Inference of Black Hole Fluid-Dynamics from
Sparse Interferometric Measurements

Aviad Levis1    Daeyoung Lee2    Joel A. Tropp1
Charles F. Gammie2    Katherine L. Bouman1

1California Institute of Technology     2University of Illinois    


The unknown statistics of an evolving source are estimated directly from interferometric measurements of the Event Horizon Telescope. The source is modeled as a composition of static and dynamic structures. The dynamic component is a random field generated as a solution to a partial differential equation (PDE). The unknown PDE coefficients are the spatial correlations and velocity field, which, along with the static structure, are estimated in the inverse problem.


Abstract

We develop an approach to recover the underlying properties of fluid-dynamical processes from sparse measurements. We are motivated by the task of imaging the stochastically evolving environment surrounding black holes, and demonstrate how flow parameters can be estimated from sparse interferometric measurements used in radio astronomical imaging. To model the stochastic flow we use spatio-temporal Gaussian Random Fields (GRFs). The high dimensionality of the underlying source video makes direct representation via a GRF’s full covariance matrix intractable. In contrast, stochastic partial differential equations are able to capture correlations at multiple scales by specifying only local interaction coefficients. Our approach estimates the coefficients of a space-time diffusion equation that dictates the stationary statistics of the dynamical process. We analyze our approach on realistic simulations of black hole evolution and demonstrate its advantage over state-of-the-art dynamic black hole imaging techniques.

paper [pdf] code [Github] supplement [pdf] poster [pdf]


Citation

Aviad Levis, Daeyoung Lee, Joel A. Tropp, Charles F. Gammie, and Katherine L. Bouman (2021). "Inference of Black Hole Fluid-Dynamics from Sparse Interferometric Measurements." To appear in Proc. IEEE International Conference on Computer Vision, 2021.


Video


Talks and Conferences

Highlighted in keynote talks at CVPR 2021 and CMU’s Quarks to Cosmos Workshop.
See here for a recording (@ ~30 minutes)