10 papers
Convergence Rate of Birkhoff Average for Toral Quasi-Periodic Rotations and Applications
Son N. T. Tu, Jianlu Zhang, Siyao Zhu
In this paper, we establish quantitative Denjoy--Koksma type estimates for higher-dimensional quasi-periodic torus rotations. For Diophantine frequency vectors, we establish quanti…
A Structure-Preserving Neural-Spectral Method for Reconstructing Controls of Wave Equations
Tan-Phuc Nguyen, Minh-Binh Tran, Son Tu
The numerical reconstruction of controls for partial differential equations remains comparatively underdeveloped, despite the extensive analytical literature on controllability. Th…
Quantitative homogenization for static contact Hamilton-Jacobi equations
Gengyu Liu, Son N. T. Tu, Jianlu Zhang
We characterize possible pairs addressing the homogenization problem for Hamilton…
Operator Splitting, Policy Iteration, and Machine Learning for Stochastic Optimal Control
Alain Bensoussan, Thien P. B. Nguyen, Minh-Binh Tran +1
We propose a splitting approach to solve the second-order Hamilton--Jacobi equation, reducing it to a heat step and a purely first-order step. The latter is implemented using a gra…
Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
Yuxi Han, Son Tu
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation o…
On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
Prerona Dutta, Khai T. Nguyen, Son N. T. Tu
In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every $p>…