PINNeik: Eikonal solution using physics-informed neural networks

@article{Waheed2021PINNeikES,
  title={PINNeik: Eikonal solution using physics-informed neural networks},
  author={Umair bin Waheed and Ehsan Haghighat and Tariq Alkhalifah and Chao Song and Qi Hao},
  journal={Comput. Geosci.},
  year={2021},
  volume={155},
  pages={104833}
}
The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical algorithms have been developed over the years to solve the eikonal equation. However, these methods require considerable modifications to incorporate additional physics, such as anisotropy, and may even breakdown for certain complex forms of the eikonal… Expand
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References

SHOWING 1-10 OF 71 REFERENCES
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinearExpand
TensorFlow: Large-scale machine learning on heterogeneous systems. URL: https://www.tensorflow.org/. software available from tensorflow.org
  • 2015
Accelerating geostatistical modeling using geostatistics-informed machine Learning
TLDR
A geostatistics-informed machine learning (GIML) model is developed to improve the efficiency of Ordinary Kriging by reducing the number of points required to be estimated using OK. Expand
PINNtomo: Seismic tomography using physics-informed neural networks
Seismic traveltime tomography using transmission data is widely used to image the Earth’s interior from global to local scales. In seismic imaging, it is used to obtain velocity models for subsequentExpand
Solving the frequency-domain acoustic VTI wave equation using physics-informed neural networks
Frequency-domain wavefield solutions corresponding to the anisotropic acoustic wave equation can be used to describe the anisotropic nature of the Earth. To solve a frequency-domain wave equation,Expand
When and why PINNs fail to train: A neural tangent kernel perspective
TLDR
A novel gradient descent algorithm is proposed that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error and a series of numerical experiments are performed to verify the correctness of the theory and the practical effectiveness of the proposed algorithms. Expand
A nonlocal physics-informed deep learning framework using the peridynamic differential operator
TLDR
Nonlocal PDDO-PINN is applied to the solution and identification of material parameters in solid mechanics and, specifically, to elastoplastic deformation in a domain subjected to indentation by a rigid punch, for which the mixed displacement--traction boundary condition leads to localized deformation and sharp gradients in the solution. Expand
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
TLDR
It is proved that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposedmethod is not achievable by base methods with any (adaptive) learning rates. Expand
Physics informed machine learning: Seismic wave equation
Abstract Similar to many fields of sciences, recent deep learning advances have been applied extensively in geosciences for both small- and large-scale problems. However, the necessity of using largeExpand
SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks
In this paper, we introduce SciANN, a Python package for scientific computing and physics-informed deep learning using artificial neural networks. SciANN uses the widely used deep-learning packagesExpand
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