Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity

• URL: http://arxiv.org/abs/2112.08676v1
• Date: Thu, 16 Dec 2021 07:39:50 GMT
• Title: Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity
• Authors: Rajat Arora
• Abstract summary: We leverage the governing equations and boundary conditions of the physical system to train the model without using any high-resolution labeled data. We demonstrate that the super-resolved fields match the accuracy of an advanced numerical solver running at 400 times the coarse mesh resolution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage the governing equations and boundary conditions of the physical system to train the model without using any high-resolution labeled data. The proposed approach is applied to obtain the super-resolved deformation fields from the low-resolution stress and displacement fields obtained by running simulations on a coarse mesh for a body undergoing linear elastic deformation. We demonstrate that the super-resolved fields match the accuracy of an advanced numerical solver running at 400 times the coarse mesh resolution, while simultaneously satisfying the governing laws. A brief evaluation study comparing the performance of two deep learning based super-resolution architectures is also presented.

Related papers

• Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations [0.0]
  We propose a novel definition of super-resolution tailored for PDE-based problems. We use coarse-grid simulated data as our input and predict fine-grid simulated outcomes. Our method enables the generation of fine-mesh solutions bypassing traditional simulation.
  arXiv  Detail & Related papers  (2023-11-16T10:13:09Z)
• 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)
• Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching [55.28394191394675]
  We develop an adaptive inexact Newton method for equality-constrained nonlinear, nonIBS optimization problems. We demonstrate the superior performance of our method on benchmark nonlinear problems, constrained logistic regression with data from LVM, and a PDE-constrained problem.
  arXiv  Detail & Related papers  (2023-05-28T06:33:37Z)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• PhySRNet: Physics informed super-resolution network for application in computational solid mechanics [0.0]
  This work aims at developing a physics-informed deep learning based super-resolution framework (PhySRNet) It enables reconstruction of high-resolution deformation fields from their low-resolution counterparts without requiring high-resolution labeled data.
  arXiv  Detail & Related papers  (2022-06-30T17:51:50Z)
• Calibrating constitutive models with full-field data via physics informed neural networks [0.0]
  We propose a physics-informed deep-learning framework for the discovery of model parameterizations given full-field displacement data. We work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. We demonstrate that informed machine learning is an enabling technology and may shift the paradigm of how full-field experimental data is utilized to calibrate models.
  arXiv  Detail & Related papers  (2022-03-30T18:07:44Z)
• Physics informed neural networks for continuum micromechanics [68.8204255655161]
  Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $mu$CT-scans.
  arXiv  Detail & Related papers  (2021-10-14T14:05:19Z)
• 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)
• The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations [0.0]
  In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation.
  arXiv  Detail & Related papers  (2021-08-14T15:13:35Z)
• Reinforcement Learning for Adaptive Mesh Refinement [63.7867809197671]
  We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning to train refinement policies directly from simulation. The model sizes of these policy architectures are independent of the mesh size and hence scale to arbitrarily large and complex simulations.
  arXiv  Detail & Related papers  (2021-03-01T22:55:48Z)

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.