Related papers: Enhancing Dynamic-Mode Decomposition via Multi-Sca…
The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in…
Dynamic multi-objective optimization problems (DMOPs) are widely accepted to be more challenging than stationary problems due to the time-dependent nature of the objective functions and/or constraints. Evaluation of purpose-built algorithms…
Unsupervised anomaly detection stands as an important problem in machine learning, with applications in financial fraud prevention, network security and medical diagnostics. Existing unsupervised anomaly detection algorithms rarely perform…
The blind image deconvolution is a challenging, highly ill-posed nonlinear inverse problem. We introduce a Multiscale Hierarchical Decomposition Method (MHDM) that is iteratively solving variational problems with adaptive data and…
We consider an application of modification of our variational-wavelet approach to some nonlinear collective model of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy related to modeling of propagation of…
This paper focuses on improved edge model based on Curvelet coefficients analysis. Curvelet transform is a powerful tool for multiresolution representation of object with anisotropic edge. Curvelet coefficients contributions have been…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes one process at a time and obtains a noisy binary indicator of whether or not the…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
Deep models are designed to operate on huge volumes of high dimensional data such as images. In order to reduce the volume of data these models must process, we propose a set-based two-stage end-to-end neural subsampling model that is…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…