PhD in Systems Science

The international PhD program in Systems Science (SyS) is hosted by the IMT School, one of the seven Schools of Excellence in Italy, and one of the highest-rated graduate schools in Europe, according to the most recent U-Multirank survey. This program offers rigorous training and personalized supervision in technical, social, human, and natural sciences, and encourages interdisciplinary and multidisciplinary approaches that push disciplinary boundaries.

The IMT School fosters a genuinely global atmosphere by welcoming students from diverse geographical locations. Additionally, the School boasts a successful track record of placing its graduates in prestigious universities, companies, and public institutions across the world. Notably, English is the official language at the School.

SyS aims to equip students with the necessary skills to conduct advanced research in the field of analysis and design of a range of technological, natural, economic, and social systems. This is achieved through the use of descriptive and predictive mathematical models.

SyS students work on diverse projects, such as improving the efficiency of industrial systems, comprehending the complexity of biological, ecological, social, and economic systems, and ensuring the reliability and autonomy of cyber-physical systems that combine physical modules and software. The potential application areas of SyS include several industries such as automotive, aerospace, communication, chemical, infrastructure, energy, biomedicine, financial, and manufacturing, as well as governmental sectors such as central banking and official statistics.

Throughout their doctoral studies, SyS students learn various skills that enable them to create, employ, and implement techniques for analyzing and predicting complex phenomena. These techniques involve the use of analytical and computational models that originate from first principles or data, incorporating a range of interdisciplinary fields such as mathematics, operations research, physics, statistics, computer science, and engineering.

The Program's curriculum comprises several subjects such as machine learning, network science, analysis and control of dynamical systems, time-series analysis, statistical physics, complex systems theory, numerical optimization, numerical integration of differential equations, statistics, stochastic processes, agent-based models, specification languages, programming, and software analysis. SyS students acquire proficiency in these areas of study by pursuing one of four specialization tracks:

• Complex Systems and Networks (CN)
• Computational Mechanics (CM)
• Learning and Control (LC)
• Software Quality (SQ)

All four tracks offer a comprehensive level of training that is highly valued in both academic and non-academic professions. Basic courses are designed to expose students from various tracks to the techniques and methodologies employed in related fields of study, thereby expanding their skill set.

SyS students have the opportunity to study abroad during their course of study, either through the Erasmus+ program or other specific mobility agreements.

The Systems Science Ph.D. program typically lasts for three years and may be extended to four years. In the first year, students are required to complete a set of courses that cover at least 150 teaching hours. The study plan is selected together with the Ph.D. supervisor to meet the specific requirements of the planned research activities. A diverse selection of topics is available for students to choose from:

List of Ph.D. courses

• Advanced Methods for Complex Systems

• Advanced Topics in Machine Learning

• Advanced Topics in Computational Mechanics

• Applications of Stochastic Processes

• Basics of Technological, Social, and Legal Aspects of Cybersecurity

• Brain Networks

• Complexity and Sustainability

• Computational Contact and Fracture Mechanics

• Computational Fluid Dynamics for Incompressible Fluids

• Concurrent Programming

• Dynamics on Complex Networks

• Foundations of Probability and Statistical Inference

• Fundamentals of Academic Entrepreneurship

• Fundamentals of Numerical Analysis

• Funding Opportunities and Management of Intellectual Property

• Game Theory

• Introduction to Formal Methods

• Introduction to Machine Learning

• Introduction to Network Science

• Markov Processes

• Maximum-Entropy Models of Complex Systems

• Model Predictive Control

• Modelling and Verification of Reactive Systems

• Network Reconstruction

• Numerical Methods for Optimal Control

• Numerical Methods for the Solution of Partial Differential Equations

• Numerical Optimization

• Optimal Control and Differential Games

• Publication Strategies and Scientific Dissemination

• Python for Data Science

• Principles of Programming with Python

• Reduced Order Models and Applications

• Reinforcement Learning

• Research Topics in Software Quality

• Software Verification

• Software Security

• Stochastic Processes

• Vulnerability Assessment and Penetration Testing

Upon completion of the first year, Ph.D. students are required to dedicate themselves full-time to their research. They are also encouraged to spend part of their studies abroad, either via the Erasmus+ framework or through customized mobility agreements. Throughout the duration of the program, students have the opportunity to meet with leading researchers from around the world who visit IMT School to present their work in a seminar series or as visiting scholars.

Graduates of the SyS program can pursue a variety of career paths, including academic positions in engineering, computer science, physics, applied mathematics, and other related fields. Additionally, they can get opportunities in various industries, services, public and private research laboratories, study centers, regulatory centers, consulting firms, and the public sector.

Former SyS students have secured positions at top universities, prestigious companies, international institutions, research centers, and innovative startups, as evidenced on the Past Students page.

Applicants who hold a master's degree in computer science, engineering, physics, mathematics, statistics, or other related fields are eligible to apply for the SyS program.