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Application of physics-informed neural networks to inverse problems in unsaturated groundwater flow

Abstract

This paper investigates the application of Physics-Informed Neural Networks (PINNs) to inverse problems in unsaturated groundwater flow. PINNs are applied to the types of unsaturated groundwater flow problems modelled with the Richards partial differential equation and the van Genuchten constitutive model. The inverse problem is formulated here as a problem with known or measured values of the solution to the Richards equation at several spatio-temporal instances, and unknown values of solution at the rest of the problem domain and unknown parameters of the van Genuchten model. PINNs solve inverse problems by reformulating the loss function of a deep neural network such that it simultaneously aims to satisfy the measured values and the unknown values at a set of collocation points distributed across the problem domain. The novelty of the paper originates from the development of PINN formulations for the Richards equation that requires training of a single neural network. The results demonstrate that PINNs are capable of efficiently solving the inverse problem with relatively accurate approximation of the solution to the Richards equation and estimates of the van Genuchten model parameters.
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Category

Academic article

Language

English

Author(s)

  • Ivan Depina
  • Saket Jain
  • Sigurdur Mar Valsson
  • Hrvoje Gotovaca

Affiliation

  • SINTEF Community / Infrastructure
  • Croatia
  • University of Split
  • Vestfold og Telemark fylkeskommune
  • Norwegian public roads administration

Year

2021

Published in

Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards

ISSN

1749-9518

View this publication at Norwegian Research Information Repository