We compare two different physics-based machine learning approaches, the Physics-Informed Neural Network (PINN) and the non-intrusive reduced-basis (NI-RB) method, and conventional (data-driven) machine learning approaches. We find out that physics-based machine learning approach based on the NI-RB method is suitable for geothermal applications where measurement data is limited. It requires a small number of training samples to achieve high accuracy and gives a significant speed-up (the running time is in the order of miliseconds) over a Finite Element-based model run. The NI-RB method then enables performing a robust uncertainty quantification of large-scale, multi-physics models.
The NI-RB method also works for reactive transport simulations where it can capture non-linear responses due to a hydro-chemical coupling with a small number of training samples. We also implemented the NI-RB method for uncertainty quantification of available heat energy in The Hague, Netherlands. The Hague model is high-dimensional and requires High-Performance Computing (HPC) infrastructure to perform thermal and thermo-hydraulic analysis. Here, the NI-RB method significantly reduces the computational time to perform model runs and is proven to enable such a large-scale uncertainty quantification. This result is useful to plan the future drilling program.
We are currently investigating the use of NI-RB method for accelerating chemical equilibrium calculation and for optimizing coaxial borehole heat-exchanger design in Cornwall, UK.