5 papers
Data-Driven Parameter Identification for Tumor Growth Models
Liu Liu, Yifei Wang, Qinyu Xu +1
Modeling tumor growth accurately is essential for understanding cancer progression and informing treatment strategies. To estimate the parameters in the tumor growth model describe…
Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs
Chenyang An, Xiaoqian Xu
We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial bound for inviscid shears with , a uni…
Phase separation for the 2D Cahn-Hilliard equation with a background shear flow
Yu Feng, Yuanyuan Feng, Anna L. Mazzucato +1
We consider the Cahn-Hilliard equation, which models phase separation in binary fluids, on the two-dimen\-sional torus in the presence of advection by a given background shear flow…
Accelerating sampling via asymptotic relaxation enhancing flows
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
In this paper, we accelerate Langevin Monte Carlo sampling from Gibbs measures by adding a large drift that preserves the invariant measure. For warm-start ini…
Sequential Exponential Lower Bounds for the Advection-Diffusion Equation with Shear Flows
Yupei Huang, Xiaoqian Xu
In this paper, we prove that the norm of spatial mean-free solutions to the advection--diffusion equation on with shear drifts satisfies an \emph{exponential l…