Advances in the pilot point inverse method: Où En Sommes-Nous maintenant?

At a conference some years ago, one of the attendees came up to Ghislain de Marsily and asked, "Excuse me, but aren't you the de Marsily who developed the Pilot Point Method? It is an honor to meet you." His response highlights one of Ghislain's greatest qualities, his humility: "Yes I am, thank you, you are very kind, but that was a very long time ago." Since Ghislain de Marsily first developed the Pilot Point Method (PPM) in 1978, its development and use has grown significantly in applied decision-supportmodeling settings including hydrogeology, aswell as in other industries, e.g., petroleum reservoir engineering. A technique that was once confined to academic realms, the PPM is now widely accepted as one of the industry pillars of inversion and uncertainty quantification for predictive groundwater modeling. Herein, we provide an update to de Marsily's paper entitled "Four Decades of Inverse Problems in Hydrogeology" [DeMarsily et al., 2000], but with a particular focus on the incredible adoption and advancement of deMarsily's PPM and related inverse techniques over the last twenty years in the field of predictive groundwater modeling. Much has been written about the vast array of inverse techniques developed by researchers and practitioners since the 1960s. de Marsily's PPM, like many methods developed in the late 70s and early 80s, structured its approach to parameterization to overcomemany of the challenges of applying inverse methods to real world problems, namely, limited head and transmissivity data relative to the number of unknowns to be estimated, measurement errors, inferred covariance structures of the state variables, and limited computational resources. While inversion research continues, only deMarsily's PPM has achieved wide-spread adoption within the groundwater modeling community. The reasons for the popularity of the PPM aremany but none more important than its adoption by John Doherty's PEST inversion software in the early 2000s [Doherty, 2003]. This paper will review the advancements and adaptations of the PPM over the last two decades which have led to its ubiquity. Significant reductions in inversion time are transforming the way in which practitioners are deploying thePPMto improve their understanding of hydrogeologic systems, and, ultimately, to provide decision support for water resource management. The paper ends with newly developed applications of the PPM, given modern machine learning capabilities, and some foreshadowing as to where the PPM might evolve. [ABSTRACT FROM AUTHOR]