相关论文: A Novel Optimized Decomposition Method for Smoluch…
This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing…
The semi-analytical method obtains the solution for linear/nonlinear ODEs and PDEs in series form. This article presents a novel semi-analytical approach named Daftardar-Jafari method (DJM) to solve integro-partial differential equation…
In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
In this work we demonstrate a surprising way of exploitation of the mosaic--skeleton approximations for efficient numerical solving of aggregation equations with many applied kinetic kernels. The complexity of the evaluation of the…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
Optimal margin Distribution Machine (ODM) is a newly proposed statistical learning framework rooting in the novel margin theory, which demonstrates better generalization performance than the traditional large margin based counterparts.…
Block-structured problems are central to advances in numerical optimization and machine learning. This paper provides the formalization of convergence analysis for two pivotal algorithms in such settings: the block coordinate descent (BCD)…
We present a study of the Adomian's Decomposition Method (ADM) applied to the Hamilton-Jacobi equations ut + H (ux) = 0. We recall the well known characteristics methods in the case of this type of equations to justify the existence or not…
We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…
We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
In this paper, we propose a new paradigm for program optimization which is based on aggressive aggregation, i.e., on a partial evaluation-based decomposition of acyclic program fragments into a pair of computationally optimal structures: an…
A novel design procedure for practical hierarchical distribution matchers (HiDMs) in probabilistically shaped constellation systems is presented. The proposed approach enables the determination of optimal parameters for any target…
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.…
The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
We prove well-posedness of global solutions for a class of coagulation equations which exhibit the gelation phase transition. To this end, we solve an associated partial differential equation involving the generating functions before and…
Accurate and efficient predictions of the quasiparticle properties of complex materials remain a major challenge due to the convergence issue and the unfavorable scaling of the computational cost with respect to the system size.…
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…