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Accurately simulating the properties of liquid water remains a central challenge in molecular simulations. In this work, we use machine learning potentials to investigate how the convergence settings of electronic structure calculations…
The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the…
We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…
Measurement error data or errors-in-variable data have been collected in many studies. Natural criterion functions are often unavailable for general functional measurement error models due to the lack of information on the distribution of…
We introduce a novel enhanced sampling approach named OPES flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the On-the-fly-Probability-Enhanced-Sampling (OPES)…
The estimation of parameter standard errors for semi-variogram models is challenging, given the two-step process required to fit a parametric model to spatially correlated data. Motivated by an application in the social-epidemiology, we…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical…
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments.…
In adaptive-bias enhanced sampling methods, a bias potential is added to the system to drive transitions between metastable states. The bias potential is a function of a few collective variables and is gradually modified according to the…
We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the…
A large body of research has focused on theory and computation for variable selection techniques for high dimensional data. There has been substantially less work in the big tall data paradigm, where the number of variables may be large,…
We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…
Orthogonal frequency-division multiplexing with index modulation (OFDM-IM) has become a high-profile candidate for the modulation scheme in next generation networks, and many works have been published to analyze it in recent years. Error…
We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to…
In this paper, a novel pre- and post-processing algorithm is presented that can double the convergence rate of finite element approximations for linear wave problems. In particular, it is shown that a $q$-step pre- and post-processing…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
Machine learning methods are being explored in many areas of science, with the aim of finding solution to problems that evade traditional scientific approaches due to their complexity. In general, an order parameter capable of identifying…
Expectation-maximization (EM) is a popular and well-established method for image reconstruction in positron emission tomography (PET) but it often suffers from slow convergence. Ordered subset EM (OSEM) is an effective reconstruction…
The target of human pose estimation is to determine body part or joint locations of each person from an image. This is a challenging problems with wide applications. To address this issue, this paper proposes an augmented parallel-pyramid…
In pump-probe spectroscopy, one often needs to analyse the transmission or reflection of electromagnetic waves through optically pumped media. Here, it is common practice to approximate the analysis in order to extract non-equilibrium…