applying optimal tranport map to filtering theory

Question

Hi there,

     I have seen your team has done a lot of work about developing parametric approximations of the Knothe-Rosenblatt rearrangement (Moselhy and Marzouk, 2012) to design a good map. I just want to know how many ways until now we can select to applying this Bayesian inference technology to non-linear filter .

Pengcheng

Answer 1

Hello Peng,

There are mainly two lines of work regarding filtering/smoothing/parameter estimation (or more in general data assimilation):

• The first one is along the lines of variational filters/smoothers and is presented in "Inference via low-dimensional couplings". It is already implemented in TransportMaps 2.0, in the version described in the paper.
• The second one is along the lines of ensemble filters/smoothers and is presented in "Coupling techniques for nonlinear ensemble filtering" . The lead in this case is Ricardo Baptista, and you should contact him for more details. These versions of filters are not included in the code yet (I know Ricardo has some software for it). It might be included in future releases of TransportMaps.

On both fornts there are many open questions and new challenges which we could discuss off-line.

 

Best,

  Daniele

Comments

Hi Daniele,

      Your answer is clear and helpful.  Thank you!!!!

Pengcheng.