-
Haibo Li (Huazhong University of Science and Technology)5/19/26, 3:45 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
In this talk, I will present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method for solving ill-posed linear inverse problems. This method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive reproducing kernel Hilbert space (RKHS) penalizing the spaces of small singular values. At the core of the method is a new generalized...
Go to contribution page -
Jonas Bresch (Technische Universität Berlin)5/19/26, 4:10 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra.
Go to contribution page
Conventional algorithms for its computation typically rely on matrix-adjoint products,
making them sensitive to errors arising from adjoint mismatches.
To address this issue, we introduce a stochastic zeroth-order Riemannian algorithm
that maximizes the generalized Rayleigh... -
Amit Subrahmanya (Argonne National Laboratory)5/19/26, 4:35 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
We address optimal sensor placement for Bayesian nonlinear inverse problems by formulating the task as a matrix column subset selection problem. The design matrix is derived from the expected information gain criterion. Although the resulting solutions are not necessarily globally optimal, the approach presents a rapid time to solution. The effectiveness of the method is demonstrated on...
Go to contribution page -
Aryeh Keating (Virginia Tech)5/19/26, 5:00 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and structural constraints. However, classical regularization formulations are frequently infeasible in this setting due to prohibitive memory requirements,...
Go to contribution page -
Prof. Ning Zheng (Tongji University)5/20/26, 10:45 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
For solving noisy linear ill--posed problems arising from the practical applications, the residual based iterative methods may suffer semi-convergence phenomenon, where the iterates initially get closer to the desired solution but then degrade as the iteration continues. Building upon the randomized Gram--Schmidt algorithm, a random sketching technique known to reduce inner product...
Go to contribution page -
Lucas Onisk (Emory University)5/20/26, 11:10 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Many problems in science and engineering give rise to linear systems of equations that are commonly referred to as large-scale linear discrete ill-posed problems. The matrices that define these problems are typically severely ill-conditioned and may be rank deficient. Because of this, regularization is often needed to stem the effect of perturbations caused by error in the available data. In...
Go to contribution page -
Malena Espanol (Arizona State University)5/20/26, 11:35 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Separable nonlinear inverse problems arise in many applications where a forward model depends linearly on some unknowns and nonlinearly on others, including semi-blind deconvolution. We adopt a Bayesian framework with Gaussian noise and Gaussian priors on the linear variables, leading to regularized formulations of the inverse problem. We examine prior models for the nonlinear parameters and...
Go to contribution page -
Chelsea Drum (Emory University)5/21/26, 11:00 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
In recent years, mixed-precision and reduced-precision algorithms for solving large-scale linear systems have emerged as an effective approach for exploiting modern GPU architectures. While much of this work has focused on well-conditioned systems, comparatively little attention has been given to ill-posed inverse problems, where regularization is essential. In this talk we consider projected...
Go to contribution page -
Prof. Lassi Roininen (LUT University)5/21/26, 11:25 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Edges in imaging, that is sharp discontinuities in intensity, pose a significant challenge for inverse problems algorithms that often rely on Gaussian assumptions. Non-Gaussian heavy-tailed priors, which can better model the sparsity and sharp transitions inherent in edges, offer an alternative for edge-preserving image reconstructions. We consider the inherent difficulties in handling edges...
Go to contribution page -
Abraham Reyes Velazquez (University of Manchester)5/21/26, 11:50 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
We propose a unified framework that allows for the full mechanistic reconstruction of chemical reaction networks (CRNs) from concentration data. The framework utilizes an integral formulation of the differential equations governing the chemical reactions, followed by an automatic procedure to recover admissible mass-action mechanisms from the equations. We provide theoretical justification...
Go to contribution page -
Erkki Somersalo (Case Western Reserve University)5/21/26, 2:00 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
In this talk, we revisit the Bayesian inverse problems formalism in infinite-dimensional distribution spaces, where function evaluations are replaced by evaluations by test functions. It is shown that linear inverse problems can be formulated without a reference to any infinite-dimensional representation of the unknown, e.g., in terms of basis vectors, and therefore, the forward problem has a...
Go to contribution page -
Dr Lizuo Liu (Dartmouth College)5/21/26, 2:25 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce only conservation or rely on prior knowledge of the governing equations, our method parameterizes the flux functions in a form that guarantees real...
Go to contribution page -
Dr Andrea Arnold (Worcester Polytechnic Institute)5/21/26, 2:50 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Many applications in modern day science involve unknown system parameters that must be estimated from limited data. A subset of these problems involves parameters that vary with time but have unknown evolution models and cannot be directly observed. In this work, we formulate time-varying parameter estimation in deterministic dynamical systems as an interpolation problem, where the function...
Go to contribution page -
Eric de Sturler (Virginia Tech)5/21/26, 3:15 PMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Big data applications are becoming ever more prominent, and in many applications we need to solve very large linear or nonlinear inverse problems while handling only a relatively small amount of data at a time. Moreover, we are interested in distributed, possibly asynchronous, algorithms that solve large problems while only exchanging limited information. We need algorithms that combine...
Go to contribution page -
Jonathan Lindbloom (Dartmouth College)5/22/26, 8:45 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Hybrid projection methods are an effective iterative approach for the solution of large-scale linear inverse problems, including those promoting sparsity in the recovered solution. Priorconditioned (prior-preconditioned) hybrid methods have been proposed to improve performance, but introduce additional computational costs in each iteration related to the application of a weighted pseudoinverse...
Go to contribution page -
Diego Arenas Mata (Virginia Tech)5/22/26, 9:10 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Sparse priors, such as the Laplace prior, are of considerable interest in Bayesian inverse problems because they promote sparsity and preserve edges in the solution, which are often more appropriate than the smooth reconstructions obtained with Gaussian priors. However, sampling from the resulting non-Gaussian posteriors is challenging, particularly in high-dimensional settings. To address...
Go to contribution page -
Misha Kilmer (Tufts University)5/22/26, 9:35 AMInverse Problems and Uncertainty Quantification through the Lens of Numerical Linear AlgebraMinisymposium Talk
Reconstructing high-quality images with sharp edges requires edge-preserving regularization, often imposed using the $\ell_1$-norm of the gradient. To get a computationally tractable problem, the $\ell_1$-norm term is typically replaced with a sequence of $\ell_2$-norm weighted gradient terms with the weights determined from the current solution estimate. The majorization-minimization...
Go to contribution page
Choose timezone
Your profile timezone: