Inversion of seepage parameters for one-dimensional unconfined aquifer flow equations based on PINNs algorithm
In the field of groundwater,the inversion of seepage parameters contributes to understanding the nature of groundwater flow,which is essential for determining the distribution,movement,and quality of groundwater resources.This plays a significant role in groundwater resource management,hydrological model development,and the sustainability of groundwater recharge.Despite the rapid development of neural network methods in recent years,there is limited research focused on the inversion of seepage parameters for unconfined flow.Addressing this,the present study pioneers the application of Physics-Informed Neural Networks(PINNs)combined with both soft and hard constraints to solve the problem of permeability coefficient inversion in unconfined aquifers.Taking the permeability coefficient inversion in one-dimensional steady-state heterogeneous unconfined flow as well as unsteady-state homogeneous unconfined flow(including solute transport)as examples,this paper compares the performance of the PINNs soft constraint method(PINNs-S)and hard constraint method(PINNs-H)in inverting permeability coefficients.The PINNs case studies indicate that the PINNs algorithm inverts permeability coefficients with high computational accuracy.Furthermore,the PINNs hard constraint and soft constraint methods have their advantages and disadvantages,and the appropriate approach should be selected based on the specific problem and experimental results in practical applications.
Physics-Informed Neural Networksunconfined flowhard constraintssoft constraintsinversion of seepage parameters
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