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Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
In beam shaping applications, the minimization of the number of necessary optical elements for the beam shaping process can benefit the compactness of the optical system and reduce its cost. The single freeform surface design for input…
Dynamic simulation plays a crucial role in power system transient stability analysis, but traditional numerical integration-based methods are time-consuming due to the small time step sizes. Other semi-analytical solution methods, such as…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
This paper presents a directional proximal point method (DPPM) to derive the minimum of any C1-smooth function f. The proposed method requires a function persistent a local convex segment along the descent direction at any non-critical…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one…
This study investigates the use of continuous-time dynamical systems for sparse signal recovery. The proposed dynamical system is in the form of a nonlinear ordinary differential equation (ODE) derived from the gradient flow of the Lasso…
We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can…
This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are…
In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…
Diffusion models have demonstrated promising performance in real-world video super-resolution (VSR). However, the dozens of sampling steps they require, make inference extremely slow. Sampling acceleration techniques, particularly…
This paper focuses on the Partitioned-Solution Approach (PSA) employed for the Time-Domain Simulation (TDS) of dynamic power system models. In PSA, differential equations are solved at each step of the TDS for state variables, whereas…
Distributed statistical inference has recently attracted enormous attention. Many existing work focuses on the averaging estimator. We propose a one-step approach to enhance a simple-averaging based distributed estimator. We derive the…
There have been recent efforts that combine seemingly disparate methods, extremum seeking (ES) optimization and partial differential equation (PDE) backstepping, to address the problem of model-free optimization with PDE actuator dynamics.…
An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
Nondestructive one-shot device (NOSD) testing plays a crucial role in engineering, particularly in the reliability assessment of high-stakes systems such as aerospace components, medical devices, and semiconductor technologies. Accurate…