schedule of the network, and is dynamically updated at each time step. When a link is activated, agents are allowed to move from a primary node to the first secondary node of that link. • Reception Matrix (R): it moves an agent from the last secondary node of a link to the primary node which is the end of the link. • Transfer Matrix (T): this matrix moves agents in a secondary node to the next node of the same link, so that they can travel until the destination airport; in other words, it simulates the passage of time. A deeper explanation of how to construct the new Adjacency Matrix can be found in (Zanin et al., 2009), while an example of the resulting structure of the network of Fig. 1 can be found in the following matrix note that the link from B to C is activated: A =   1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0   (2) It is easy to chain together several adjacency matrices, to represent a whole time window. The static adjacency matrix is the same in each time step, and just the Activation Matrix is updated following the given schedule. Mathematically, it can be expressed as: A = A(t) · · ·A(t + δ − 1)A(t + δ) = (3) = t+1 ∏