Parameter estimation is ubiquitous in the modeling of nature. In practice,the success of

particular methods (either MLE or MCMC, Bayesian-based techniques) depends crucially on the

loss function's choice. In general,when the observable only depends on the parameters

implicitly,an appropriate choice of the loss function is important for the parameters' identifiability.

In the context of Ito diffusion SDE's, a widely popular parameter estimation method fits the

empirical one-and two-point statistics corresponding to the system's equilibrium and dynamical

properties. In this talk, I will use linear response theory as a guideline for choosing the

appropriate statistics to be fitted. I will discuss how we overcome several challenges in turning

this idea into a numerically efficient and accurate algorithm. These include: (1) Solving the

resulting dynamic-constrained least square problem with a convergence guaranteed polynomial

surrogate model under the appropriate assumption. (2) Nonparametric estimation of Fluctuation-

Dissipation-Theorem (FDT) response operator from time series with unknown density. (3)A

generalization of this approach in the presence of modeling error. I will show numerical

applications of coarse-graining of molecular dynamics.

Link: https://meeting.tencent.com/dm/XCXTzy0H35tw

Tencent Meeting ID: 505-516-394