Progressive training strategy of physics-informed neural networks based on curriculum regularization
A progressive training strategy based on curriculum regularization was proposed to reduce the complexity and training dif-ficulty of the optimization objective function for physics-informed neural networks(PINN).In this strategy,the loss function was dynamically adjusted based on the idea of course learning.The physical information represented by the partial differential equation in the regularization term was gradually transitioned from a relatively stable state to a drastic state,which reduced the learning difficulty of task.The data constraints of initial conditions and boundary conditions in the loss function were strengthened to balance the losses between the data and physical information parts.A fixed step-size exponential decay learning rate was employed for optimization to avoid the objective function falling into the local minimum.Through experimental comparison and analysis of two types of partial dif-ferential equations,namely wave and heat conduction,the results showed that the computational efficiency could be improved by about 50%,and the prediction accuracy can be improved by an order of magnitude.The proposed method could improve the numerical stabil-ity and prediction accuracy of PINN,and accelerate the convergence rate of PINN in complex physical field learning tasks.
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