Introduction to Mathematical and Computational Modelling for Sustainability - Third Edition

Module 1
- Overview of Modelling
- Differential equation based models
- Numerical Methods for partial differential equations
Module 2
- Finite Dynamical systems - Markov Chains
- Cellular automata/Agent-based models
- Stochastic modelling, Monte Carlo methods
Module 3
- Introduction to Machine Learning – Classification, Regression problems and physics-informed neural networks
- Constraint Modeling and Constraint solving
- Local Search and Metaheuristics

- Familiarization with fundamental approaches to mathematical and computational modeling methods, techniques and tools, including differential equations, machine learning/AI, finite difference/element/volumetric methods, cellular automata and optimization algorithms.
- Develop awareness of methods that may be suitable for different types of research problems, together with the potential benefits, challenges and limitations of each approach
- Develop skills in application of these methods to real-world multidisciplinary research problems aligned to the EU Green themes
- Develop student transferable skills in group working and communication;
- Help to create a culture of international and cross-discipline collaboration in postgraduate research at the EU Green institutions

Postgraduate students will develop skills in translating broad-ranging real-world problems in a mathematical/computational framework and be familiar with fundamental tools in analysing models for problem solving, particularly in the context of sustainability. The programme will focus on familiarity with different methods, their potential applications and their limitations and will enable students to select specific topics for further in-depth study.

Within the face-to-face component, the theoretical aspects introduced within the virtual component are deepened and concrete applications of the presented theory are developed. For practical applications, either Python or Mathlab are used. To carry out practical applications, students are divided into groups as heterogeneous as possible both in terms of level of studies and scientific field, in order to stimulate interdisciplinary and team work.

The virtual component will consist of 9 x 2hr online sessions. The teaching will be delivered by different academic staff from ATU, HiG, Oradea, Evora and Angers.
The aim of the virtual component of the BIP is to provide students with the basics of mathematical and computational modeling techniques with applicability in developing digital models and supporting sustainable decision making in different domains such as health, environmental, societal and industrial domains. The program is designed for students at Master or PhD level and young researchers who wish to develop these skills to apply them in research projects aligned to the EU GREEN research themes. This programme prioritizes high-level strategic thinking in the design and analysis of modelling paradigms and how they can be applied for effective decision-making. Interpersonal skills, together with technical skills, are essential for learning outcomes.

Examination. Each group of students formed for the practical applications will have to work on a specific topic, set by the lecturers.

Students can be from any discipline but should normally have completed at least 5 ECTS relevant to Mathematics/Statistics at undergraduate level.

The way in which the appropriate models were identified for solving the problem received by each group is evaluated. At the same time, the identification of the strengths and limitations of the identified models that are chosen to be applied to the problem studied is evaluated. Last but not least, the way in which the team members communicated and worked interdisciplinary is evaluated.

The lecturers are experienced researchers from Atlantic Technological University, University of Évora, University of Gävle, University of Angers and University of Oradea. They are having 3 years experience in working as a group.