Related papers: Accelerating an ensemble of variational data assim…

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear…

As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the timescale of the latent space while…

An Ensemble of Data Assimilations (EDA) can provide valuable information on the analysis and short-range forecast uncertainties. The present ECMWF operational ocean analysis and reanalysis system, called ORAS5, produces an ensemble but does…

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Transformative innovations in model architectures have introduced hierarchical embedding augmentation as a means to redefine the representation of tokens through multi-level semantic structures, offering enhanced adaptability to complex…

Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…

Data augmentation (DA) turns seemingly intractable computational problems into simple ones by augmenting latent missing data. In addition to computational simplicity, it is now well-established that DA equipped with a deterministic…

Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…

Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state…

This paper proposes AEDA (An Easier Data Augmentation) technique to help improve the performance on text classification tasks. AEDA includes only random insertion of punctuation marks into the original text. This is an easier technique to…

Shell-model calculations play a key role in elucidating various properties of nuclei. In general, those studies require a huge number of calculations to be repeated for parameter calibration and quantifying uncertainties. To reduce the…

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…

This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…

In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…

Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…

Adaptive gradient methods like Adagrad and its variants are widespread in large-scale optimization. However, their use of diagonal preconditioning matrices limits the ability to capture parameter correlations. Full-matrix adaptive methods,…

We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…

Topic modeling has found wide application in many problems where latent structures of the data are crucial for typical inference tasks. When applying a topic model, a relatively standard pre-processing step is to first build a vocabulary of…

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated,…