Related papers: Diagonalization-Based Parallel-in-Time Preconditio…
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…
An numerical iterative framework for global modal stability analysis of compressible flows using a parallel environment is presented. The framework uses a matrix-free implementation to allow computations of large scale problems. Various…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
We present a parallel GPU-accelerated solver for branch Model Predictive Control problems. Based on iterative LQR methods, our solver exploits the tree-sparse structure and implements temporal parallelism using the parallel scan algorithm.…
We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…
In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…
Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier-Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a…
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…
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…
We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…
We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
We present a new approach to parallelization of the first-order backward difference discretization (BDF1) of the time derivative in partial differential equations, such as the nonlinear heat and viscous Burgers equations. The time…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…