Can we borrow quantum-like mathematics to model highly uncertain continuum mechanical systems?
Abstract
Most problems in fluid mechanics involve uncertainty in the parameters of the governing equations but groundwater flow is plagued by uncertainty. Limited sampling of the subsurface architecture, imperfect data, and limited direct measurements impart massive uncertainties in the response of a subsurface system, yet those uncertainties are critically important for problems like reactive transport, risk assessment, and even interpreting environmental tracers. Current workflows for uncertainty quantification (UQ) essentially do so after a model is built, after calibration and sensitivity analysis. Robust UQ is often relegated to an afterthought likely due to time constraints and excessive model runtimes. The common Monte-Carlo approach can require thousands of realizations of parameter fields for UQ, each realization being treated as deterministic then combined into an ensemble. Current workflows let modelers get away with not performing UQ for every simulation, but what if we had workflows that embedded uncertainty into the equations themselves? This presentation considers a new kind of modeling tool for problems with highly uncertain continua that includes uncertainty as part of the model from the outset. Conceptually the goal is to add an uncertainty "dimension" to the problem space using a mathematical implementation of "quantum-like" complex operators and probability amplitudes. Explicit inclusion of an uncertainty dimension increases the complexity of the problem but there may be significant computational gains to be realized since the new formulation would put the problem in a natural form for quantum computing. Flow and transport models posed in terms of linear operators could, in principle, consider every possible realization of the system simultaneously, which could radically transform UQ in groundwater models. It will take discussion and debate in the broader research community to develop this theory, but some interesting preliminary results are presented here.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2022
- Bibcode:
- 2022AGUFM.H15I0902E