A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks
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[1] Mark Ainsworth,et al. Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation , 2006, J. Sci. Comput..
[2] Donald C. Wunsch,et al. Clustering with differential evolution particle swarm optimization , 2010, IEEE Congress on Evolutionary Computation.
[3] David A. Kopriva,et al. Implementing Spectral Methods for Partial Differential Equations , 2009 .
[4] Dimitrios I. Fotiadis,et al. Artificial neural networks for solving ordinary and partial differential equations , 1997, IEEE Trans. Neural Networks.
[5] S. Orszag. Spectral methods for problems in complex geometries , 1980 .
[6] David A. Kopriva,et al. Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers , 2009 .
[7] Laurens E. Howle,et al. A comparison of the reduced galerkin and pseudo-spectral methods for simulation of steady Rayleigh-Bénard convection , 1996 .
[8] Rüdiger Verfürth,et al. A posteriori error estimates for finite element discretizations of the heat equation , 2003 .
[9] Sohrab Effati,et al. Bifurcation analysis of a cellular nonlinear network model via neural network approach , 2014, Neural Computing and Applications.
[10] Shen Furao,et al. An incremental network for on-line unsupervised classification and topology learning , 2006, Neural Networks.
[11] Silvia Ferrari,et al. A Constrained Optimization Approach to Preserving Prior Knowledge During Incremental Training , 2008, IEEE Transactions on Neural Networks.
[12] Sven Leyffer,et al. Nonlinear programming without a penalty function , 2002, Math. Program..
[13] N. Phan-Thien,et al. Neural-network-based approximations for solving partial differential equations , 1994 .
[14] Kevin Stanley McFall,et al. Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions , 2009, IEEE Transactions on Neural Networks.
[15] Lawrence F. Shampine,et al. The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..
[16] Allan D. Pierce,et al. Acoustics , 1989 .
[17] Iliya D. Iliev,et al. Spectral Methods in Soliton Equations , 1994 .
[18] Víctor M. Pérez-García,et al. Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method , 2006, SIAM J. Sci. Comput..
[19] Alaeddin Malek,et al. Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques , 2009, J. Frankl. Inst..
[20] D. Gottlieb,et al. Numerical analysis of spectral methods : theory and applications , 1977 .
[21] Frank L. Lewis,et al. Fixed-Final-Time-Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach , 2007, IEEE Transactions on Neural Networks.
[22] Peter M. Pinsky,et al. Finite element dispersion analysis for the three‐dimensional second‐order scalar wave equation , 1992 .
[23] J. Boyd. Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms , 2009 .
[24] Steven A. Orszag,et al. CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .
[25] Dimitris G. Papageorgiou,et al. Neural-network methods for boundary value problems with irregular boundaries , 2000, IEEE Trans. Neural Networks Learn. Syst..
[26] Andrew J. Meade,et al. Solution of nonlinear ordinary differential equations by feedforward neural networks , 1994 .
[27] Silvia Ferrari,et al. A constrained-optimization approach to training neural networks for smooth function approximation and system identification , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).
[28] Mohsen Hayati,et al. Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations , 2009, Appl. Soft Comput..
[29] Ganesh K. Venayagamoorthy,et al. Particle Swarm Optimization with Quantum Infusion for the design of digital filters , 2008, 2008 IEEE Swarm Intelligence Symposium.
[30] Silvia Ferrari,et al. A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations , 2014, IEEE Transactions on Neural Networks and Learning Systems.
[31] R. Peyret. Spectral Methods for Incompressible Viscous Flow , 2002 .
[32] C. Canuto. Spectral methods in fluid dynamics , 1991 .