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Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

Dynamic Range Compression (DRC) is a widely used audio effect that adjusts signal dynamics for applications in music production, broadcasting, and speech processing. Inverting DRC is of broad importance for restoring the original dynamics,…

In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking…

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

In a normal indoor environment, Raman spectrum encounters noise often conceal spectrum peak, leading to difficulty in spectrum interpretation. This paper proposes deep learning (DL) based noise reduction technique for Raman spectroscopy.…

Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…

In conducting non-linear dimensionality reduction and feature learning, it is common to suppose that the data lie near a lower-dimensional manifold. A class of model-based approaches for such problems includes latent variables in an unknown…

Sparse Bayesian learning has promoted many effective frameworks for brain activity decoding, especially for the reconstruction of muscle activity. However, existing sparse Bayesian learning mainly employs Gaussian distribution as error…

Reduced-Rank (RR) regression is a powerful dimensionality reduction technique but it overlooks any possible group configuration among the responses by assuming a low-rank structure on the entire coefficient matrix. Moreover, the temporal…

Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with smooth density. We first derive a Monte-Carlo type formula…

Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a…

We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We…

Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input…

We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the…

This article introduces a novel dynamic framework to Bayesian model averaging for time-varying parameter quantile regressions. By employing sequential Markov chain Monte Carlo, we combine empirical estimates derived from dynamically chosen…