Investigating Steady Unconfined Groundwater Flow using Physics Informed Neural Networks

TL;DR

This paper demonstrates how Physics Informed Neural Networks (PINNs) can effectively model steady unconfined groundwater flow, improve predictions over traditional models, and estimate hydraulic properties with robustness to data noise.

Contribution

The work introduces the application of PINNs to groundwater flow modeling, incorporating physics-based PDEs to enhance prediction accuracy and parameter estimation beyond existing methods.

Findings

PINNs accurately predict phreatic surface profiles under various conditions.

Including physics constraints improves model predictions compared to data-only training.

PINNs are robust to noise and reveal the applicability limits of flow models based on a dimensionless parameter.

Abstract

A novel deep learning technique called Physics Informed Neural Networks (PINNs) is adapted to study steady groundwater flow in unconfined aquifers. This technique utilizes information from underlying physics represented in the form of partial differential equations (PDEs) alongside data obtained from physical observations. In this work, we consider the Dupuit-Boussinesq equation, which is based on the Dupuit-Forchheimer approximation, as well as a recent more complete model derived by Di Nucci (2018) as underlying models. We then train PINNs on data obtained from steady-state analytical solutions and laboratory based experiments. Using PINNs, we predict phreatic surface profiles given different input flow conditions and recover estimates for the hydraulic conductivity from the experimental observations. We show that PINNs can eliminate the inherent inability of the Dupuit-Boussinesq equation to predict flows with seepage faces. Moreover, the inclusion of physics information from the Di Nucci and Dupuit-Boussinesq models constrains the solution space and produces better predictions than solely the training data. PINNs based predictions are very robust and show little effect from added noise in the training data. Further, we compare the PINNs obtained using the two different flow models to examine the effects of higher order flow terms, which are neglected by the Dupuit Forchheimer approximation. We found a dimensionless parameter $\Pi$, which is the ratio of vertical to horizontal flow effects. For $\Pi \leq 0.1$, Dupuit-Boussinesq approximation is found to be applicable but not otherwise. Lastly, we discuss the effectiveness of using PINNs for examining groundwater flow.