An Improved Physics-Informed Neural Network Algorithm for Predicting the Phreatic Line of Seepage

Abstract

As new ways to solve partial differential equations (PDEs), physics-informed neural network (PINN) algorithms have received widespread attention and have been applied in many fields of study. However, the standard PINN framework lacks sufficient seepage head data, and the method is difficult to apply effectively in seepage analysis with complex boundary conditions. In addition, the differential type Neumann boundary makes the solution more difficult. This study proposed an improved prediction method based on a PINN with the aim of calculating PDEs with complex boundary conditions such as Neumann boundary conditions, in which the spatial distribution characteristic information is increased by a small amount of measured data and the loss equation is dynamically adjusted by loss weighting coefficients. The measured data are converted into a quadratic regular term and added to the loss function as feature data to guide the update process for the weight and bias coefficient of each neuron in the neural network. A typical geotechnical problem concerning seepage phreatic line determination in a rectangular dam is analyzed to demonstrate the efficiency of the improved method. Compared with the standard PINN algorithm, due to the addition of measurement data and dynamic loss weighting coefficients, the improved PINN algorithm has better convergence and can handle more complex boundary conditions. The results show that the improved method makes it convenient to predict the phreatic line in seepage analysis for geotechnical engineering projects with measured data.

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

“…It also should be pointed out that for a long time, people have been hoping to find new numerical methods for PDEs that do not require grid partitioning or nonlinear equation solving. In recent years, PINN has led to significant changes in numerical simulation technology, and the method for solving PDEs based on PINN not only enables fast forward modeling and inversion modeling [45][46], but also effectively solves nonlinear problems [47][48][49], and can solve more complex and high-dimensional PDEs [50][51][52]. Falini et al (2023) and Zhi et al (2023) have even argued that as PINN has better stability, it can be used as an alternative to the traditional FEM in solving PDEs [53][54].…”

A novel solution for seepage problems using physics-informed neural networks

“…Less research into PINN solutions for seepage problems has been carried out. The existing research on PINN solutions to infiltration problems is focused on data-driven (Pu et al 2022) or hybrid data and physical constraint-driven approaches (Daolun et al 2021;Gao et al 2023). Data-driven methods require large amounts of data to train the model and have drawbacks such as poor generalization (Kim et al 2022).…”