Related papers: Optimizing Geometric Multigrid Methods with Evolut…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
Gene expression programming is an evolutionary optimization algorithm with the potential to generate interpretable and easily implementable equations for regression problems. Despite knowledge gained from previous optimizations being…
Multiobjective feature selection seeks to determine the most discriminative feature subset by simultaneously optimizing two conflicting objectives: minimizing the number of selected features and the classification error rate. The goal is to…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
In this paper, a nonlinear symbolic regression technique using an evolutionary algorithm known as multi-gene genetic programming (MGGP) is applied for a data-driven modelling between the dependent and the independent variables. The…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
Ensemble weather forecasts based on multiple runs of numerical weather prediction models typically show systematic errors and require post-processing to obtain reliable forecasts. Accurately modeling multivariate dependencies is crucial in…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
The digital transformation of automation places new demands on data acquisition and processing in industrial processes. Logical relationships between acquired data and cyclic process sequences must be correctly interpreted and evaluated. To…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…