Runge Kutta neural network for identification of continuous systems

2002 ◽  
Author(s):  
Yi-Jen Wang ◽  
Chin-Teng Lin
Keyword(s):  
Neural Network ◽  
Continuous Systems ◽  
Runge Kutta

scholarly journals A Neural Network Technique for the Derivation of Runge-Kutta Pairs Adjusted for Scalar Autonomous Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1842
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Yuri A. Khakhalev ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Neural Network ◽  
Differential Evolution ◽  
Initial Value Problem ◽  
Fitness Function ◽  
Initial Value ◽  
Runge Kutta

We consider the scalar autonomous initial value problem as solved by an explicit Runge-Kutta pair of orders 6 and 5. We focus on an efficient family of such pairs, which were studied extensively in previous decades. This family comes with 5 coefficients that one is able to select arbitrarily. We set, as a fitness function, a certain measure, which is evaluated after running the pair in a couple of relevant problems. Thus, we may adjust the coefficients of the pair, minimizing this fitness function using the differential evolution technique. We conclude with a method (i.e. a Runge-Kutta pair) which outperforms other pairs of the same two orders in a variety of scalar autonomous problems.

scholarly journals Tool Presentation: Isabelle/HOL for Reachability Analysis of Continuous Systems

10.29007/b3wr ◽  
2018 ◽  
Author(s):  
Fabian Immler
Keyword(s):  
Distinctive Feature ◽  
Reachability Analysis ◽  
Theorem Prover ◽  
Continuous Systems ◽  
Affine Arithmetic ◽  
Discretization Errors ◽  
Runge Kutta

We present a tool for reachability analysis of continuous systems based onaffine arithmetic and Runge-Kutta methods. The distinctive feature of our toolis its verification in the interactive theorem prover Isabelle/HOL: thealgorithm is guaranteed to compute safe overapproximations, taking into accountall round-off and discretization errors.

Synthesizing Barrier Certificates of Neural Network Controlled Continuous Systems via Approximations

2021 ◽  
Author(s):  
Meng Sha ◽  
Xin Chen ◽  
Yuzhe Ji ◽  
Qingye Zhao ◽  
Zhengfeng Yang ◽  
...  
Keyword(s):  
Neural Network ◽  
Continuous Systems

NEURAL NETWORK-BASED DERIVATION OF EFFICIENT HIGH-ORDER RUNGE–KUTTA–NYSTRÖM PAIRS FOR THE INTEGRATION OF ORBITS

2011 ◽  
Vol 22 (12) ◽  
pp. 1309-1316
Author(s):  
I. TH. FAMELIS
Keyword(s):  
Neural Network ◽  
Kepler Problem ◽  
Optimization Technique ◽  
Network Approach ◽  
Specific Test ◽  
Neural Network Approach ◽  
Orbital Problems ◽  
Free Parameters ◽  
Runge Kutta ◽  
Specific Tolerance

We use a neural network approach to derive a Runge–Kutta–Nyström pair of orders 8(6) for the integration of orbital problems. We adopt a differential evolution optimization technique to choose the free parameters of the method's family. We train the method to perform optimally in a specific test orbit from the Kepler problem for a specific tolerance. Our measure of efficiency involves the global error and the number of function evaluations. Other orbital problems are solved to test the new pair.

scholarly journals Identification of Nonlinear Continuous Systems by Using Neural Network Compensator

1994 ◽  
Vol 114 (5) ◽  
pp. 595-602 ◽  
Author(s):  
Chun-Zhi Jin ◽  
Kiyoshi Wada ◽  
Koutaro Hirasawa ◽  
Junichi Murata ◽  
Setsuo Sagara
Keyword(s):  
Neural Network ◽  
Continuous Systems ◽  
Neural Network Compensator
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