CMX Lunch Seminar

Speaker's Bio:
I compute the derivatives of marginal or stationary distributions of random dynamical systems, which is typically chaotic / high-dimensional / small-noise. Conventionality, there are three basic methods: the path-perturbation method, the divergence method, and the kernel-differentiation method. I gave all combinations of two (out of three) basic methods, thus overcoming some major shortcomings of each basic method. More specifically, I gave 4. Divergence-kernel method for scores, linear responses, and diffusion models. This allows optimization of distributions with respect to diffusion coefficients. 3. Path-Kernel method and its backpropagation for linear responses. 2. Ergodic and foliated kernel differentiation (or likelihood ratio) method. 1. Path-divergence formula (also called the fast response formula), which is the pointwise expression for linear responses of hyperbolic deterministic chaos. This builds on several of my previous results, such as the equivariant divergence formula, the adjoint shadowing lemma, and the nonintrusive shadowing algorithm. I am also interested in dynamical system and probability and their interaction with all fields, such as fluids, geophysics, inference, data assimilation, and machine learning.