Physics Informed Neural Network for Dynamic Stress Prediction

• URL: http://arxiv.org/abs/2211.16190v1
• Date: Mon, 28 Nov 2022 16:03:21 GMT
• Title: Physics Informed Neural Network for Dynamic Stress Prediction
• Authors: Hamed Bolandi, Gautam Sreekumar, Xuyang Li, Nizar Lajnef, Vishnu Naresh Boddeti
• Abstract summary: A Physics Informed Neural Network (PINN) model is proposed to predict the entire sequence of stress distribution based on Finite Element simulations. Using automatic differentiation, we embed a PDE into a deep neural network's loss function to incorporate information from measurements and PDEs. The PINN-Stress model can predict the sequence of stress distribution in almost real-time and can generalize better than the model without PINN.
• Score: 10.588266927411434
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity methods, such as Finite Element Models (FEMs), suffer from their inherent high complexity. Therefore, to reduce computational cost while maintaining accuracy, a Physics Informed Neural Network (PINN), PINN-Stress model, is proposed to predict the entire sequence of stress distribution based on Finite Element simulations using a partial differential equation (PDE) solver. Using automatic differentiation, we embed a PDE into a deep neural network's loss function to incorporate information from measurements and PDEs. The PINN-Stress model can predict the sequence of stress distribution in almost real-time and can generalize better than the model without PINN.

Related papers

• PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems [31.006807854698376]
  We propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN) We incorporate a GNN into a numerical integrator to approximate the temporal marching of partialtemporal dynamics for a given PDE system. PhyMPGN is capable of accurately predicting various types of operatortemporal dynamics on coarse unstructured meshes.
  arXiv  Detail & Related papers  (2024-10-02T08:54:18Z)
• Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting [60.03169701753824]
  We propose a novel Dynamic Diffusion-al Graph Neural Network (DVGNN) fortemporal forecasting. The proposed DVGNN model outperforms state-of-the-art approaches and achieves outstanding Root Mean Squared Error result.
  arXiv  Detail & Related papers  (2023-05-16T11:38:19Z)
• 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)
• Characteristics-Informed Neural Networks for Forward and Inverse Hyperbolic Problems [0.0]
  We propose characteristic-informed neural networks (CINN) for solving forward and inverse problems involving hyperbolic PDEs. CINN encodes the characteristics of the PDE in a general-purpose deep neural network trained with the usual MSE data-fitting regression loss. Preliminary results indicate that CINN is able to improve on the accuracy of the baseline PINN, while being nearly twice as fast to train and avoiding non-physical solutions.
  arXiv  Detail & Related papers  (2022-12-28T18:38:53Z)
• Neuro-DynaStress: Predicting Dynamic Stress Distributions in Structural Components [10.588266927411434]
  It is crucial to predict dynamic stress distributions during highly disruptive events in real-time. Deep learning model, Neuro-DynaStress, is proposed to predict the entire sequence of stress distribution based on finite element simulations.
  arXiv  Detail & Related papers  (2022-12-19T03:02:26Z)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Learning Physics-Informed Neural Networks without Stacked Back-propagation [82.26566759276105]
  We develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is two orders of magnitude faster.
  arXiv  Detail & Related papers  (2022-02-18T18:07:54Z)
• Robust Learning of Physics Informed Neural Networks [2.86989372262348]
  Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE.
  arXiv  Detail & Related papers  (2021-10-26T00:10:57Z)
• Characterizing possible failure modes in physics-informed neural networks [55.83255669840384]
  Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena even for simple PDEs. We show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize.
  arXiv  Detail & Related papers  (2021-09-02T16:06:45Z)
• Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch [0.0]
  PINNs approach allows training neural networks while respecting the PDEs as a strong constraint in the optimization. In standard small-scale circulation simulations, it is shown that the conventional approach incorporates a pseudo diffusive effect that is almost as large as the effect of the turbulent diffusion model. Of all the schemes tested, only the PINNs approximation accurately predicted the outcome.
  arXiv  Detail & Related papers  (2021-03-15T05:39:17Z)
• Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction [79.81193813215872]
  We develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. We show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions.
  arXiv  Detail & Related papers  (2020-07-08T21:23:19Z)

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.