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Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions.
Numerical solution of the navier-stokes equations
Alexandre Joel Chorin · 1968
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Applied optimal control: optimization, estimation and control
Arthur Earl Bryson · 1975
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Numerical solution of partial differential equations: finite difference methods
Gordon D Smith · 1985
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Learning representations by back-propagating errors
David E Rumelhart, Geoffrey E Hinton, Ronald J Williams, et al · 1988
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
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Approximation of a function and its derivative with a neural network
Pierre Cardaliaguet and Guillaume Euvrard · 1992
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Vera Kurkova · 1992
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A direct adaptive method for faster backpropagation learning: The rprop algorithm
Martin Riedmiller and Heinrich Braun · 1993
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IE Lagaris, A Likas, and DI Fotiadis · 1997
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Robert Eymard, Michaël Gutnic, and Danielle Hilhorst · 1999
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Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey
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Accelerating preconditioned iterative linear solvers on gpu
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
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Allen Taflove and Susan C Hagness · 2005
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Geometric numerical integration: structure-preserving algorithms for ordinary differential equations
Ernst Hairer, Christian Lubich, and Gerhard Wanner · 2006
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Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations
Yazdan Shirvany, Mohsen Hayati, and Rostam Moradian · 2009
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Xavier Glorot and Yoshua Bengio · 2010
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Enhancing approximation abilities of neural networks by training derivatives
V.I. Avrutskiy · 2017
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