Solving nonlinear transient heat conduction forward/inverse problem using physics-informed neural networks
This study proposes a physics-informed neural networks(PINN)approach to solve transient nonlinear heat conduction problems and estimate the temperature-dependent thermal conductivity.First,a loss function is formulated using the residuals of partial differential equation,initial conditions,and boundary conditions specific to heat conduction.Then,automatic differentiation is applied to compute the temperature's partial derivatives within the equation.The heat conduction problem is solved by minimizing the loss function through a gradient descent algorithm,which updates the network parameters.The influences of varying the number of hidden layers,neurons and interior collection points on the results are also examined.Finally,the PINN is applied to identify temperature-dependent thermal conductivities by formulating a loss function that includes residuals from the governing equation,measured temperature,and computed temperature.The network parameters and thermal conductivity values are updated by gradient descent algorithm to approximate the true solution.Additionally,the influences of different measurement points and errors on the results are compared.The findings show that the proposed method effectively solves transient heat conduction problems and accurately estimates temperature-dependent thermal conductivity.
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