项目介绍

2024年1月6日

The NUMA section of KU Leuven, Numerical Analysis and Applied Mathematics, aims at the development, analysis and implementation of numerical algorithms, and their application in science and engineering. In NUMA, the research focus lies on fundamental algorithmic innovations and a detailed analysis of their accuracy and efficiency. This work relies on a combination of mathematical modelling, analysis, design of algorithms and software development. Where possible and desirable, NUMA aims at producing software, that makes the research results useful for the academic and industrial communities. NUMA focuses its activities around emerging topics such as multiscale simulation, uncertainty quantification, highly oscillatory problems, data science, tensor computations, multivariate approximation, design and topology optimization, robust optimization, parameter estimation, control and optimization of hyperconnected systems, digital twins, computational material science, dynamic combinatorial optimization, integer programming, decomposition methods, heuristics and matheuristics. NUMA also aims to strengthen its leadership in traditional topics including (high dimensional) numerical integration, approximation theory, (partial) differential equations, numerical linear algebra and High Performance Computing, modelling and heuristic development, that are ubiquitous in science and engineering.

Project

Topology Optimization (TO) is a powerful method for optimizing the design of industrial systems. In many industrial problems, the optimized design need to be robust with respect to various forms of uncertainties coming e.g. from the load conditions or from the manufacturing process. The optimized design needs to perform well in a continuum of (many) possible scenarios. This is especially challenging because solving physical models for all these possible situations (and accounting them in the optimization program) is not computationally tractable for realistic problems. Incorporating uncertainty analysis into the design process is essential for devising more robust and reliable systems that are better suited to real-world conditions. Unfortunately, current TO methods have limitations when it comes to dealing with uncertainty in three-dimensional real-world large- scale situations featuring multiple physics, design constraints, and requiring flexible risk controls.

The goal of this PhD thesis is to bridge these gaps by adressing three main objectives: 1) achieving significant speed-up in the propagation of uncertainties using geometric low-rank methods and High Performance Computing leveraging GPU implementations for physical state solvers, 2) developing new optimization methods for accounting for uncertain design constraints and flexible formulations of robust optimization, and 3) demonstrating the efficiency of the methods on ambitious three- dimensional large scale Topology Optimization test cases featuring multiple physics and uncertainty. The methodologies of this project will allow to systematically account for uncertainty in optimal design in contexts close to realistic industrial needs.

Profiel

The work will involve a fair balance between the invention and implementation of numerical algorithms and their mathematical analysis. The ideal candidate should have an outstanding mathematical background in numerical analysis and applied mathematics, with specializations in either of the following domains: 

• Uncertainty Quantification
• Model Order Reduction
• Partial Differential Equations
• Finite Element Methods
• Nonlinear Constrained Optimization,
• Topology Optimization
• Domain Decomposition Methods, GPU computing

Candidates must hold a master’s degree in Mathematical Engineering, Applied Mathematics, or equivalent.Candidates should have experience with scientific programming and the will to use it as a daily and powerful research tool (Python and C/C++).Excellent proficiency in English is required, as well as good communication skills, both oral and written.

Aanbod

As a PhD researcher at NUMA, we offer:

• A high-level and exciting international research environment 
• A supportive and collaborative team in which you can develop know-how and expertise in state-of-the-art numerical methods and their mathematical analysis
• The opportunity to build up research and innovation skills that are essential for a future career in research and development, both in an industrial and academic context
• A competitive salary and travel funding 

Applications will be continuously evaluated upon submission until a suitable candidate is selected. The starting date will be agreed upon between the candidate and the promotor but should be no later than October 1, 2024.

Interesse

For more information please contact Prof. dr. Florian Feppon (florian.feppon@kuleuven.be).You can also have a look at  ongoing and past research projects at https://people.cs.kuleuven.be/~florian.feppon/

KU Leuven strives for an inclusive, respectful and socially safe environment. We embrace diversity among individuals and groups as an asset. Open dialogue and differences in perspective are essential for an ambitious research and educational environment. In our commitment to equal opportunity, we recognize the consequences of historical inequalities. We do not accept any form of discrimination based on, but not limited to, gender identity and expression, sexual orientation, age, ethnic or national background, skin colour, religious and philosophical diversity, neurodivergence, employment disability, health, or socioeconomic status. For questions about accessibility or support offered, we are happy to assist you at this email address.

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