Deep learning for stochastic computations and/or numerical PDE

Företag Syntronic


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Deep learning for stochastic computations and/or numerical PDE

Syntronic is a global consultant company with soon 1000 employees. The company is based in Gävle with offices in Göteborg, Kista, Kumla, Linköping, Lund, Sandviken, Beijing, Chengdu, Tianjin, Ottawa, Jakarta, Kuala Lumpur and Penang. Our main competence is within embedded systems but in Göteborg we have a big focus on algorithm development in the scopes of machine learning, computer vision, sensor fusion/statistics, automatic control, modeling and simulation. Every spring we run master thesis projects at our office but we are positive to supervising projects any time of the year. Master thesis students should have a strong mathematical background, good skills in programming and a great interest in technology.

Deep neural networks (DNN) are powerful function approximators. They have proved to provide good approximate solutions to previously computationally infeasible problems from, e.g., computer vision and partial differential equations (PDE). They are so powerful that it is easy to use them without too much thinking and get working results. Our philosophy is that they should be used wisely. If the problem at hand has some additional known structure this structure should be utilized and DNN used for function approximation in the bottle necks of the algorithm. One example is the generation of smoke in computer games. It can be done with Euler’s equations from fluid dynamics in a two step algorithm.

Without the neural network step 2 is very costly. Another example is the computation of 100 dimensional parabolic PDE in option pricing. It is done by a utilizing a relation between the PDE and a backward stochastic differential equation (BSDE). The BSDE is solved approximately with a DNN and an approximate solution to the PDE follows for free. At Syntronic we are interested in control and filtering applications of this method.

We can offer one project to 1-2 dedicated top students specializing in computational methods for stochastic or partial differential equations and who are interested in broadening their scope to machine learning. We have several ideas along these lines with applications mainly in stochastic control and filtering, but possibly numerical PDE. Students should write their thesis from our office in Göteborg but the university does not matter. We know good supervisors at Chalmers and KTH. We have hired more than half of our students so there are great career possibilities after a successful thesis. For this particular project also students aspiring for an academic research career will be considered. The thesis topic will be advanced and meriting for such a path.


Supervisor at Syntronic: Adam Andersson (PhD)

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Deep learning for stochastic computations and/or numerical PDE