Related papers: A hybrid iterative method based on MIONet for PDEs…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…
We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems,…
A fundamental problem in robotic perception is matching identical objects or data, with applications such as loop closure detection, place recognition, object tracking, and map fusion. While the problem becomes considerably more challenging…
In this paper, we study the nonexpansive properties of metric resolvent, and present a convergence rate analysis for the associated fixed-point iterations (Banach-Picard and Krasnosel'skii-Mann types). Equipped with a variable metric, we…
Certain features of the method of characteristics are of considerable interest in relation with Vlasov simulation [H. Abbasi {\it et al}, Phys. Rev. E \textbf{84}, 036702 (2011)]. A Vlasov simulation scheme of this kind can be recurrence…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
Nonlinear systems arising from time integrators like Backward Euler can sometimes be reformulated as optimization problems, known as incremental potentials. We show through a comprehensive experimental analysis that the widely used…
In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…
As further progress in the accurate and efficient computation of coupled partial differential equations (PDEs) becomes increasingly difficult, it has become highly desired to develop new methods for such computation. In deviation from…
Several widely-used first-order saddle-point optimization methods yield an identical continuous-time ordinary differential equation (ODE) that is identical to that of the Gradient Descent Ascent (GDA) method when derived naively. However,…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labelling. Our method employs Bayesian…
Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…
We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve…
In this paper, we adapt proximal incremental aggregated gradient methods to saddle point problems, which is motivated by decoupling linear transformations in regularized empirical risk minimization models. First, the Primal-Dual Proximal…
In this paper we investigate adaptive discretization of the iteratively regularized Gauss- Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution…