Related papers: A parallel-in-time approach for accelerating direc…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We design a randomised parallel version of Adaboost based on previous studies on parallel coordinate descent. The algorithm uses the fact that the logarithm of the exponential loss is a function with coordinate-wise Lipschitz continuous…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
Anytime search algorithms are useful for planning problems where a solution is desired under a limited time budget. Anytime algorithms first aim to provide a feasible solution quickly and then attempt to improve it until the time budget…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
While Graph Neural Networks (GNNs) are popular in the deep learning community, they suffer from several challenges including over-smoothing, over-squashing, and gradient vanishing. Recently, a series of models have attempted to relieve…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations.…
Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
Parallel thinking has emerged as a promising paradigm for reasoning, yet it imposes significant computational burdens. Existing efficiency methods primarily rely on local, per-trajectory signals and lack principled mechanisms to exploit…
An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…