5 papers
Numerical Construction of Quasi-Periodic Solutions for Nonlinear PDEs: I. Bounded Perturbation
Mingwei Fu, Bin Shi
In this paper, we propose an alternating numerical scheme for constructing quasi-periodic solutions to a class of nonlinear partial differential equations (PDEs) with bounded pertu…
Numerical Construction of Elliptic Lower-Dimensional Quasi-Periodic Solutions with a Priori Bound
Mingwei Fu, Bin Shi
A numerical framework for constructing full-dimensional quasi-periodic solutions in nearly integrable systems was recently developed by Fu and Shi[2026]. Based on an alternating sc…
Numerical Construction of Quasi-Periodic Solutions Beyond Symplectic Integrators
Mingwei Fu, Bin Shi
Symplectic integrators are the established standard for long-term simulations of nearly-integrable Hamiltonian systems due to their preservation of geometric structures. However, t…
A Family of Controllable Momentum Coefficients for Forward-Backward Accelerated Algorithms
Mingwei Fu, Bin Shi
Nesterov's accelerated gradient method (NAG) marks a pivotal advancement in gradient-based optimization, achieving faster convergence compared to the vanilla gradient descent metho…
Lyapunov Analysis For Monotonically Forward-Backward Accelerated Algorithms
Mingwei Fu, Bin Shi
Nesterov's accelerated gradient method (NAG) achieves faster convergence than gradient descent for convex optimization but lacks monotonicity in function values. To address this, B…