Results 151 to 160 of about 1,001,967 (186)

Inferring complex evolutionary history of the closely related East Asian wild roses in Rosa sect. Synstylae (Rosaceae) based on genomic evidence from conserved orthologues. [PDF]

Ann Bot
Jeon JH, Maki M, Chiang YC, Kim SC.
europepmc   +1 more source

The Deep Ritz Method for parametric p-Dirichlet problems

Advances in Continuous and Discrete Models, 2022
We establish error estimates for the approximation of parametric p-Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries and exponents p∈(1,∞)\documentclass[12pt]{minimal} \usepackage{amsmath ...
A. Kaltenbach, Marius Zeinhofer
semanticscholar   +3 more sources

Variational volume reconstruction with the Deep Ritz Method

CoRR
We present a novel approach to variational volume reconstruction from sparse, noisy slice data using the Deep Ritz method. Motivated by biomedical imaging applications such as MRI-based slice-to-volume reconstruction (SVR), our approach addresses three ...
Conor Rowan, Sumedh Soman, John A. Evans
semanticscholar   +3 more sources

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Higher-order multi-scale deep Ritz method (HOMS-DRM) and its convergence analysis for solving thermal transfer problems of composite materials

Computational Mechanics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junzhi Cui, Jiale Linghu, Hao Dong
exaly   +4 more sources

Finding geodesics with the Deep Ritz method

arXiv.org
Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy.
Conor Rowan
semanticscholar   +3 more sources

Free vibration analysis of deep doubly curved open shells using the Ritz method

Aerospace Science and Technology, 2017
Abstract This paper develops a unified semi-analytical method for the free vibration analysis of moderately thick doubly curved open shells with arbitrary geometry and classic boundary conditions. The only restriction on the shell's geometry is that boundaries are being coincided by the principal curvature lines of the shell. The formulation is based
K Malekzadeh Fard
exaly   +3 more sources

Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure

Journal of Computational Science
This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials.
E. Mema, Ting Wang, Jaroslaw Knap
semanticscholar   +3 more sources

Inexact Uzawa-Double Deep Ritz Method for Weak Adversarial Neural Networks

arXiv.org
The emergence of deep learning has stimulated a new class of PDE solvers in which the unknown solution is represented by a neural network. Within this framework, residual minimization in dual norms -- central to weak adversarial neural network approaches
Emin Benny-Chacko, I. Brevis, L. Espath, K. G. V. D. Zee   +3 more
semanticscholar   +3 more sources

Refined generalization analysis of the Deep Ritz Method and Physics-Informed Neural Networks

CoRR
In this paper, we derive refined generalization bounds for the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). For the DRM, we focus on two prototype elliptic partial differential equations (PDEs): Poisson equation and static Schr ...
Xianliang Xu, Zhongyi Huang
semanticscholar   +3 more sources

Error Analysis of Three-Layer Neural Network Trained With PGD for Deep Ritz Method

IEEE Transactions on Information Theory
Machine learning is a rapidly advancing field with diverse applications across various domains. One prominent area of research is the utilization of deep learning techniques for solving partial differential equations (PDEs). In this work, we specifically
Yuling Jiao, Yanming Lai, Yang Wang
semanticscholar   +4 more sources