Related papers: Weighted-norm preconditioners for a multi-layer ti…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We consider the plane wave weighted least squares (PWLS) method…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
We study the problem of preconditioning in sequential prediction. From the theoretical lens of linear dynamical systems, we show that convolving the target sequence corresponds to applying a polynomial to the hidden transition matrix.…
The development of surrogate models to study uncertainties in hydrologic systems requires significant effort in the development of sampling strategies and forward model simulations. Furthermore, in applications where prediction time is…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
Despite the simplicity of its molecular unit, water is a challenging system because of its uniquely rich polymorphism and predicted but yet unconfirmed features. Introducing a novel space of generalized coordinates that capture changes in…
Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly…
Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex aqueous systems such as solid-liquid interfaces. Here, we present a machine learning…
We study active surface wetting using a minimal model of bacteria that takes into account the intrinsic motility diversity of living matter. A mixture of "fast" and "slow" self-propelled Brownian particles is considered in the presence of a…
This paper develops the preconditioning technique as a method to address the accuracy issue caused by ill-conditioning. Given a preconditioner $M$ for an ill-conditioned linear system $Ax=b$, we show that, if the inverse of the…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
Model calibration and debiasing are fundamental yet operationally expensive challenges in large-scale recommendation systems. Existing approaches treat them as separate problems requiring distinct infrastructure: post-hoc calibration…
With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…
We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…
Neural networks have increasingly influenced people's lives. Ensuring the faithful deployment of neural networks as designed by their model owners is crucial, as they may be susceptible to various malicious or unintentional modifications,…
Learned data models based on sparsity are widely used in signal processing and imaging applications. A variety of methods for learning synthesis dictionaries, sparsifying transforms, etc., have been proposed in recent years, often imposing…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…