Related papers: The Role of Data in Model Building and Prediction:…

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…

Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines…

In this Chapter, I will explore the use of modeling in order to understand how Science works. I will discuss the modeling of scientific communities, providing a general, non-comprehensive overview of existing models, with a focus on the use…

Scientific research is a major driving force in a knowledge based economy. Income, health and wellbeing depend on scientific progress. The better we understand the inner workings of the scientific enterprise, the better we can prompt,…

Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…

Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban development, such models influence decisions that affect…

The large majority of inferences drawn in empirical political research follow from model-based associations (e.g. regression). Here, we articulate the benefits of predictive modeling as a complement to this approach. Predictive models aim…

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are…

We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty…

Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…

Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…

One of the main goals of scientific research is to provide a description of the empirical data which is as accurate and comprehensive as possible, while relying on as few and simple assumptions as possible. In this paper, I propose a…

Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…

Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…

In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in…

The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…

In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…

A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy,…

Challenges due to the rapid urbanization of the world -- especially in emerging countries -- range from an increasing dependence on energy, to air pollution, socio-spatial inequalities, environmental and sustainability issues. Modelling the…

Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…