Related papers: A Parareal Algorithm with Spectral Coarse Solver
A key component of many robotics model-based planning and control algorithms is physics predictions, that is, forecasting a sequence of states given an initial state and a sequence of controls. This process is slow and a major computational…
The Parareal parallel-in-time integration method often performs poorly when applied to hyperbolic partial differential equations. This effect is even more pronounced when the coarse propagator uses a reduced spatial resolution. However,…
We consider the initial-boundary value problem for a quasilinear time-fractional diffusion equation, and develop a fully discrete solver combining the parareal algorithm in time with a L1 finite-difference approximation of the Caputo…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they require the user to build coarse models to handle the…
This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
In this paper, we investigate the strong convergence analysis of parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed parareal algorithms proceed as two-level temporal…
This paper analyzes the SParareal algorithm for stochastic differential equations (SDEs). Compared to the classical Parareal algorithm, the SParareal algorithm accelerates convergence by introducing stochastic perturbations, achieving…
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…
In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
We present a full implementation of the parareal algorithm---an integration technique to solve differential equations in parallel---in the Julia programming language for a fully general, first-order, initial-value problem. We provide a…
In diffusion models, samples are generated through an iterative refinement process, requiring hundreds of sequential model evaluations. Several recent methods have introduced approximations (fewer discretization steps or distillation) to…
The aim of this paper is to analyze the robust convergence of a class of parareal algorithms for solving parabolic problems. The coarse propagator is fixed to the backward Euler method and the fine propagator is a high-order single step…
Asynchronous iterations arise naturally in parallel computing if one wants to solve large problems with a minimization of the idle times. This paper presents an original model of asynchronous iterations for a time-domain decomposition…
This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial…