Related papers: Improved scalar auxiliary variable schemes for ori…
We present a new numerical scheme for one dimensional dynamical systems. This is a modification of the discrete gradient method and keeps its advantages, including the stability and the conservation of the energy integral. However, its…
The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH) equation. In this paper, based on the exponential…
This work proposes a novel method for scaling multi-timestep security-constrained optimal power flow in large power grids. The challenge arises from dealing with millions of variables and constraints, including binary variables and…
We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…
The nonlocal Allen-Cahn equation with nonlocal diffusion operator is a generalization of the classical Allen-Cahn equation. It satisfies the energy dissipation law and maximum bound principle (MBP), and is important for simulating a series…
The incompressible smoothed particle hydrodynamics method (ISPH) is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical…
The challenge of Out-of-Distribution (OOD) generalization poses a foundational concern for the application of machine learning algorithms to risk-sensitive areas. Inspired by traditional importance weighting and propensity weighting…
In this paper, we consider a class of convex programming problems with linear equality constraints, which finds broad applications in machine learning and signal processing. We propose a new adaptive balanced augmented Lagrangian (ABAL)…
We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the condition…
Load forecasting has always been a challenge for grid operators due to the growing complexity of power systems. The increase in extreme weather and the need for energy from customers has led to load forecasting sometimes failing. This…
Affine variational inequalities (AVI) are an important problem class that generalize systems of linear equations, linear complementarity problems and optimality conditions for quadratic programs. This paper describes PATHAVI, a…
Recently, sharpness-aware minimization (SAM) has attracted much attention because of its surprising effectiveness in improving generalization performance. However, compared to stochastic gradient descent (SGD), it is more prone to getting…
This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization process into simpler subproblems, and more importantly, the…
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…
Several methods exist for finding ground (as well as excited) states of nonlinear waves equations. In this paper we first introduce two modifications of the so-called accelerated imaginary-time evolution method (AITEM). In our first…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical…
Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…