Related papers: A self adjusting multirate algorithm based on the …

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…

This paper presents a combined sliding-mode control and subspace stabilization methodology for orbital stabilization of periodic trajectories in underactuated mechanical systems with one degree of underactuation. The approach starts with…

In this paper, we extend the adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse to the multistage stochastic programming setting. The proposed algorithms integrate the adaptive partition-based…

We develop an efficient, unconditionally stable, variable step second order exponential time differencing scheme for the incompressible Navier Stokes equations in two and three spatial dimensions under periodic boundary conditions, together…

A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value…

This paper proposes a multitask learning framework for probabilistic model updating by jointly using strain and acceleration measurements. This framework can enhance the structural damage assessment and response prediction of existing steel…

We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…

Stabilized Runge-Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized…

The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…

We develop a general distributed implementation of an adaptive fast multipole method in three space dimensions. We rely on a balanced type of adaptive space discretisation which supports a highly transparent and fully distributed…

Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…

In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…

We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR…

We propose two variants of the Primal Dual Hybrid Gradient (PDHG) algorithm for saddle point problems with block decomposable duals, hereafter called Multi-Timescale PDHG (MT-PDHG) and its accelerated variant (AMT-PDHG). Through novel…

Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…

This research addresses the numerical simulation of the Boltzmann transport equation for semiconductor devices by proposing a multidimensional self-adaptive numerical simulation framework. This framework is applied to two important…

Distributionally robust optimization (DRO) is an effective framework for controlling real-world systems with various uncertainties, typically modeled using distributional uncertainty balls. However, DRO problems often involve infinitely…

We study the convergence rate of a class of linear multi-step methods for BSDEs. We show that, under a sufficient condition on the coefficients, the schemes enjoy a fundamental stability property. Coupling this result to an analysis of the…

We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM). For {\em incompressible} flows, multirate…

Multi-agent planning under Signal Temporal Logic (STL) is often hindered by collaborative tasks that lead to computational challenges due to the inherent high-dimensionality of the problem, preventing scalable synthesis with satisfaction…