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Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) that incorporate \emph{a posteriori} solution information.…
Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is presented for an adaptive spectral decomposition of self-adjoint…
Recent work has shown that parameterizing and optimizing coordinate transformations using normalizing flows, i.e., invertible neural networks, can significantly accelerate the convergence of spectral approximations. We present the first…
Though unsupervised domain adaptation (UDA) has achieved very impressive progress recently, it remains a great challenge due to missing target annotations and the rich discrepancy between source and target distributions. We propose Spectral…
Sequential, multiple assignment randomized trials (SMARTs), which assist in the optimization of adaptive interventions, are growing in popularity in education and behavioral sciences. This is unsurprising, as adaptive interventions reflect…
Since the scale factor and the crossover rate significantly influence the performance of differential evolution (DE), parameter adaptation methods (PAMs) for the two parameters have been well studied in the DE community. Although PAMs can…
Spectral methods employing non-standard polynomial bases, such as M\"untz polynomials, have proven effective for accurately solving problems with solutions exhibiting low regularity, notably including sub-diffusion equations. However, due…
Adaptive filtering algorithms are pervasive throughout signal processing and have had a material impact on a wide variety of domains including audio processing, telecommunications, biomedical sensing, astrophysics and cosmology, seismology,…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…
This work is devoted to the study of uncertainty principles for finite combinations of Hermite functions. We establish some spectral inequalities for control subsets that are thick with respect to some unbounded densities growing almost…
Parameter-efficient fine-tuning methods have emerged as a promising solution for adapting pre-trained models to various downstream tasks. While these methods perform well in single-task learning, extending them to multi-task learning…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptability but lacking spectral constraints, and spectral-based…
Source-free domain adaptation (SFDA) is compelling because it allows adapting an off-the-shelf model to a new domain using only unlabelled data. In this work, we apply existing SFDA techniques to a challenging set of naturally-occurring…
This report contributes to the field of unsupervised domain adaptation by providing an analysis of existing methods, introducing a new approach, and demonstrating the potential for improving visual recognition tasks across different…
In this paper, we focus on a less explored, but more realistic and complex problem of domain adaptation in LiDAR semantic segmentation. There is a significant drop in performance of an existing segmentation model when training (source…