Optimization of parameter-dependent systems with applications (OPT-PEDESTAL)

Main information

Project ID: IP-2025-02-4862

Summary
Parameter-dependent systems play a crucial role in various research fields, including mathematics, engineering, and physics, as they arise in applications involving parameter analysis and optimization. This project examines systems with structured parameter variations, emphasizing damping optimization in partial and ordinary differential equations (PDEs and ODEs). It also explores Model Order Reduction (MOR) methods to enhance the efficiency of parameter analysis in structured parametric systems. A primary application is damping optimization, where parameters govern both the damping position (geometry) and viscosity. Another key application comes from nuclear physics, where we will study nuclear two-body scattering using the radial Schrödinger equation and similarity renormalization group flow equations. To enhance efficiency, we will apply Model Order Reduction (MOR) methods to analyze system dynamics, optimize parameters, and apply the results to significant real-world applications such as those stated above. This project aims to develop new models and accelerate the calculation of various damping optimization criteria in real-world applications. Our approach integrates innovative theoretical insights to ensure faster convergence and more precise evaluations of objective functions. This research focuses on four key topics: i) Damping optimization at the PDE level, ii) Damping optimization for LTI systems, iii) MOR for parameter-dependent systems, and iv) MOR approaches in practical applications. Our work will introduce novel modeling perspectives and methodologies that rival existing techniques, and thus further advancing the field. This research is crucial for efficient parameter analysis in structured parametric systems. Additionally, this research will integrate cutting-edge numerical computations, leveraging the synergy between new theoretical insights and structured MOR techniques to enhance computational efficiency.

Project duration: 01.12.2025. – 30.11.2028.

Research topics:

• i) Damping optimization on the PDE level
• ii) Damping optimization considering LTI systems
• iii) Model order reduction for parameter-dependent systems
• iii) Model order reduction approaches in applications

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