Energy-based error bound of physics-informed neural network solutions in elasticity

• URL: http://arxiv.org/abs/2010.09088v2
• Date: Sun, 29 May 2022 13:32:23 GMT
• Title: Energy-based error bound of physics-informed neural network solutions in elasticity
• Authors: Mengwu Guo, Ehsan Haghighat
• Abstract summary: An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. Such an error estimator provides an upper bound of the global error of neural network discretization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstrating example.

Related papers

• A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks [52.5899851000193]
  We develop an ODE based IVP solver which prevents the network from getting ill-conditioned and runs in time linear in the number of parameters. We show that current methods based on this approach suffer from two key issues. First, following the ODE produces an uncontrolled growth in the conditioning of the problem, ultimately leading to unacceptably large numerical errors.
  arXiv  Detail & Related papers  (2023-04-28T17:28:18Z)
• An Analysis of Physics-Informed Neural Networks [0.0]
  We present a new approach to approximating the solution to physical systems - physics-informed neural networks. The concept of artificial neural networks is introduced, the objective function is defined, and optimisation strategies are discussed. The partial differential equation is then included as a constraint in the loss function for the problem, giving the network access to knowledge of the dynamics of the physical system it is modelling.
  arXiv  Detail & Related papers  (2023-03-06T04:45:53Z)
• 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)
• Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs [0.0]
  We present a rigorous upper bound on the prediction error of physics-informed neural networks. We apply this to four problems: the transport equation, the heat equation, the Navier-Stokes equation and the Klein-Gordon equation.
  arXiv  Detail & Related papers  (2022-10-07T09:49:18Z)
• Physics-Informed Neural Networks for Quantum Eigenvalue Problems [1.2891210250935146]
  Eigenvalue problems are critical to several fields of science and engineering. We use unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The network optimization is data-free and depends solely on the predictions of the neural network.
  arXiv  Detail & Related papers  (2022-02-24T18:29:39Z)
• 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)
• Conditional physics informed neural networks [85.48030573849712]
  We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.
  arXiv  Detail & Related papers  (2021-04-06T18:29:14Z)
• Formalizing Generalization and Robustness of Neural Networks to Weight Perturbations [58.731070632586594]
  We provide the first formal analysis for feed-forward neural networks with non-negative monotone activation functions against weight perturbations. We also design a new theory-driven loss function for training generalizable and robust neural networks against weight perturbations.
  arXiv  Detail & Related papers  (2021-03-03T06:17:03Z)
• ResiliNet: Failure-Resilient Inference in Distributed Neural Networks [56.255913459850674]
  We introduce ResiliNet, a scheme for making inference in distributed neural networks resilient to physical node failures. Failout simulates physical node failure conditions during training using dropout, and is specifically designed to improve the resiliency of distributed neural networks.
  arXiv  Detail & Related papers  (2020-02-18T05:58:24Z)

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.