Related papers: Regularized Stokeslet Surfaces
Smoothness is a key inductive bias in machine learning and is closely related to generalization. Existing smoothness-inducing methods typically rely either on explicit gradient regularization, which often incurs substantial computational…
Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its…
Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap…
Lens modeling of resolved image data has advanced rapidly over the past two decades. More recently pixel-based approaches, wherein the source is reconstructed on an irregular or adaptive grid, have become popular. Generally, the source…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
Spatially referenced data are increasingly available thanks to the development of modern GPS technology. They also provide rich opportunities for spatial analytics in the field of marketing science. Our main interest is to propose a new…
Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
The Fr\'echet regression is a useful method for modeling random objects in a general metric space given Euclidean covariates. However, the conventional approach could be sensitive to outlying objects in the sense that the distance from the…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…
In this paper the full and exhaustive algorithm of formation of a smooth molecular Solvent Excluded Surface- SES, and also Solvent Accessible Surface- SAS is presented. These surfaces are a boundary between molecule and solvent. The basis…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…
First-order methods in convex optimization offer low per-iteration cost but often suffer from slow convergence, while second-order methods achieve fast local convergence at the expense of costly Hessian inversions. In this paper, we…