Fig. 1: Classical physics-informed neural network framework for solving high-order partial differential equations (PDEs). | Communications Engineering

Fig. 1: Classical physics-informed neural network framework for solving high-order partial differential equations (PDEs).

From: Multi-level physics informed deep learning for solving partial differential equations in computational structural mechanics

Fig. 1

Lb() and Lp() represent the loss functions from boundary constraints and loss functions from the partial differential equation (PDE), respectively. LB/C and LPDE represent the loss of boundary condition and physical PDE. Here, ω represents the differentiated physical variable as well as the output of the single NN, and ω’, ω” and ω(n) are first-order derivative, second-order derivative, and n-order derivative. {W, b}i presents the model parameter of neural networks (NNs).

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