Título: Stochastic algorithms for trace estimation and inverse problems involving many PDE inversions
Palestrante: Prof. Uri Ascher, University of British Columbia, Canada.
Local: CT, SALA G-205
Inverse problems involving systems of partial differential equations (PDEs) can be very expensive to solve numerically. This is so especially when many experiments, involving different combinations of sources and receivers, are employed in order to obtain reconstructions of acceptable quality.
The mere evaluation of a mist function (the distance between predicted and observed data) often requires thousands of PDE solves. We develop and assess randomized algorithms for dimensionality reduction, to make the corresponding computational burden tolerable.
The essence of such algorithms boils down to estimating the least squares mist function, which in turns leads to Monte-Carlo methods for trace estimation for implicit matrices. We state and prove theoretical probabilistic bounds regarding the efficiency of such methods, depending on the probability distribution and the matrix properties.
We demonstrate our approach and algorithms on the DC resistivity and EIT problems with rough solutions. Highly efficient variants of the resulting algorithms are identified.