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Fast algorithms in cryo-electron microscopy and beyond

Owen Hall 101

Speaker: Oscar Mickelin

This talk presents a number of numerical problems that arise from a computational imaging technique known as cryo-electron microscopy. This technique solves the non-linear inverse problem of recovering the three-dimensional structures of molecules from randomly oriented tomographic projection images, with important applications in biology.We will focus on a fast and provably accurate algorithm to expand discretized image-valued data into the basis of eigenfunctions of the Dirichlet Laplacian on the unit disk. For LxL images, the algorithm computes O(L^2) basis coefficients in complexity O(L^2 log(L)), for a fixed accuracy, which is significantly lower than brute-force approaches. We will also discuss a fast algorithm to perform rotationally invariant covariance estimation of cryo-EM images, and extensions to three-dimensional basis functions. Read more.


Reduced Order Modeling in the Age of Data

Rogers Hall 230

Speaker: Changhong Mou

Data-driven modeling of complex dynamical systems is becoming increasingly popular across various domains of science and engineering. In this talk, I will introduce a systematic multiscale data-driven closure reduced order model (ROM) framework for complex systems with strong chaotic or turbulent behavior. I will utilize available data to construct novel ROM closure terms, thereby capturing the interaction between resolved and unresolved modes. Next, I will explain how the new data-driven closure ROM can be integrated with a conditional Gaussian data assimilation framework that employs cost-effective, conditionally linear functions to capture the statistical features of the closure terms. This leads to the stochastic data-driven closure ROM that facilitates an efficient and accurate scheme for nonlinear data assimilation (DA), the solution of which is provided by closed analytic formulae that do not require ensemble methods. It also allows the ROM to avoid many potential numerical and… Read more.


TBA

Speaker: J. D. Quigley

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Accelerating solvers for fluids with (continuous) data assimilation

TBA

Speaker: Leo Rebholz

We consider nonlinear solvers for the incompressible, steady Navier-Stokes equations in the setting where partial solution data is available, e.g. from physical measurements or sampled solution data from a (too big to send) very high-resolution computation. The measurement data is incorporated/assimilated into the solver through a nudging term addition that penalizes at each iteration the difference between the coarse mesh interpolants of the true solution and solver solution, analogous to how continuous data assimilation (CDA) is implemented at each time step for time dependent dissipative PDEs. For a Picard solver, we quantify the acceleration provided by the data in terms of the density of the measurement locations and the level of noise in the data. For Newton, we show how the convergence basin for the initial condition is expanded as more data is assimilated.Numerical tests illustrate the results. While the setting is for Navier-Stokes, the ideas are applicable to solvers for a… Read more.


TBA

Speaker: Julie Simons

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