6 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…
Neural-Spectral and Newton-HUM Methods for Reconstructing Controls of Wave Equations
Tan-Phuc Nguyen, Minh-Binh Tran, Son Tu
We develop a framework for constructing and rigorously validating controls for semilinear wave equations with localized interior control. We analyze the continuous energy-space pro…
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…
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>…
Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
Bingyang Hu, Son N. T. Tu, Jianlu Zhang
In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the co…