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. 2024 Oct 12;14:23874. doi: 10.1038/s41598-024-74600-4

Table 1.

PINN algorithm.

Algorithm1: PINN
Step1: Specification of training set
Training data: Inline graphic network Inline graphic.
Residual training points: f network Inline graphic.
Step2: Construct neural network Inline graphic with random initialization of parameters Inline graphic.
Step3: Construct the residual neural network f by substituting surrogate Inline graphic into
the governing equations using automatic differentiation and other arithmetic operations.
Step4: Specification of loss function:
Inline graphic
Step5: Find the best parameters using suitable optimization method for minimizing the loss function
Inline graphic