1. Divergence-kernel method for scores, linear responses, and diffusion models.
2. Path-Kernel method and its backpropagation for linear responses.
3. Ergodic and foliated kernel differentiation (or likelihood ratio) method.
4. Path-divergence formula (also called the fast response formula), which is the pointwise expression for linear responses of hyperbolic deterministic chaos.
Research Experience
Postdoc at PKU BICMR, then Assistant Professor at YMSC in Tsinghua University, where he also served as Manager of undergrad affairs in Qiuzhen College.
Education
PhD from UC Berkeley Math, mentored by John Strain, Pingwen Zhang, Mark Pollicott, Jack Xin, Qing Nie, Long Chen.
Background
Research interests include computing the derivatives of marginal or stationary distributions of random dynamical systems, particularly chaotic/high-dimensional/small-noise systems. He combines two out of three basic methods (path-perturbation, divergence, and kernel-differentiation) to overcome some major shortcomings of each. He is also interested in dynamical systems and probability and their interactions with fields such as fluids, geophysics, inference, data assimilation, and machine learning.