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Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…
To accelerate deep CNN models, this paper proposes a novel spatially adaptive framework that can dynamically generate pixel-wise sparsity according to the input image. The sparse scheme is pixel-wise refined, regional adaptive under a…
Kolmogorov-Arnold Networks (KANs) have recently demonstrated promising potential in scientific machine learning, partly due to their capacity for grid adaptation during training. However, existing adaptation strategies rely solely on input…
Positional encodings are a common component of neural scene reconstruction methods, and provide a way to bias the learning of neural fields towards coarser or finer representations. Current neural surface reconstruction methods use a…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
We propose a communicationally and computationally efficient algorithm for high-dimensional distributed sparse learning. At each iteration, local machines compute the gradient on local data and the master machine solves one shifted $l_1$…
Function approximation using Haar basis systems offers an efficient implementation when compressed via Patricia trees while retaining the flexibility of wavelets for both global and local fitting. However, like B-spline-based…
Tuning the step size of stochastic gradient descent is tedious and error prone. This has motivated the development of methods that automatically adapt the step size using readily available information. In this paper, we consider the family…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting…
Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…
In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, wherein only a sequence of reduced problems with much smaller…
Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high-contrast coefficients. To resolve the challenge, we propose…
We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth…