PhD position on PDE-extraction for semiconductor manufacturing processes

Are you eager to contribute to a still further improvement of ASML's nanolithography technology, and are you fascinated by partial differential equations (PDEs) and machine learning?
If yes, then this vacancy, a cooperation between ASML Research and TU/e's Centre for Analysis, Scientific Computing and Applications, might be something for you.

Job Description
Department of Mathematics and Computer Science (M&CS) The PhD position is in the Department of Mathematics and Computer Science (M&CS) of Eindhoven University of Technology. M&CS is the largest department of TU/e and one of the largest departments in the Netherlands in the area of mathematics and computer science. M&CS has research collaborations with the other departments at TU/e, with many companies in the Eindhoven area, and with universities and companies in the Netherlands and abroad. M&CS contributes to science and engineering by performing both fundamental and applied research. Through M&CS's close relationship with the high-tech industry in the Eindhoven area, staff and students contribute directly to the development of relevant technological innovations. M&CS is organized in three different domains: mathematics, computer science, and data science. Each domain consists of several clusters. The mathematics domain has three clusters: CASA (Center for Analysis, Scientific Computing, and Applications), DM (Discrete Mathematics), and SPOR (Statistics, Probability, and Operations Research). The domain of computer science is organized into five different clusters: ALGA (Algorithms, Geometry and Applications), FSA (Formal System Analysis), IRIS (Interconnected Resource-aware Intelligent Systems), SEC (Security), and SET (Software Engineering and Technology). Data science has three clusters: DAI (Data and Artificial Intelligence), PA (Process Analytics), and VIS (Visualization). The PhD position for which this call is, is in the cluster CASA.

Center for Analysis, Scientific Computing and Applications (CASA)
The research objective of CASA is to develop new and improve existing mathematical (both analytical and numerical) methods for a wide range of applications in science and engineering. Mathematics research within CASA is often driven by models from science and engineering, for instance by mathematical expressions of physical laws (often systems of coupled nonlinear partial differential equations). Stimulated by the immense growth in the availability and use of data, mathematics in CASA is also becoming data-driven, with a crucial role in this for machine learning. There is enormous potential for the use of data and machine learning (particularly neural networks) in analysis and scientific computing, in combination with the use of first-principle models. CASA is continuing its longstanding expertise and success in variational calculus, functional analysis, numerical methods for partial differential equations, numerical linear algebra, and model-order reduction methods while extending its research into the direction of data science, machine learning, uncertainty quantification, and high-performance computing.

Knowledge and Physics-Informed Artificial Intelligence (KPAI)
The availability and importance of data for the design, manufacturing, operation and maintenance of
semiconductor machinery has increased significantly. Classical engineering methods can be augmented by
data taken from observations in machines or from documented knowledge sources based upon earlier
design and manufacturing steps. The translation of these diverse forms of information requires novel
approaches that extract meaningful outputs, which are then utilizable for engineering goals.
From the national program TKI (Top consortia for Knowledge and Innovation), funding has been acquired for
the research program Knowledge and Physics Informed Artificial Intelligence (KPAI), including two PhD
projects, each focused on a different type of source information. The program KPAI will be co-funded by and
carried out in cooperation with ASML Research. The two PhD projects in the KPAI program are:

• Extraction and representation in the form of partial differential equations (PDEs) of the physics governing semiconductor manufacturing processes (model discovery).
• Information extraction from semi-structured sources of information and their representation in a knowledge graph and a large language model for trustworthy conversational AI.

Both projects will bring these two forms of information together in such a way that a tool is realized for quick support to engineers. The first of above two projects, for which the present call is, will be carried out in the cluster CASA, the second in the cluster DAI.

Requirements:

We are looking for a talented, enthusiastic PhD candidate meeting the following requirements:

• Master degree in (applied) mathematics or related discipline.
• Experience with numerically solving ordinary and partial differential equations.
• Experience with optimization methods and interest in machine learning.
• Experience with programming (Python, Matlab, C, C++ or alike).
• Creative pro-active team player with good analytical skills.
• Research-oriented attitude.
• Ability to work in interdisciplinary team and to collaborate with industrial partner.
• Motivated to develop teaching skills and coach students.
• Fluent in spoken and written English.

Salary Benefits:

A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months. You will spend 10% of your employment on teaching tasks.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. €2,770 max. €3,539).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

38 hours per week

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