20 citations · 87 across the 20 of their papers we have counts for
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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…
Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs
Cheng Chang, Liu Liu, Tieyong Zeng
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving…
A deep neural network approach on solving the linear transport model under diffusive scaling
Liu Liu, Tieyong Zeng, Zecheng Zhang
In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is c…