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PhD position: Modeling and Analysis of Optical Neural Networks

PhD position: Modeling and Analysis of Optical Neural Networks

Electrical Engineering, Mathematics & Computer Science


The Eindhoven University of Technology has a vacancy for 1 PhD student on the interdisciplinary topic of Modeling and Analysis of Optical Neural Networks, funded by the NETWORKS Gravitation program with the University of Amsterdam, University of Leiden, and Centrum Wiskunde & Informatica (CWI):

The project is a collaboration between the Mathematics & Computer Science and Electrical Engineering departments.


Neural Networks (NNs) are biologically inspired computational systems that mimic the signal processing architecture in the brain, and have recently received an explosion of interest in theoretical machine learning. NNs have dramatically improved speech recognition, visual object recognition, object detection and genomic reconstruction techniques, and rely typically on powerful computers. All Optical Neural Networks (ONNs) on photonic platforms offer an alternative approach to microelectronics, being potentially able to outperform in computing speed and power efficiency.


You (the PhD student) will work on an exciting intersection between the fields of theoretical machine learning and physics. Your goals will be to accurately model ONNs, to improve our designs of ONNs, and to deepen our understanding of ONNs. The work comprises analytical modeling, simulation activities, and collaboration with experimentalists. Your investigation should start with a high photon density operating regime, and go all the way to a low photon density operating regime. The former regime describes most closely current state-of-the-art implementations of ONNs, and the latter regime will challenge you to investigate a futuristic implementation in which we expect attractive new regularization properties to emerge.


In this project, you will encounter challenges of both theoretical as well as practical nature.

Theoretically, a full mathematical understanding of NNs is missing. Key unanswered questions that affect this project include the surprising success of stochastic gradient descent at finding good local minima on a highly nonconvex risk function, and why overparameterized NNs perform well in spite of the concern of overfitting. Their answers have not quite been established yet, because the nonlinearities in NNs lead to highly challenging mathematics. This is because in order to arrive at any useful result, one has to combine techniques from a plethora of fields: analysis, statistics, stochastics, and algebra.

Practically, Indium Phosphide based photonics offer us the rich platform for creating the ONNs. The main features needed to create an all ONN occur in this platform: there is amplification, (de)multiplexing, nonlinear effects, and scalability. However, crosstalk, noise, and nonlinearities also occur and this makes their development highly challenging. As we aim to also investigate an operating regime with low photon density, we expect relatively high levels of noise. Continuous-time learning of ONNs on chip may also still turn out be an essential paradigm, and this is still entirely uncharted territory.

The teams

You will embed in the Stochastic Operations Research (SOR) research group, part of the Statistics, Probability, and Operations Research (SPOR) cluster and thus the M&CS department, and the Electro-Optical Communication Systems (ECO) research group, part of the Institute for Photonic Integration (IPI) and thus the Electrical Engineering (EE) department.

The SOR research group is concerned with complex systems operating under randomness and uncertainty, and aims to develop mathematical models and techniques for the analysis and optimization of such systems. Methodologically, SOR’s research program falls at the intersection of Applied Probability and Operations Research, and SOR in particular engages in cutting-edge research in the area of queueing theory and analysis of random walks and higher-dimensional Markov processes. A key aim is to develop analytic, probabilistic, algorithmic and asymptotic methods, with emphasis on asymptotic laws and scaling limits for large-scale critical systems. While fundamental and methodological in nature, the research is deeply inspired by applications in computer-communications, logistics and service operations, but also biological systems, particle interactions and social networks. SOR comprises of approximately 10 faculty, and 20 PhDs.

ECO has about 30 members, 20 of which are PhD students. The IPI has five dynamic and ambitious research groups, which are closely cooperating: a systems group, a photonic integration technology group and three materials research groups. IPI has obtained a prestigious NWO Zwaartekracht research grant for interdisciplinary research into integrated photonics, including research into novel photonic materials, devices and systems. The PhD student will incidentally also find intriguing ties to that research program, especially since he or she will collaborate intensely with the Photonic Integration group, also part of IPI. The IPI (previously COBRA) is internationally leading on advanced InP-based photonic integrated circuits technology and optical system and sub-system demonstration.

The NETWORKS Gravitation program

You will also partake in a national, scientific training program provided by NETWORKS ( This program will give the PhD student a broad view on the mathematical aspects of networks, and comprises the following activities:

  • NETWORKS will offer a PhD training program consisting of training weeks, mini courses and internships.
  • NETWORKS is actively involved in organizing and sponsoring various workshops in the area of analysis and network design.
  • Each year there will be a at least two general NETWORKS Days, where all members of NETWORKS assemble. The goal of this day is to discuss progress, exchange ideas, plan new activities, foster collaboration, and target possible joint grant applications.
  • Every three years NETWORKS will organize a major international conference on networks, envisaged to attract 100 researchers worldwide.


You are an ideal candidate if you:

  • Have a double degree in Mathematics, and Electrical Engineering or Physics; alternatively, you have a degree in one, and strong affinity with the other
  • Are familiar with techniques of the fields of stochastics, machine learning, optimization, linear algebra and statistics;
  • Have general knowledge about semiconductor physics, modelling and network architectures;
  • Are motivated to work on the challenging intersection between theoretical machine learning and experimental optical computing; and is capable of developing, analyzing and communicating mathematical abstractions of real-life ONNs.
  • Have strong independency in thinking and is intrinsically deeply driven to problem solving;
  • Have great communication skills, excellent team-working capabilities, and is fluent in English (CEFR level C1 or above).


We offer you:

  • An exciting job in a dynamic work environment
  • The possibility to present your work at international conferences.
  • A full time appointment for four years at Eindhoven University of Technology (
  • The salary is in accordance with the Collective Labour Agreement of the Dutch Universities, increasing from € 2,395 per month initially, to € 3,061 in the fourth year.
  • An attractive package of fringe benefits, including end-of-year bonus (8,3% in December), an extra holiday allowance (8% in May), moving expenses and excellent sports facilities.

Informatie en sollicitatie

If you are interested in this PhD student position, use the ‘solliciteer nu’ button. 

You can submit to this position by the 1st of December 2020 at the latest.

To be considered, you must upload the following documents (in pdf):

  • A cover letter explaining your motivation, background and qualifications for the position,
  • A detailed Curriculum Vitae (including a list of publications and awards),
  • Contact information of two references,
  • Copies of diplomas and a list of your courses taken and grades obtained,
  • Half-page summary of your MSc thesis,
  • Proof of English language skills (if applicable), and
  • All other information that might be relevant.

Please be aware that you can upload only 5 documents up to 2 MB each.

Questions regarding the academic content of the position can be directed to:

  • Dr. Jaron Sanders (phone +31 40 2478230, email: jaron.sanders[at], M&CS
  • Dr. Patty Stabile (phone +31 40 2475387 , email: r.stabile[at], EE

For information concerning employment conditions you can contact:

  • HR Services Mathematics and Computer Science HRServices.MCS[at]
  • Yvonne van Bokhoven (HRServices.flux[at], EE

More information on employment conditions can also be found here.