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Mykhailo Kuian (Case Western Reserve University)5/18/26, 3:45 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
We consider the numerical solution of linear operator equations involving compact operators. Since compact operators do not admit bounded inverses, the associated equations are ill-posed and require regularization. The Arnoldi process provides a natural framework for approximating a compact operator by a nearby operator of finite rank, thereby reducing the infinite-dimensional problem to a...
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Toluwani Okunola (Tufts University)5/18/26, 4:10 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
Many imaging inverse problems assume a known linear forward operator, yet practical systems often suffer from uncertainty in acquisition geometry, such as projection angles in computed tomography, sensor positions in photoacoustic tomography. These uncertainties introduce nonlinearity and require joint estimation of both the image and the forward model parameters.
We propose a nonlinear...
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Riley Yizhou Chen (Emory University)5/18/26, 4:35 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
Learning solution operators in a manner that is independent of discretization and resolution remains a central challenge in data-driven modeling. The latent twins framework addresses this problem by constructing operators in a task-adaptive latent space for inverse problems and differential equations. However, in its classical form, latent twins relies on autoencoder architectures that are...
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Dr Malena Sabate Landman (University of Bath)5/18/26, 5:00 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
This talk presents a new family of algorithms for large-scale linear inverse problems built on flexible and inexact variants of the Golub–Kahan factorization. The proposed approach constructs regularized solutions through a sequence of projected (re)weighted least-squares problems, where the projection spaces are adaptively generated and endowed with iteration-dependent preconditioning and...
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Malena Espanol (Arizona State University)5/19/26, 2:00 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
Block-structured matrices arise as operators in many contexts, including image deblurring and discretized differential equations. These matrices are often large and computationally difficult to work with. By rewriting these operators as a sum of Kronecker products, we may be able to alleviate these challenges. In this talk, we show how we can use the structure of a matrix to impose bounds on...
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Nathaniel Pritchard (The University of Oxford)5/19/26, 2:25 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed using SVD-based approaches such as truncated SVD or RandomizedSVD. Although these SVD approaches---especially RandomizedSVD---have proven to be very...
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James Nagy (Emory University)5/19/26, 2:50 PMComputational Advances in Discrete Inverse ProblemsMinisymposium Talk
In recent years a substantial amount of work has been done on developing mixed-precision algorithms for linear systems, methods that can exploit capabilities of modern GPU architectures. However, very little work has been done for ill-conditioned problems that arise from large-scale inverse problems. Special considerations, which normally do not arise when solving well-conditioned problems,...
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