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This paper proposes a decentralized dynamic state estimation (DSE) algorithm with bimodal Gaussian mixture measurement noise. The decentralized DSE is formulated using the Ensemble Kalman Filter (EnKF) and then compared with the unscented…
This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…
Implicit Neural Representations have gained prominence as a powerful framework for capturing complex data modalities, encompassing a wide range from 3D shapes to images and audio. Within the realm of 3D shape representation, Neural Signed…
This work presents a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers, which has many applications for shape modeling across diverse fields. Unlike prior approaches that either exclusively…
In light of recent work studying massive functional/longitudinal data, such as the resulting data from the COVID-19 pandemic, we propose a novel functional/longitudinal data model which is a combination of the popular varying coefficient…
Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…
The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
We present a new Unbiased Minimal Variance (UMV) estimator for the purpose of reconstructing the large--scale structure of the universe from noisy, sparse and incomplete data. Similar to the Wiener Filter (WF), the UMV estimator is derived…
We introduce the notion of multiscale covariance tensor fields (CTF) associated with Euclidean random variables as a gateway to the shape of their distributions. Multiscale CTFs quantify variation of the data about every point in the data…
This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…
This paper introduces an efficient sub-model ensemble framework aimed at enhancing the interpretability of medical deep learning models, thus increasing their clinical applicability. By generating uncertainty maps, this framework enables…
This work introduces an end-to-end framework for inverse design of elastic networks directly in the space of constitutive behaviors. A constitutive prior is constructed from noisy stress-strain data using a latent representation that…
In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation…
The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods…
Uncertainty quantification (UQ) plays a critical role in verifying and validating forward integrated computational materials engineering (ICME) models. Among numerous ICME models, the crystal plasticity finite element method (CPFEM) is a…
(Part of the abstract) In this thesis, we investigate the use of unsupervised spoken term discovery in tackling this problem. Unsupervised spoken term discovery aims to discover topic-related terminologies in a speech without knowing the…
Continuous-variable (CV) quantum systems provide a versatile platform for quantum information processing, in which quantum states can be represented in the quadrature phase space. In realistic implementations, environmental noise, primarily…
Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial…