Related papers: GParareal: A time-parallel ODE solver using Gaussi…
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and…
We cast motion planning under uncertainty as a stochastic optimal control problem, where the optimal posterior distribution has an explicit form. To approximate this posterior, this work frames an optimization problem in the space of…
We present the Parareal-CG algorithm for time-dependent differential equations in this work. The algorithm is a parallel in time iteration algorithm utilizes Chebyshev-Gauss spectral collocation method for fine propagator F and backward…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine…
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite generalized eigenvalue problem lying in an interval on the real…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
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…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
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,…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
As has been shown in our previous work, the parallel-in-time direct inverse (ParaDIn) method introduced by Yamaleev and Paudel in (arXiv: 2406.00878v1, 2024) imposes some constraint on the maximum number of time levels, $N_t$, that can be…
This work proposes a data-driven method for enabling the efficient, stable time-parallel numerical solution of systems of ordinary differential equations (ODEs). The method assumes that low-dimensional bases that accurately capture the time…
In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…
In this paper, we present a novel pseudospectral (PS) method for solving a new class of initial-value problems (IVPs) of time-dependent one-dimensional fractional partial differential equations (FPDEs) with variable coefficients and…
Gaussian Processes (GPs) provide a flexible and statistically principled foundation for modelling spatiotemporal phenomena, but their $O(N^3)$ scaling makes them intractable for large datasets. Approximate methods such as variational…
The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…