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<p>The stochastic Burgers’ equation (SBE) is a sophisticated mathematical model to describe the turbulence phenomenon in the fluid motion. In this paper, the artificial neural network (ANN) has been studied for solution representation of the SBE with the space-time white noise with variable coefficients. Observations of the proposed work has been compared with the Itô calculus based exact method, and the Runge–Kutta-Central-Difference on stochastic mesh, the stochastic forward Euler method and the shifted Legendre polynomial based numerical methods (NMs). The comparison benchmarks are solution accuracy, computation speed, space-saving for the solution representation and possible trade-off among them. The ANN based method outperformed the NMs in terms of computation speed and space-saving, and solution accuracy of both kind of the methods are nearly equal. The computation speed of the ANN is near to the the exact method. Also, the ANN can be a good choice for data compression of solution of the SBE, as more than 98 % space-saving has been observed at the cost of an average error of the order E−03.</p>

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Artificial neural network: a data compression model for solution to stochastic Burgers’ equation

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Himanshu Agarwal,
  • Vikas Kumar Pandey

摘要

The stochastic Burgers’ equation (SBE) is a sophisticated mathematical model to describe the turbulence phenomenon in the fluid motion. In this paper, the artificial neural network (ANN) has been studied for solution representation of the SBE with the space-time white noise with variable coefficients. Observations of the proposed work has been compared with the Itô calculus based exact method, and the Runge–Kutta-Central-Difference on stochastic mesh, the stochastic forward Euler method and the shifted Legendre polynomial based numerical methods (NMs). The comparison benchmarks are solution accuracy, computation speed, space-saving for the solution representation and possible trade-off among them. The ANN based method outperformed the NMs in terms of computation speed and space-saving, and solution accuracy of both kind of the methods are nearly equal. The computation speed of the ANN is near to the the exact method. Also, the ANN can be a good choice for data compression of solution of the SBE, as more than 98 % space-saving has been observed at the cost of an average error of the order E−03.