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The Semi-Analytical Finite Element (SAFE) method is widely used for computing guided wave dispersion curves in waveguides of arbitrary cross-section. Accurate mode tracking across consecutive wavenumber steps remains challenging,…
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…
The distribution of block maxima of sequences of independent and identically-distributed random variables is used to model extreme values in many disciplines. The traditional extreme value (EV) theory derives a closed-form expression for…
Over several decades, electromechanical impedance (EMI) measurements have been employed as a basis for structural health monitoring and damage detection. Traditionally, Root-mean-squared-deviation (RMSD) and Cross-correlation (XCORR) based…
The proposed method introduces a parameter determination approach based on the minimum Fractal box dimension (FBD) of Variational Mode Decomposition (VMD) components, aiming to address the issue of manual determination of VMD decomposition…
Probabilistic Latent Variable Models (LVMs) provide an alternative to self-supervised learning approaches for linguistic representation learning from speech. LVMs admit an intuitive probabilistic interpretation where the latent structure…
By extending the classical analysis techniques due to Samokish, Faddeev and Faddeeva, and Longsine and McCormick among others, we prove the convergence of preconditioned steepest descent with implicit deflation (PSD-id) method for solving…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated…
This study proposes a novel portfolio optimization framework that integrates statistical social network analysis with time series forecasting and risk management. Using daily stock data from the S&P 500 (2020-2024), we construct dependency…
High-fidelity simulations are essential for predicting material behavior under high-velocity impact (HVI), but their accuracy depends on material models and parameters that are often calibrated by manual fitting to multiple costly…
In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise. We propose a new class of…
In this paper we discuss the application of nonconforming virtual element methods(VEM) for the second order diffusion dominated convection diffusion reaction equation. Stability of the virtual element methods has been proved for the…
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…
Federated Composite Optimization (FCO) has emerged as a promising framework for training models with structural constraints (e.g., sparsity) in distributed edge networks. However, simultaneously achieving communication efficiency and…
Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees(HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence…
This study presents fast and accurate analytical methods for transient thermal modeling in multi-layer composites with an arbitrary number of layers. The proposed approach accounts for internal heat generation and non-homogeneities in the…
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…
Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…