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Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…

Machine Learning · Computer Science 2020-11-09 Haoran Zhu , Pavankumar Murali , Dzung T. Phan , Lam M. Nguyen , Jayant R. Kalagnanam

We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…

Numerical Analysis · Mathematics 2024-04-29 Alexandre L. Madureira , Marcus Sarkis

Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…

Machine Learning · Computer Science 2025-08-12 Yichen Luo , Jia Wang , Dapeng Lan , Yu Liu , Zhibo Pang

A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…

Numerical Analysis · Mathematics 2016-09-27 Hehu Xie , Zhimin Zhang

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e.,…

Numerical Analysis · Mathematics 2023-02-15 Michael Pilosov , Carlos del-Castillo-Negrete , Tian Yu Yen , Troy Butler , Clint Dawson

A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…

Numerical Analysis · Mathematics 2012-01-12 Hehu Xie

In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert…

Functional Analysis · Mathematics 2016-10-10 L. B. Mohammed , A. Kılıçman

Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…

Optimization and Control · Mathematics 2024-12-10 Willem Esterhuizen , Kathrin Flaßkamp , Matthias Hoffmann , Karl Worthmann

The single nucleotide polymorphism (SNP) is the most widely studied type of genetic variation. A haplotype is defined as the sequence of alleles at SNP sites on each haploid chromosome. Haplotype information is essential in unravelling the…

Genomics · Quantitative Biology 2020-06-19 Sina Majidian , Mohammad Hossein Kahaei , Dick de Ridder

The problem of solving partial differential equations (PDEs) on manifolds can be considered to be one of the most general problem formulations encountered in computational multi-physics. The required covariant forms of balance laws as well…

Numerical Analysis · Mathematics 2021-01-19 Robert L. Gates , Maximilian Bittens

We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…

Numerical Analysis · Mathematics 2013-03-25 Mårten Gulliksson , Sverker Edvardsson , Andreas Lind

We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to…

Quantum Gases · Physics 2021-04-27 Corbinian Wellenhofer , Daniel R. Phillips , Achim Schwenk

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…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

The explicit analytic solution of the Thomas Fermi equation thorough a new kind of analytic technique, namely the homotopy analysis method, was employed by Liao (Appl. Math. Comp. 144, (2003)). However, the base functions and the auxiliary…

Mathematical Physics · Physics 2009-09-08 M. Turkyilmazoglu

We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…

Numerical Analysis · Mathematics 2023-11-10 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity…

Mathematical Physics · Physics 2022-08-25 Nikhil Singh , Anupam Saxena

Multi-objective parametric optimization problem is presented for overwrapped composite pressure vessels under internal pressure for storage and heating water. It is solved using the developed iterative optimization algorithm. Optimal values…

Optimization and Control · Mathematics 2024-10-08 Lyudmyla Rozova , Bilal Meemary , Salim Chaki , Mylène Deléglise-Lagardère , Dmytro Vasiukov

This work investigates the Bicluster Graph Editing Problem (BGEP) and how it can be applied to solve the Manufacturing Cell Formation Problem (MCFP). We develop an exact method for the BGEP that consists of a Branch-and-Cut approach…

Optimization and Control · Mathematics 2013-12-12 Rian G. S. Pinheiro , Ivan C. Martins , Fábio Protti , Luiz S. Ochi , Luidi G. Simonetti , Anand Subramanian

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

Numerical Analysis · Mathematics 2015-11-13 Yunhui He , Yu Li , Hehu Xie

Many real world optimization problems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search…

Artificial Intelligence · Computer Science 2024-08-31 El-Ghazali Talbi