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We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes introduce the adaptivity and admit an extensive permitted range of the…
Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…
Functional ANOVA provides a nonparametric modeling framework for multivariate covariates, enabling flexible estimation and interpretation of effect functions such as main effects and interaction effects. However, effect-wise inference in…
We study a class of optimization problems on Riemannian manifolds, where the objective function consists of a smooth term and quasi-norm type penalties with exponent $p \in (0, 1]$. The essential difficulty lies in the fact that the…
This scientific paper explores two distinct approaches for identifying and approximating the simulation model, particularly in the context of the snap process crucial to medical device assembly. Simulation models play a pivotal role in…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
Generalizing wavelets by adding desired redundancy and flexibility,framelets are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing…
A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…
In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness)…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
Implicit Processes (IPs) represent a flexible framework that can be used to describe a wide variety of models, from Bayesian neural networks, neural samplers and data generators to many others. IPs also allow for approximate inference in…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…