44 citations · 154 across the 14 of their papers we have counts for
7 papers · 1 filter
A non-intrusive bi-fidelity reduced basis method for time-independent problems
Jun Sur Richard Park, Xueyu Zhu
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However…
Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread
Giulia Bertaglia, Chuan Lu, Lorenzo Pareschi +1
When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibrati…
Multi-fidelity methods for uncertainty propagation in kinetic equations
Giacomo Dimarco, Liu Liu, Lorenzo Pareschi +1
The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computation…
Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
Giulia Bertaglia, Liu Liu, Lorenzo Pareschi +1
Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertain…
A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs
Liu Liu, Lorenzo Pareschi, Xueyu Zhu
In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the pr…
A bi-fidelity method for the multiscale Boltzmann equation with random parameters
Liu Liu, Xueyu Zhu
In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C.…
An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models
Ming Cheng, Yi Qin, Akil Narayan +3
We develop a numerical framework to implement the cumulative density function (CDF) method for obtaining the probability distribution of the system state described by a kinematic w…