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Optimal Sobolev Approximation by Deterministic and Random Shallow Sigmoidal Networks
Zhaohui Fu, Yangshuai Wang
Shallow networks with prescribed or randomly sampled hidden parameters are widely used as numerical trial spaces, yet their optimal Sobolev approximation power with standard smooth…
A Discrete-Time Random Feature Method for Nonlinear Evolution Equations with Implicit-Explicit Runge--Kutta Time Stepping
Haoran Zhou, Zhaohui Fu, Yangshuai Wang +1
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an addit…
Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows
Zhaohui Fu, Jie Shen, Jiang Yang
In this paper, we develop a general framework for constructing higher-order, unconditionally energy-stable exponential time differencing Runge-Kutta methods applicable to a range o…
Energy plus maximum bound preserving Runge-Kutta methods for the Allen-Cahn equation
Zhaohui Fu, Tao Tang, Jiang Yang
It is difficult to design high order numerical schemes which could preserve both the maximum bound property (MBP) and energy dissipation law for certain phase field equations. Stro…
Energy diminishing implicit-explicit Runge--Kutta methods for gradient flows
Zhaohui Fu, Tao Tang, Jiang Yang
This study focuses on the development and analysis of a group of high-order implicit-explicit (IMEX) Runge--Kutta (RK) methods that are suitable for discretizing gradient flows wit…