Deep Learning and Partial Differential Equations Partial Differential Equations (PDEs) are used in an extremely wide range of fields in computer science and engineering, ranging from critical domains such as solid mechanics and fluid dynamics, to entertainments/education such as visual effects, computer graphics, animation and virtual reality. One key fundamental aspect to such research is a well-balanced trade-off between accuracy and speed. We look into how to leverage Deep Learning to help solving PDEs and physical simulations in general. Examples can be found here.

Robustness of Deep Learning Deep learning has been the 'go to' solution nowadays. But its vulnerability to adversarial attacks has a wide implication in many applications fields regarding the robustness of their deep learning models. Why are deep learning models vulnerable to such attacks and how to make them robust is the key question here. Examples can be found here.

Crowd Simulation and Evaluation. Whenever you see massive battle scenes in movies or games these days, it is almost for sure generated by crowd simulation. Beyond entertainment, crowd simulation is also widely used in design, urban planning, logistics, etc. where collective behaviours of humans matter. To simulate crowds, we need to understand people's behaviour patterns ranging from navigation skills to socio-psychological factors. My primary research interest is to learn these patterns from data which involves simulation and evaluation. Technical-wise, I leverage the knowledge from the four fields mentioned. Examples can be found here, here and here.

Motion Planning, Analysis and Synthesis. We humans have amazing motion planning skills which are very difficult to be encoded by current algorithms, especially when it involves interactions with the environment. Think putting on clothes for example. The complexity of this motion planning problem goes up exponentially when the environment just gets mildly complex. My research interest in this area is to find good representations (topological, geometric, etc.) to enable algorithms to find solutions easily. Examples can be found here, here and here.

Scene Analysis. In today's renaissance of Virtual Reality, the urge of understanding the virtual world is as much desired as the the understanding of the real world. My research interest in this area is to leverage geometric and topological knowledge to describe the virtual world so that alrogrithms can be designed for applications such as virtual agents, design, search, etc. Examples can be found here and here.

Other topics. I am also in general intersted in other graphics topics (geometric processing, visualization, physical simulation), machine learning (non-parametric Bayesian models, Deep Learning, Reinforcement Learning), and computer vision(crowd analysis, tracking).