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Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they…

In the complex multi-state system (MSS), reliability analysis is a significant research content, both for equipment design, manufacturing, usage and maintenance. Universal Generating Function (UGF) is an important method in the reliability…

Reliable uncertainty quantification (UQ) in machine learning (ML) regression tasks is becoming the focus of many studies in materials and chemical science. It is now well understood that average calibration is insufficient, and most studies…

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the…

With increasing computational demand, Neural-Network (NN) based models are being developed as pre-trained surrogates for different thermohydraulics phenomena. An area where this approach has shown promise is in developing higher-fidelity…

This paper is the second of a two-part series that discusses the implementation issues and test results of a robust Unscented Kalman Filter (UKF) for power system dynamic state estimation with non-Gaussian synchrophasor measurement noise.…

Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is…

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKF-GPS) is…

Efficient high-rank approximations of the Hessian can accelerate seismic full waveform inversion (FWI) and uncertainty quantification (UQ). In FWI, approximations of the inverse of the Hessian may be used as preconditioners for Newton-type…

The existing control barrier function literature generally relies on precise mathematical models to guarantee system safety, limiting their applicability in scenarios with parametric uncertainties. While incremental control techniques have…

Modern container ships face higher wind loads due to increased windage areas, making accurate predictions of wind loads essential for mooring design. Existing empirical models, largely developed for container ships with smaller windage…

Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…

We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is on practical accuracy, robustness and efficiency. To address…

Uncertainty quantification (UQ) for foundation models is essential to identify and mitigate potential hallucinations in automatically generated text. However, heuristic UQ approaches lack formal guarantees for key metrics such as the false…

Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they enable numerical methods to approximate very…

Measurements and state estimates are often imperfect in control practice, posing challenges for safety-critical applications, where safety guarantees rely on accurate state information. In the presence of estimation errors, several prior…

This paper proposes a safety controller for control-affine nonlinear systems with unmodelled dynamics and disturbances to improve closed-loop robustness. Uncertainty estimation-based control barrier functions (CBFs) are utilized to ensure…

Quantum reservoir computing (QRC) is a promising quantum machine learning framework for near-term quantum platforms, yet the performance of different QRC architectures under realistic constraints remains largely unexplored. Here, we provide…

Uncrewed Surface Vehicles (USVs) are a popular and efficient type of marine craft that find application in a large number of water-based tasks. When multiple USVs operate in the same area, they may be required to dock to each other to…