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The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Accurate prediction of dynamical response of structural system depends on the correct modeling of that system. However, modeling becomes increasingly challenging when there are many candidate models available to describe the system…

Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run…

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…

Quantification of the impact of uncertainty in material properties as well as the input ground motion on structural responses is an important step in implementing a performance-based earthquake engineering (PBEE) framework. Among various…

Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…

Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petro-elastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Finite element model updating utilizing frequency response functions as inputs is an important procedure in structural analysis, design and control. This paper presents a highly efficient framework that is built upon Gaussian process…

Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries.…

Multi-fidelity Gaussian process is a common approach to address the extensive computationally demanding algorithms such as optimization, calibration and uncertainty quantification. Adaptive sampling for multi-fidelity Gaussian process is a…

Uncertainty quantification approaches have been more critical in large language models (LLMs), particularly high-risk applications requiring reliable outputs. However, traditional methods for uncertainty quantification, such as…

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

Online map generation and trajectory prediction are critical components of the autonomous driving perception-prediction-planning pipeline. While modern vectorized mapping models achieve high geometric accuracy, they typically treat map…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…

Multimodal learning combines information from multiple data modalities to improve predictive performance. However, modalities often contribute unequally and in a data dependent way, making it unclear which data modalities are genuinely…