Dynamic Mode Decomposition for Aquifer Thermal Energy Storage

Abstract

This thesis investigates the application of dynamic mode decomposition (DMD) for the mod-
elling of aquifer thermal energy storage (ATES) systems, which are crucial for reducing the
energy used for heating and cooling of buildings. ATES systems store thermal energy un-
derground, using the natural temperature differences between seasons. The research aims to
develop a linear model suitable for control purposes, specifically for integration into model
predictive controllers (MPC).

DMD is a data-driven method for finding the discrete-time Koopman operator. The required
data for DMD is gathered by running high-fidelity simulations in MODFLOW. To identify
the Koopman operator, the data is lifted with spatial and time-delayed coordinates. Three
DMD algorithms are applied to this lifted data. Firstly, DMD with control (DMDc), this is
the most basic DMD algorithm for systems with control input. Secondly, we apply physics-
informed DMD (piDMD). This algorithm enforces a local physical constraint. This means
that points are only influenced by nearby points. Thirdly, a new DMD algorithm is developed.
Gershgorin DMD (GeDMD) combines ideas from piDMD with a constraint on the Gershgorin
norm in the DMD optimization to penalize instability. A stable and local system can now be
learned.

The DMD models are evaluated on a multi-year prediction horizon and compared to a non-
linear analytical ATES temperature model from the literature. The DMDc algorithm out-
performs both the analytical model from the literature and the other two DMD algorithms,
piDMD and GeDMD. PiDMD is able to correctly enforce the local structure in the model but
creates unstable models. The GeDMD algorithm creates a stable and local model but does
not reach the same performance as DMDc.

In conclusion, DMDc is able to learn a linear hybrid model of ATES that is usable in an MPC.
If better predictions are desired at the cost of more model complexity, research into bi-linear
DMD is recommended since this approximates the dynamics from the PDEs better. Also,
deep DMD is recommended to discover more complex observables in order to find a better
approximation of the Koopman operator. To validate the models, they should be tested more
extensively on more challenging ATES conditions.