Meshless physics-informed deep learning method for three-dimensional solid mechanics

• URL: http://arxiv.org/abs/2012.01547v2
• Date: Mon, 8 Feb 2021 18:11:31 GMT
• Title: Meshless physics-informed deep learning method for three-dimensional solid mechanics
• Authors: Diab W. Abueidda, Qiyue Lu, Seid Koric
• Abstract summary: Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We consider different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We show that the DCM can capture the response qualitatively and quantitatively, without the need for any data generation using other numerical methods such as the FEM. Data generation usually is the main bottleneck in most data-driven models. The deep learning model is trained to learn the model's parameters yielding accurate approximate solutions. Once the model is properly trained, solutions can be obtained almost instantly at any point in the domain, given its spatial coordinates. Therefore, the deep collocation method is potentially a promising standalone technique to solve partial differential equations involved in the deformation of materials and structural systems as well as other physical phenomena.

Related papers

• Network scaling and scale-driven loss balancing for intelligent poroelastography [2.665036498336221]
  A deep learning framework is developed for multiscale characterization of poroelastic media from full waveform data. Two major challenges impede direct application of existing state-of-the-art techniques for this purpose. We propose the idea of emphnetwork scaling where the neural property maps are constructed by unit shape functions composed into a scaling layer.
  arXiv  Detail & Related papers  (2024-10-27T23:06:29Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks [68.8204255655161]
  We introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization. The results of our physics-aware CNN are compared to a state-of-the-art data-based approach.
  arXiv  Detail & Related papers  (2023-08-04T05:09:06Z)
• Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification [0.0]
  Information field theory (IFT) provides the tools necessary to perform statistics over fields that are not necessarily Gaussian. We extend IFT to physics-informed IFT (PIFT) by encoding the functional priors with information about the physical laws which describe the field. The posteriors derived from this PIFT remain independent of any numerical scheme and can capture multiple modes. We numerically demonstrate that the method correctly identifies when the physics cannot be trusted, in which case it automatically treats learning the field as a regression problem.
  arXiv  Detail & Related papers  (2023-01-18T15:40:19Z)
• Dynamic Latent Separation for Deep Learning [67.62190501599176]
  A core problem in machine learning is to learn expressive latent variables for model prediction on complex data. Here, we develop an approach that improves expressiveness, provides partial interpretation, and is not restricted to specific applications.
  arXiv  Detail & Related papers  (2022-10-07T17:56:53Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• A deep learning energy method for hyperelasticity and viscoelasticity [0.0]
  The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation.
  arXiv  Detail & Related papers  (2022-01-15T05:52:38Z)
• DeepPhysics: a physics aware deep learning framework for real-time simulation [0.0]
  We propose a solution to simulate hyper-elastic materials using a data-driven approach. A neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond.
  arXiv  Detail & Related papers  (2021-09-17T12:15:47Z)
• ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks [86.37110868126548]
  In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
  arXiv  Detail & Related papers  (2021-02-16T04:07:13Z)
• Dense Non-Rigid Structure from Motion: A Manifold Viewpoint [162.88686222340962]
  Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. We show that our approach significantly improves accuracy, scalability, and robustness against noise.
  arXiv  Detail & Related papers  (2020-06-15T09:15:54Z)
• Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem [0.0]
  We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms.
  arXiv  Detail & Related papers  (2020-01-15T08:20:11Z)

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.