Research Fellow, Mathematics
The successful candidate will work with Dr Li Qianxiao on research topics on the intersection of deep learning and dynamical systems under a project on “Deep Learning and Dynamical Systems”. The main responsibilities of the position include conducting cutting-edge research in the connection between differential equations, stochastic processes and machine learning, in particular, deep learning.
Research topics are grouped into two major directions:
- Dynamical systems for machine learning. Recent work shows that a deep residual network can be interpreted as a discretization of a continuous-time dynamical system. With this connection, training a deep neural network corresponds to the solution of an optimal control problem. This project aims to explore this connection in greater depth, including studying the problem of approximation, optimization and generalization of deep learning in the continuous-time framework.
- Machine learning for dynamical systems. The following is a basic question in data-driven approximation of time-series arising from physical modelling: can we learn a dynamical system from the (partial) observation of its trajectories? This part of the project aims to investigate the mathematical aspects of modern approaches for data-driven approximation of dynamical systems, such as recurrent neural networks and related architectures.
- PhD in Applied Mathematics, Computer Science, Physics or related fields Skills:
- Knowledge in machine learning and deep learning
- Familiarity with basic theory of dynamical systems, ODEs, PDEs, and stochastic processes.
- Programming Skills (Python and at least one of the popular deep learning frameworks, e.g. Tensorflow, Pytorch) Experience: Academic research with good publication record
Location: Kent Ridge Campus
Department : Mathematics