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Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…
By integrating two powerful methods of density reduction and intrinsic dimensionality estimation, a new data-driven method, referred to as OLPP-MLE (orthogonal locality preserving projection-maximum likelihood estimation), is introduced for…
Following the trends of index modulated (IM) techniques for optical communications, in the last few years several new waveform proposals have been made, aiming at conveying a higher density of information by driving different signal…
Permutationally invariant polynomial (PIP) regression has been used to obtain machine-learned (ML) potential energy surfaces, including analytical gradients, for many molecules and chemical reactions. Recently, the approach has been…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the…
We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
Electromagnetic methods have become one of the most widely used techniques in geological exploration. With the remarkable success of deep learning, applying such techniques to EM methods has emerged as a promising research direction to…
Channel estimation and extrapolation are fundamental issues in MIMO communication systems. In this paper, we proposed the quasi-Newton orthogonal matching pursuit (QNOMP) approach to overcome these issues with high efficiency while…
The orthogonal multi-matching pursuit (OMMP) is a natural extension of orthogonal matching pursuit (OMP). We denote the OMMP with the parameter $M$ as OMMP(M) where $M\geq 1$ is an integer. The main difference between OMP and OMMP(M) is…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
This paper gives an overview of our current Optical Music Recognition (OMR) research. We recently released the OMR dataset \emph{DeepScores} as well as the object detection method \emph{Deep Watershed Detector}. We are currently taking some…
The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {\em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on…
We show that in the limit of small Rossby number $\eps$, the primitive equations of the ocean (OPEs) can be approximated by ``higher-order quasi-geostrophic equations'' up to an exponential accuracy in $\eps$. This approximation assumes…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
Accurate and reliable probabilistic forecasts of hydrological quantities like runoff or water level are beneficial to various areas of society. Probabilistic state-of-the-art hydrological ensemble prediction models are usually driven with…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
This paper investigates maximal estimates of the wave operators for orthonormal families of initial data. We extend the classical maximal estimates for the wave operator by making partial progress on maximal estimates for orthonormal…
Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the…