A Sniffer Technique for an Efficient Deduction of Model Dynamical Equations Using Genetic Programming

Ahalpara, Dilip P.; Sen, Abhijit

doi:10.1007/978-3-642-20407-4_1

Cited by 3 publications

(4 citation statements)

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“…In this paper we studied a scale-invariant analogue of the KdV equation, u t + 2u xx u x /u = u xxx , which we named the SIdV equation. SIdV is one of the two simplest translation, scale and spacetime parity-invariant non-linear advection-dispersion equations 12 . The dimensionless parameter measures the strength of dispersion relative to advection.…”

Section: Discussionmentioning

confidence: 99%

“…We were therefore excited to find that the KdV equation is not the only one with the sech 2 solitary wave solution. This serendipitous discovery happened in the course of an investigation undertaken by two of the present authors [12] to improve the efficiency and accuracy of a genetic programming (GP) based method (see A) to deduce model equations from a known analytic solution [13]. As a benchmark exercise to test out the method for application to nonlinear PDEs, the travelling wave (2) was given to the program, expecting it to find the KdV equation.…”

Section: Introductionmentioning

confidence: 99%

“…Due to a stochastic search procedure adopted by GP, it was found to be too slow. We improved and accelerated it by introducing a sniffer technique [12] that carried out a local search at regular intervals to enhance the minimization procedure. Our improved GP approach was quite successful in inferring PDEs.…”

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confidence: 99%

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A KdV-like advection–dispersion equation with some remarkable properties

Sen

Ahalpara

Thyagaraja

et al. 2012

Communications in Nonlinear Science and Numerical Simulation

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We discuss a new non-linear PDE, u t + (2u xx /u)u x = u xxx , invariant under scaling of dependent variable and referred to here as SIdV. It is one of the simplest such translation and space-time reflection-symmetric first order advection-dispersion equations. This PDE (with dispersion coefficient unity) was discovered in a genetic programming search for equations sharing the KdV solitary wave solution. It provides a bridge between non-linear advection, diffusion and dispersion. Special cases include the mKdV and linear dispersive equations. We identify two conservation laws, though initial investigations indicate that SIdV does not follow from a polynomial Lagrangian of the KdV sort. Nevertheless, it possesses solitary and periodic travelling waves. Moreover, numerical simulations reveal recurrence properties usually associated with integrable systems. KdV and SIdV are the simplest in an infinite dimensional family of equations sharing the KdV solitary wave. SIdV and its generalizations may serve as a testing ground for numerical and analytical techniques and be a rich source for further explorations.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A KdV-like advection–dispersion equation with some remarkable properties

Sen

Ahalpara

Thyagaraja

et al. 2012

Communications in Nonlinear Science and Numerical Simulation

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“…This is explained by a schematic diagram in Figure 2. It may be noted that we have earlier applied the sniffer technique [10] for solving the inverse problem, namely inference of dynamical system equations (ODE and PDE) in their symbolic form, where data is used in the form of its solution defined either numerically or in a symbolic form. Figure 2 shows a hypothetical search space in which the true solution is shown by an isolated thick circle.…”

Section: Heuristic Methods For Solving One-dimensional Kdv Equationmentioning

confidence: 99%

Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm

Nadiad¹

2015

JAMP

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A novel heuristic technique has been developed for solving Ordinary Differential Equation (ODE) numerically under the framework of Genetic Algorithm (GA). The method incorporates a sniffer procedure that helps carry out a memetic search within the solution domain in the vicinity of the currently found best chromosome. The technique has been successfully applied to the Kortewegde Vries (KdV) equation, a well-known nonlinear Partial Differential Equation (PDE). In the present study we consider its solution in the regime of solitary waves, or solitons that is first used to convert the PDE into an ODE. It is then shown that using the sniffer technique assisted GA procedure, numerical solution has successfully been generated quite efficiently for the one-dimensional ODE version of the KdV equation in space variable (x). The technique is quite promising for its applications to systems involving ODE equations where analytical solutions are not directly available.

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Inference of hidden variables in systems of differential equations with genetic programming

Cornforth

Lipson

2012

Genet Program Evolvable Mach

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A Sniffer Technique for an Efficient Deduction of Model Dynamical Equations Using Genetic Programming

Cited by 3 publications

References 8 publications

A KdV-like advection–dispersion equation with some remarkable properties

A KdV-like advection–dispersion equation with some remarkable properties

Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm

Inference of hidden variables in systems of differential equations with genetic programming

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