LANS Informal Seminar: Carlo Graziani

Seminar Title: Jeff Nagged Me To Give A Seminar, So Here It Is
Speaker: Carlo Graziani, Computational Scientist, MCS/ANL

Date/Time: 2019-06-19 10:30
Location: Bldg. 240, Rm. 1404-05

Description:
I’ll discuss some work in progress on Bayesian parameter estimation for
chaotic nonlinear dynamical systems with noisy observations. This is a
tricky problem, largely because trajectories in chaotic systems have the
well-known property that small perturbations in initial conditions lead
to large trajectory deviations in finite time. As a consequence a
naively-constructed Bayesian posterior density over parameter space
based on trajectory data has an unusable, essentially cryptographic
structure — parameter values adjoining the true parameters are assigned
negligible probability. I’ll describe an alternate approach, adapted to
Bayesianism from the SINDY dynamical-law inference method, in which the
analysis is cleverly conducted in ODE law space rather than in
trajectory space. This approach mostly works, although some frustration
results from the determined efforts of chaos to defy cleverness by
creeping back in over a subtle side-channel. I’ll try to provide some
suitable rant, since Jeff seems to expect this of me for some reason.