Related papers: Smooth supersaturated models
We show that two smooth nearby Riemannian metrics can be glued interpolating their scalar curvature. The resulting smooth metric is the same as the starting ones outside the gluing region and has scalar curvature interpolating between the…
We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler-Reinsch basis in terms…
This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis, their properties depend on…
We analyze the space of bivariate functions that are piecewise polynomial of bi-degree \textless{}= (m, m') and of smoothness r along the interior edges of a planar T-mesh. We give new combinatorial lower and upper bounds for the dimension…
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct…
We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…
The ability of overparameterized deep networks to interpolate noisy data, while at the same time showing good generalization performance, has been recently characterized in terms of the double descent curve for the test error. Common…
Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighbourhood of each atom in the system. Symmetry considerations support the use of…
We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants…
Sampling one or more effective solutions from large search spaces is a recurring idea in machine learning, and sequential optimization has become a popular solution. Typical examples include data summarization, sample mining for predictive…
In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…
In recent years, geotagged social media has become popular as a novel source for geographic knowledge discovery. Ground-level images and videos provide a different perspective than overhead imagery and can be applied to a range of…
Quadratic interpolation models and simplex derivatives are fundamental tools in numerical optimization, particularly in derivative-free optimization. When constructed in suitably chosen affine subspaces, these tools have been shown to be…
Overparametrized neural networks tend to perfectly fit noisy training data yet generalize well on test data. Inspired by this empirical observation, recent work has sought to understand this phenomenon of benign overfitting or harmless…
Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay…