The numerical solution of linear ordinary differential equations by feedforward neural networks

By A. Meade, A. Fernandez. 1994

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Citations in the corpus

Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data (2019, neutral): “[30, 31, 32].”
Artificial neural networks for solving ordinary and partial differential equations (1997, background): “Another approach to the solution of ordinary differential equations is based on the fact that certain types of splines, for instance -splines, can be derived by the superposition of piecewise linear activation functions [3], [4].”
DeepXDE: A Deep Learning Library for Solving Differential Equations (2019, background): “However, not all PDEs can be derived from a known functional, and thus Galerkin type projections have also been considered [39].”
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks (2019, background): “[11, 13, 15, 19]), our convolutional neural network surrogate”
Weak Adversarial Networks for High-dimensional Partial Differential Equations (2019, methodology): “In [20,21], the solution of ordinary differential equations (ODE) is approximated by the combination of splines, where the combination parameters are determined by training a neural network with piecewise linear activation functions.”
A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations (2018, methodology): “Also, the authors in [16, 17] adopted linear B-splines to approximate the solution of ordinary differential equations and used feed-forward neural networks to determine the spline parameters.”
Relu Deep Neural Networks and Linear Finite Elements (2018, background): “This topic can be traced back to [22, 23, 21] in which collocation methods are studied.”