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

> **NSF 01002627DB NSF RESEARCH & RELATED ACTIVIT** · Washington State University (WA) · $352,443

## Abstract

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 sp

## Key facts

- **NSF award ID:** 2603483
- **Awardee organization:** Washington State University (WA)
- **SAM.gov UEI:** XRJSGX384TD6
- **PI:** Nicholas B Engdahl
- **Primary program:** 01002627DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $352,443
- **Funds obligated:** $352,443
- **Transaction type:** Standard Grant
- **Period:** 09/01/2026 → 08/31/2029

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2603483

## Citation

> US National Science Foundation, Award 2603483, Quantum-Inspired Amplitude-Phase Frameworks for Uncertainty-Centric Groundwater Flow and Transport Modeling. Retrieved via AI Analytics 2026-07-03 from https://api.ai-analytics.org/grant/nsf/2603483. Licensed CC0.

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