Automatically extracting knowledge from small datasets with a valid causal ordering is a challenge for current state-of-the-art methods in machine learning. Extracting other type of knowledge is important but challenging for multiple engineering fields where data are scarce and difficult to collect. This research aims to address this problem by presenting a machine learning-based modeling framework leveraging the knowledge available in fundamental units of the variables recorded from data samples, to develop parsimonious, explainable, and graph-based simulation models during the early design stages. The developed approach is exemplified using an engineering design case study of a spherical body moving in a fluid. For the system of interest, two types of intricated models are generated by (1) using an automated selection of variables from datasets and (2) combining the automated extraction with supplementary knowledge about functions and dimensional homogeneity associated with the variables of the system. The effect of design, data, model, and simulation specifications on model fidelity are investigated. The study discusses the interrelationships between fidelity levels, variables, functions, and the available knowledge. The research contributes to the development of a fidelity measurement theory by presenting the premises of a standardized, modeling approach for transforming data into measurable level of fidelities for the produced models. This research shows that structured model building with a focus on model fidelity can support early design reasoning and decision making using for example the dimensional analysis conceptual modeling (DACM) framework.

In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412]. We study a random walk in ${\mathbb Z}^2$ with random orientations.We suppose that the orientation of the kth flooris given by $\xi_k$ , where $(\xi_k)_{k\in\mathbb Z}$ isa stationary sequence of random variables.Once the environment fixed, the random walk can goeither up or down or can stay in the present floor (but moving with respect to its orientation).This model was introduced by Campanino and Pétritisin [Markov Process. Relat. Fields 9 (2003) 391–412] whenthe $(\xi_k)_{k\in\mathbb Z}$ is a sequence ofindependent identically distributed random variables. In [Theory Probab. Appl. 52 (2007) 815–826], Guillotin-Plantard and Le Ny extend thisresult to a situation where the orientations of the floors are independentbut chosen with stationary probabilities (not equal to 0and to 1). In the present paper, we generalize the result of [Markov Process. Relat. Fields 9 (2003) 391–412]to some cases when $(\xi_k)_k$ is stationary. Moreover we extend slightlya result of [Theory Probab. Appl.52 (2007) 815–826].

We investigate a random collision model for competition between types of individuals in a population. There are dominance relations defined for each pair of types such that if two individuals of different types collide then after the collision both are of the dominant type. These dominance relations are represented by an oriented graph, called a tournament. It is shown that tournaments having a particular form are relatively stable, while other tournaments are relatively unstable. A measure of the stability of the stable tournaments is given in the main theorem.