Related papers: Error Analysis for the Implicit Boundary Integral …
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
We present a numerical stability analysis of the immersed boundary(IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
Iso-surface extraction from an implicit field is a fundamental process in various applications of computer vision and graphics. When dealing with geometric shapes with complicated geometric details, many existing algorithms suffer from high…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the…
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could…
We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…
The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present…
Modern mobile communication receivers are often implemented with a direct-conversion architecture, which features a number of advantages over competing designs. A notable limitation of direct-conversion architectures, however, is their…
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…
We consider a fictitious domain formulation for fluid-structure interaction problems based on a distributed Lagrange multiplier to couple the fluid and solid behaviors. How to deal with the coupling term is crucial since the construction of…
Two recently introduced quadrature schemes for weakly singular integrals [Calabr\`o et al. J. Comput. Appl. Math. 2018] are investigated in the context of boundary integral equations arising in the isogeometric formulation of Galerkin…
In many areas of science, complex phenomena are modeled by stochastic parametric simulators, often featuring high-dimensional parameter spaces and intractable likelihoods. In this context, performing Bayesian inference can be challenging.…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
A key challenge in machine learning is to explain how learning dynamics select among the many solutions that achieve identical loss values in overparameterized models - a phenomenon known as implicit bias. Controlling this bias provides a…
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…