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The primal-dual hybrid gradient method (PDHG) is useful for optimization problems that commonly appear in image reconstruction. A downside of PDHG is that there are typically three user-set parameters and performance of the algorithm is…
Tensor decomposition is a fundamental technique widely applied in signal processing, machine learning, and various other fields. However, traditional tensor decomposition methods encounter limitations when jointly analyzing multi-block…
Nonlinear systems arising from time integrators like Backward Euler can sometimes be reformulated as optimization problems, known as incremental potentials. We show through a comprehensive experimental analysis that the widely used…
Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. Proposed M-IHS techniques are obtained by incorporating the Heavy…
Preconditioners are generally essential for fast convergence in the iterative solution of linear systems of equations. However, the computation of a good preconditioner can be expensive. So, while solving a sequence of many linear systems,…
This report investigates the fitting of the Hessian or its inverse for stochastic optimizations using a Hessian fitting criterion derived from the preconditioned stochastic gradient descent (PSGD) method. This criterion is closely related…
IFOSMONDI iterative algorithm for implicit co-simulation of coupled physical systems (introduced by the authors in july 2019 during the Simultech conference, p.176-186) enables us to solve the nonlinear coupling function while keeping the…
Model Predictive Control (MPC) is a popular strategy for controlling robots but is difficult for systems with contact due to the complex nature of hybrid dynamics. To implement MPC for systems with contact, dynamic models are often…
With the advancement of modern applications, an increasing number of composite optimization problems arise whose smooth component does not possess a globally Lipschitz continuous gradient. This setting prevents the direct use of the…
Metric-based few-shot approaches have gained significant popularity due to their relatively straightforward implementation, high interpret ability, and computational efficiency. However, stemming from the batch-independence assumption…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods.…
Massive multiple-input multiple-output (MIMO) promises improved spectral efficiency, coverage, and range, compared to conventional (small-scale) MIMO wireless systems. Unfortunately, these benefits come at the cost of significantly…
An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
Implicit Neural Point Cloud (INPC) is a recent hybrid representation that combines the expressiveness of neural fields with the efficiency of point-based rendering, achieving state-of-the-art image quality in novel view synthesis. However,…
Relativistic magnetic reconnection is a non-ideal plasma process that is a source of non-thermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique.…