Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation,
and optimization under uncertainty, typically require several thousand evaluations of the …

As we shift from population‐based medicine towards a more precise patient‐specific regime
guided by predictions of verified and well‐established cardiovascular models, an urgent …

The generalized polynomial chaos (gPC) method recently advocated in the literature,
exhibits impressive efficiency and accuracy in probabilistic power flow (PPF) calculations of …

This letter proposes a new polynomial-chaos-based Kalman filter (PCKF) that is able to track
the dynamics of nonlinear dynamical systems subject to strong nonlinearities. Specifically …

In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with
random coefficients in the multiquery setting using an optimization approach. The …

In this paper, we propose a multiscale data-driven stochastic method (MsDSM) to study
stochastic partial differential equations (SPDEs) in the multiquery setting. This method …

We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive,
adaptive algorithm for the solution of elliptic partial differential equations with random …

Based on the alternating direction method of multipliers (ADMM), we develop three
numerical algorithms incrementally for solving the optimal control problems constrained by …

While the conventional generalized polynomial chaos method exhibits excellent
computational efficiency and accuracy in the probabilistic power flow calculations applied to …

Polynomial chaos (PC) has been proven to be an efficient method for uncertainty
quantification, but its applicability is limited by two strong assumptions: the mutual …