A polynomial neural network can implement a truncated Lie map, allowing its weights to be computed directly from a differential equation instead of trained, or fitted from data when the equation is unknown.
Constructing Runge-Kutta Methods with the Use of Artificial Neural Networks
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abstract
A methodology that can generate the optimal coefficients of a numerical method with the use of an artificial neural network is presented in this work. The network can be designed to produce a finite difference algorithm that solves a specific system of ordinary differential equations numerically. The case we are examining here concerns an explicit two-stage Runge-Kutta method for the numerical solution of the two-body problem. Following the implementation of the network, the latter is trained to obtain the optimal values for the coefficients of the Runge-Kutta method. The comparison of the new method to others that are well known in the literature proves its efficiency and demonstrates the capability of the network to provide efficient algorithms for specific problems.
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cs.NE 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Matrix Lie Maps and Neural Networks for Solving Differential Equations
A polynomial neural network can implement a truncated Lie map, allowing its weights to be computed directly from a differential equation instead of trained, or fitted from data when the equation is unknown.