Unsupervised learning method for the wave equation based on finite difference residual constraints loss
The wave equation is an important physical partial differential equation,and in recent years,deep learning has shown potential to accelerate or replace traditional numerical methods for solving it.However,existing deep learning methods suffer from high data acquisition costs,low training efficiency,and insufficient generalization capability for boundary conditions.To address these issues,this paper proposes an unsuper-vised learning method for the wave equation based on finite difference residual constraints.The authors con-struct a novel finite difference residual constraint based on structured grids and finite difference methods,as well as an unsupervised training strategy,enabling convolutional neural networks to train without data and predict the forward propagation process of waves.Experimental results demonstrate that finite difference re-sidual constraints have advantages over Physics-Informed Neural Networks(PINNs)type physical informa-tion constraints,such as easier fitting,lower computational costs,and stronger source term generalization ca-pability,making our method more efficient in training and potent in application.
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