Related papers: PFASST-ER: Combining the Parallel Full Approximati…
This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
The ParaOpt algorithm was recently introduced as a time-parallel solver for optimal-control problems with a terminal-cost objective, and convergence results have been presented for the linear diffusive case with implicit-Euler time…
Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…
We investigate the use of possibly the simplest scheme for the parallelisation of the standard particle filter, that consists in splitting the computational budget into $M$ fully independent particle filters with $N$ particles each, and…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…
For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
We present a proof of concept for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED) by adapting the finite-difference time-domain (FDTD) method. The…
This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…
Fourier and related transforms is a family of algorithms widely employed in diverse areas of computational science, notoriously difficult to scale on high-performance parallel computers with large number of processing elements (cores). This…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear…
Following AI scaling trends, frontier models continue to grow in size and continue to be trained on larger datasets. Training these models requires huge investments in exascale computational resources, which has in turn driven developtment…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…