Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates

• URL: http://arxiv.org/abs/2010.05698v1
• Date: Fri, 9 Oct 2020 09:26:33 GMT
• Title: Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates
• Authors: Xiaoying Zhuang, Hongwei Guo, Naif Alajlan, Timon Rabczuk
• Abstract summary: We present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle.
• Score: 1.7205106391379024
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on random generated points inside the physical domain so that the total potential energy is minimized at all points. For vibration and buckling analysis, the loss function is constructed based on Rayleigh's principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending analysis. The DAEM can be easily implemented and we employed the Pytorch library and the LBFGS optimizer. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions.

Related papers

• Kernel Approximation of Fisher-Rao Gradient Flows [52.154685604660465]
  We present a rigorous investigation of Fisher-Rao and Wasserstein type gradient flows concerning their gradient structures, flow equations, and their kernel approximations. Specifically, we focus on the Fisher-Rao geometry and its various kernel-based approximations, developing a principled theoretical framework.
  arXiv  Detail & Related papers  (2024-10-27T22:52:08Z)
• DimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning [63.5925701087252]
  We introduce DimOL (Dimension-aware Operator Learning), drawing insights from dimensional analysis. To implement DimOL, we propose the ProdLayer, which can be seamlessly integrated into FNO-based and Transformer-based PDE solvers. Empirically, DimOL models achieve up to 48% performance gain within the PDE datasets.
  arXiv  Detail & Related papers  (2024-10-08T10:48:50Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Higher-order topological kernels via quantum computation [68.8204255655161]
  Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. We propose a quantum approach to defining Betti kernels, which is based on constructing Betti curves with increasing order.
  arXiv  Detail & Related papers  (2023-07-14T14:48:52Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Static, dynamic and stability analysis of multi-dimensional functional graded plate with variable thickness using deep neural network [0.0]
  The goal of this paper is to analyze and predict the central deflection, natural frequency, and critical buckling load of the multi-directional functionally graded (FG) plate. The material properties are assumed to vary smoothly and continuously throughout three directions of the plate.
  arXiv  Detail & Related papers  (2023-01-14T11:37:01Z)
• Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization [0.0]
  We introduce a framework based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and its key properties analytically and numerically. The prototype is establish a discretization of Born-Infeld dynamics, depending on the objective function.
  arXiv  Detail & Related papers  (2022-01-26T19:00:05Z)
• Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis [0.0]
  gradient descent (SGD) is one of the most popular algorithms in modern machine learning. In this article, we discuss some of the common properties of energy landscapes and the noise encountered in machine learning problems.
  arXiv  Detail & Related papers  (2021-05-04T17:52:20Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate [0.0]
  In this paper, a deep collocation (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. The proposed DCM uses a deep neural network to approximate the continuous deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate geometries.
  arXiv  Detail & Related papers  (2021-02-04T14:01:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.