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Graphic Era University

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PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models

Jun 15, 2025

This work addresses the numerical solution of strongly nonlinear, multidimensionally coupled 1D/2D Burgers-type PDEs—including both scalar and coupled systems—where conventional discretization methods suffer from instability and poor generalization under complex boundaries or sparse data. We propose a data-free, end-to-end physics-informed neural network (PINN) framework. Our method introduces two key innovations: (i) a trial function construction strategy ensuring strict compatibility with initial and boundary conditions, and (ii) an adaptive residual weighting scheme that significantly enhances training stability and convergence speed. Evaluated on five representative Burgers models—including strongly nonlinear cases admitting analytical solutions—the approach achieves solution accuracy of $10^{-3}$–$10^{-4}$. It consistently outperforms traditional mesh-based methods in generalization capability under irregular geometries and limited supervision, requiring no observational data. The framework demonstrates strong robustness and modeling flexibility for high-dimensional, time-dependent, nonlinear PDEs.

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PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models

Jun 15, 2025

This work addresses the numerical solution of strongly nonlinear, multidimensionally coupled 1D/2D Burgers-type PDEs—including both scalar and coupled systems—where conventional discretization methods suffer from instability and poor generalization under complex boundaries or sparse data. We propose a data-free, end-to-end physics-informed neural network (PINN) framework. Our method introduces two key innovations: (i) a trial function construction strategy ensuring strict compatibility with initial and boundary conditions, and (ii) an adaptive residual weighting scheme that significantly enhances training stability and convergence speed. Evaluated on five representative Burgers models—including strongly nonlinear cases admitting analytical solutions—the approach achieves solution accuracy of $10^{-3}$–$10^{-4}$. It consistently outperforms traditional mesh-based methods in generalization capability under irregular geometries and limited supervision, requiring no observational data. The framework demonstrates strong robustness and modeling flexibility for high-dimensional, time-dependent, nonlinear PDEs.

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