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Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity data.
On the distribution of points in a cube and the approximate evaluation of integrals
I. M. Sobol · 1967
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
T. Chen and H. Chen · 1995
Earlier work this paper cites.
Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
I. Podlubny · 1998
Earlier work this paper cites.
Multidimensional advection and fractional dispersion
M. M. Meerschaert, D. A. Benson, and B. Bäumer · 1999
Earlier work this paper cites.
Application of a fractional advection-dispersion equation
D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert · 2000
Earlier work this paper cites.
Reformulation of elasticity theory for discontinuities and long-range forces
S. Silling · 2000
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Deformation of a peridynamic bar
S. Silling, M. Zimmermann, and R. Abeyaratne · 2003
Earlier work this paper cites.
Peridynamic modeling of membranes and fibers
S. Silling and F. Bobaru · 2005
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Using neural networks for parameter estimation in ground water
L. A. Garcia and A. Shigidi · 2006
Earlier work this paper cites.
Understanding the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
Earlier work this paper cites.
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X. Chen and M. Gunzburger · 2011
Earlier work this paper cites.
Analysis and approximation of nonlocal diffusion problems with volume constraints
Q. Du, M. Gunzburger, R. Lehoucq, and K. Zhou · 2012
Earlier work this paper cites.
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P. K. Kundu, I. M. Cohen, and D. R. Dowling · 2012
Earlier work this paper cites.
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Optimal distributed control of nonlocal steady diffusion problems
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Hidden physics models: Machine learning of nonlinear partial differential equations
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Approximation of parametrized kernels arising in nonlocal and fractional laplace models
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A priori error estimates for the optimal control of the integral fractional laplacian
M. D’Elia, C. Glusa, and E. Otarola · 2019
Later among the works it cites.
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D. P. Kingma and J. Ba · 2014
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Tempered fractional calculus
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Inverse problems in heterogeneous and fractured media using peridynamics
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A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives
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Identification of the diffusion parameter in nonlocal steady diffusion problems
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What is the fractional laplacian? a comparative review with new results
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Discovering a universal variable-order fractional model for turbulent couette flow using a physics-informed neural network
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fpinns: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations
X. Zheng, J. Cheng, and H. Wang · 2019
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Optimal control of fractional semilinear PDEs
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