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math.NA2023
On a neural network approach for solving potential control problem of the semiclassical Schrödinger equation
Yating Wang, Liu Liu
Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semicl…
math.NA2022★ 1 cited
Convergence of the Fourier-Galerkin spectral method for the Boltzmann equation with uncertainties
Liu Liu, Kunlun Qi
It is well-known that the Fourier-Galerkin spectral method has been a popular approach for the numerical approximation of the deterministic Boltzmann equation with spectral accurac…
math.NA2018★ 9 cited
A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings
Liu Liu
In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior leading to the drift diff…