Register now After registration you will be able to apply for this opportunity online.
This opportunity is not published. No applications will be accepted.
Topics in data-driven model reduction
Complex physical processes are often modeled by large-scale dynamical systems that are difficult to simulate, predict and control. Model reduction is the art of approximating the behavior of such dynamical systems, while preserving their main features. A popular way to approach the model reduction problem is through methods based on moment matching (or rational interpolation), because of superior scalability and tractability properties as well as efficient data-driven implementations, such as Vector Fitting [1] and the Loewner framework [2]. The project hinges on recent advances in the area and explores new least-squares algorithms based on moment matching.
References: [1] B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting", IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, July 1999. [2] A. Mayo and A. Antoulas. A framework for the solution of the generalized realization problem.
Linear Algebra Appl., 425(2):634–662, 2007. Special Issue in honor of Paul Fuhrmann.
See also: https://en.wikipedia.org/wiki/Model_order_reduction
Keywords: model reduction, moment matching, Sylvester equations, numerical methods, low-rank factors
The purpose of this thesis is quite malleable. For practically oriented students, the focus will be on applying and evaluating new data-driven least squares model reduction methods. Applications may be drawn from problems arising in the field of power systems. For theoretically oriented students, the focus will be on studying and possibly developing new least squares model reduction methods, leveraging on classical control theory as well as state of the art numerical linear algebra and optimization tools.
The purpose of this thesis is quite malleable. For practically oriented students, the focus will be on applying and evaluating new data-driven least squares model reduction methods. Applications may be drawn from problems arising in the field of power systems. For theoretically oriented students, the focus will be on studying and possibly developing new least squares model reduction methods, leveraging on classical control theory as well as state of the art numerical linear algebra and optimization tools.
The student will: (1) learn and understand concepts related to the topic, including model reduction approaches based on moment matching as well as handling and solving large scale Sylvester equations; (2) explore and review the relevant literature; (3) study a problem statement with potential applications arising in the setting of power systems; (4) evaluate the performance of the proposed methodology using and developing model reduction software tools in Matlab.
Prerequisites: The project is well suited for a student who enjoys numerical mathematics. A background in analysis and linear algebra is required. Some basic knowledge of optimization and numerical linear algebra is beneficial.
The student will: (1) learn and understand concepts related to the topic, including model reduction approaches based on moment matching as well as handling and solving large scale Sylvester equations; (2) explore and review the relevant literature; (3) study a problem statement with potential applications arising in the setting of power systems; (4) evaluate the performance of the proposed methodology using and developing model reduction software tools in Matlab.
Prerequisites: The project is well suited for a student who enjoys numerical mathematics. A background in analysis and linear algebra is required. Some basic knowledge of optimization and numerical linear algebra is beneficial.
Do not hesitate to contact us if you are interested in the project or, more broadly, in the research topic. When applying, please include your CV, current grade transcript, and optionally other documentation helpful to evaluate your background.
Dr A. Padoan - Email: apadoan@ethz.ch
Dr I. V. Gosea - Email: gosea@mpi-magdeburg.mpg.de
Do not hesitate to contact us if you are interested in the project or, more broadly, in the research topic. When applying, please include your CV, current grade transcript, and optionally other documentation helpful to evaluate your background.
Dr A. Padoan - Email: apadoan@ethz.ch Dr I. V. Gosea - Email: gosea@mpi-magdeburg.mpg.de