Quantum-Inspired Amplitude-Phase Frameworks for Uncertainty-Centric Groundwater Flow and Transport Modeling

Groundwater models are computer models that scientists and engineers use to predict the flow of water in subsurface environments. They can also be used to predict the transport and fate of contaminants in aquifers. The models usually require some knowledge about the subsurface structure and other hydrological parameters. However, this knowledge is often incomplete, leading to predictions that may not be accurate. This project will develop new computer simulation tools that account for uncertainties in aquifer parameters to make predictions that also report uncertainties in the results in plain terms. The mathematics underlying the new tools is borrowed from quantum mechanics. The tools use quantum theory to represent possible states, such as multiple possible transport pathways, at the same time, which is novel for groundwater models. The team will test the methods on controlled benchmarks and on well-known field datasets and will compare results to industry standard workflows. All codes and test cases will be shared openly. An AI-chatbot support tool will help users understand concepts, run examples, and interpret outputs. The outcomes of the project will have the potential to transform the way model results are reported, which can influence the management of environmental challenges. The project will develop a “Quantum-Enhanced Hydrology (QEH)” through three complementary, quantum-inspired amplitude-phase frameworks for groundwater flow and transport that embed uncertainty directly in the evolving model state while guaranteeing recovery of the classical advection dispersion equation (ADE) in the defined limit cases. Framework 1 will implement a Hydro-Madelung style amplitude-phase formulation in which amplitudes represent probabilistic occupancy across modes conditioned on facies structure and phases act as velocity potentials, enabling low dimensional calibration of effective parameters linked to conductivity structure and multiple possible transport speeds. Framework 2 will implement a facies-aware, Markovian transport evolution of a complex amplitude field with a dephasing operator tied to facies correlation length scales to represent sub-grid mixing and pre-asymptotic behavior on practical grids, while collapsing to ADE behavior in limiting cases. Framework 3 will represent transport with a density matrix evolution whose diagonal corresponds to concentration and whose localized off-diagonals encode short-range correlation structure, providing a compact “mixed-state” closure for unresolved heterogeneity and mixing. Validation will proceed from synthetic impulse/step plume benchmarks to heterogeneous ensembles and then to the MADE (Macrodispersion Experiment) site datasets, using withheld-data experiments to quantify robustness under limited information and to define when added model complexity is warranted. Each framework will be benchmarked against established tools (e.g., MODFLOW/MT3DMS with PEST++) using identical grids and calibration targets, with predictive performance assessed using distribution shape and decision-relevant metrics and computational cost reported transparently (outer-loop evaluations, CPU-hours, and time-to-target error), and all three frameworks have strong potential for acceleration on quantum computers. Deliverables include three open QEH prototypes with ADE-consistency tests, a documented comparison of accuracy-cost tradeoffs across regimes relevant to remediation risk assessment, complete ready-to-run code for all examples, and an AI-assisted, documentation-grounded guide that helps practitioners reproduce benchmark results and deploy uncertainty-centric predictions to real-world problems in their own workflows. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2603483 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Nicholas Engdahl | Institution: Washington State University, PULLMAN, WA | Award Amount: $352,443 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2603483 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2603483.html