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Physics and equality constrained artificial neural networks (PECANN) are grounded in methods of constrained optimization to properly constrain the solution of partial differential equations (PDEs) with their boundary and initial conditions and any high-fidelity data that may be available.
Multiplier and gradient methods
Magnus R Hestenes · 1969
Earlier work this paper cites.
A method for nonlinear constraints in minimization problems
Michael JD Powell · 1969
Earlier work this paper cites.
Updating quasi-Newton matrices with limited storage
Jorge Nocedal · 1980
Earlier work this paper cites.
High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
U Ghia, K.N Ghia, and C.T Shin · 1982
Earlier work this paper cites.
Heat conduction in layered, composite materials
James Baker-Jarvis and Ramarao Inguva · 1985
Earlier work this paper cites.
Evaluation of various high-order-accuracy schemes with and without flux limiters
Panos Tamamidis and Dennis N. Assanis · 1993
Earlier work this paper cites.
Neural-network-based approximations for solving partial differential equations
M. W. M. G. Dissanayake and N. Phan-Thien · 1994
Earlier work this paper cites.
Neural network differential equation and plasma equilibrium solver
B. Ph. van Milligen, V. Tribaldos, and J. A. Jiménez · 1995
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
Earlier work this paper cites.
Characterizing the dynamics of constrained physical systems with an unsupervised neural network
Christopher Monterola and Caesar Saloma · 1998
Earlier work this paper cites.
Numerical optimization
Stephen Wright, Jorge Nocedal, et al · 1999
Earlier work this paper cites.
The boundary-element method for the determination of a heat source dependent on one variable
Adrian Farcas and Daniel Lesnic · 2006
Earlier work this paper cites.
Numerical optimization
Jorge Nocedal and Stephen Wright · 2006
Earlier work this paper cites.
Determination of a spacewise dependent heat source
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Identification of spacewise and time dependent source terms in 1d heat conduction equation from temperature measurement at a final time
Alemdar Hasanov · 2012
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