Lax-integrable systems are (typically nonlinear) partial differential equations that can be expressed though a compatibility condition between two linear operators, the so-called Lax pair. This special structure provides them with many desirable properties. However, given an arbitrary partial differential equation, it is not trivial to decide whether it is Lax-integrable. Furthermore, it is even harder to find suitable Lax pairs. The process usually involves human intervention, a lot of expertise, and, finally, some luck.

The goal of this Ph.D. project is to investigate automatic methods for finding Lax pairs. While there are semi-automatic methods for finding Lax pairs from given partial differential equations based on symbolic computations, the focus in this Ph.D. project will be on numerical methods that identify Lax pairs from given input-output data. The successful candidate will join a team of Ph.D. students that are investigating the exploitation of Lax integrability in engineering applications.

We are looking for a candidate with a strong academic background, who has or is close to obtaining a Master of Science degree in systems and control, applied mathematics, physics, electrical engineering, or another related discipline. Experience with classic system identification, nonlinear systems, or numerical methods is a plus.

Fixed-term contract: 4 years.

TU Delft offers a customisable compensation package, a discount for health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. An International Children’s Centre offers childcare and an international primary school. Dual Career Services offers support to accompanying partners. Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities.

As a PhD candidate you will be enrolled in the TU Delft Graduate School. TU Delft Graduate School provides an inspiring research environment; an excellent team of supervisors, academic staff and a mentor; and a Doctoral Education Programme aimed at developing your transferable, discipline-related and research skills. Please visit www.tudelft.nl/phd for more information.

Delft University of Technology

Delft University of Technology (TU Delft) is a multifaceted institution offering education and carrying out research in the technical sciences at an internationally recognised level. Education, research and design are strongly oriented towards applicability. TU Delft develops technologies for future generations, focusing on sustainability, safety and economic vitality. At TU Delft you will work in an environment where technical sciences and society converge. TU Delft comprises eight faculties, unique laboratories, research institutes and schools.

https://www.tudelft.nl

Faculty Mechanical, Maritime and Materials Engineering

The 3mE Faculty trains committed engineering students, PhD candidates and post-doctoral researchers in groundbreaking scientific research in the fields of mechanical, maritime and materials engineering. 3mE is the epitome of a dynamic, innovative faculty, with a European scope that contributes demonstrable economic and social benefits.

The Delft Center for Systems and Control (DCSC) coordinates the education and research activities in systems and control at Delft University of Technology. The Center's research mission is to conduct fundamental research in systems dynamics and control, involving dynamic modelling, advanced control theory, optimisation and signal analysis. The research is motivated by advanced technology development in physical imaging systems, robotics and transportation systems. For more information see https://www.tudelft.nl/en/dcsc.

https://www.tudelft.nl/en/3me