Prediction of velocity and pressure of gas-liquid flow using spectrum-based physics-informed neural networks

doi:10.1007/s10483-025-3217-8

Abstract

Abstract:

This research introduces a spectrum-based physics-informed neural network (SP-PINN) model to significantly improve the accuracy of calculation of two-phase flow parameters, surpassing existing methods that have limitations in global and continuous data sampling. SP-PINNs address the challenges of traditional methods in terms of continuous sampling by integrating the spectral analysis and pressure correction into the Navier-Stokes (N-S) equations, enhancing the predictive accuracy especially in critical regions like gas-phase boundaries and velocity peaks. The novel introduction of a pressure-correction module within SP-PINNs mitigates prediction errors, achieving a substantial reduction to 1‰ compared with the conventional physics-informed neural network (PINN) approaches. Experimental applications validate the model’s ability to accurately and rapidly predict flow parameters with different sampling time intervals, with the computation time of predicting unsampled data less than 0.01 s. Such advancements signify a 100-fold improvement over traditional DNS calculations, underscoring the model’s potential in the real-time calculation and analysis of multiphase flow dynamics.

Key words: physics-informed neural network (PINN), spectral method, two-phase flow, parameter prediction

2010 MSC Number:

O359

Nanxi DING, Hengzhen FENG, H. Z. LOU, Shenghua FU, Chenglong LI, Zihao ZHANG, Wenlong MA, Zhengqian ZHANG. Prediction of velocity and pressure of gas-liquid flow using spectrum-based physics-informed neural networks. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 341-356.

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Figures/Tables 18

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Table 1

Algorithm pseudocode"

SP-PINN algorithm
Initialize neural network parameters $θ$ and $θ p$ .
Randomly set weights $(ω)$ and biases $(b)$ for the neural network.
Start the training loop with epoch $E epoch$ being 1.
While $L > L threshold$ :
	$E epoch$ := $E epoch$ + 1.
	Randomly select data from the datasets, and input them into the neural network.
	Calculate $u, v$ , and $p$ (velocity components and pressure).
	Use the obtained $u, v$ , and $p$ values as inputs to $L PDE$ .
	Calculate losses for initial conditions, boundary conditions, and observations.
	$L = ω 1 L PDE + ω 2 L init + ω 3 L boundary + ω 4 L data$ .
	Compute gradients $∇ L PDE$ , $∇ L init$ , $∇ L boundary$ , and $∇ L data$ .
	Calculate the gradient $∇ L p$ for the pressure loss function separately.
	Update neural network parameter $θ p$ using the pressure loss gradient.
	Calculate the total loss based on different weight parameters.
	Update the neural network parameter $θ$ .
End

Table 1

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Table 2

Training parameters"

Parameter		Value
Learning rate		0.001
	Batch	32
	$E epoch$	650
	$λ 1, λ 2$	1, 1
	$L threshold$	0.002

Table 2

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