Aquifer Thermal Energy Storage (ATES) offers a sustainable, low-carbon heating and cooling solution for the built environment. However, maintaining ATES system efficiency requires careful optimisation of both design and operation, involving computationally expensive numerical simulations of groundwater flow and heat transport in heterogeneous aquifers. Machine Learning (ML) provides a rapid modelling alternative to conventional numerical simulations of complex subsurface flow and transport processes. Here, we introduce the Adaptive Physics Transformer (APT), a transformer-based ML model employing an auto-regressive approach with native support for adaptive meshing. Unlike conventional ML models such as Convolutional Neural Networks (CNNs), Graph Neural Networks (GNNs), or Neural Operators, which require interpolation onto fixed grids, APT seamlessly handles arbitrary gridding schemes that adapt dynamically at each timestep throughout the simulation rollout. The APT model is trained using outputs on adaptive meshes from the open-source Imperial College Finite Element Reservoir Simulator (IC-FERST), a high-order reservoir simulator that employs dynamic unstructured mesh optimisation to enhance solution accuracy and reduce computational costs compared to fixed-grid methods. Consequently, the mesh evolves adaptively between the solution snapshots used during training. High spatial resolution is essential to accurately capture detailed variations in pressure, flow, and temperature fields; adaptive meshing achieves this efficiently by dynamically adjusting mesh resolution where required. The native support of adaptive mesh data in APT eliminates the need for interpolation, reduces potential sources of error, and enables the model to directly learn the underlying physics and transport processes. Our experiments with a synthetic ATES dataset demonstrate that the APT model significantly accelerates simulations, reducing the runtime of a 10-year ATES scenario from tens of hours to mere seconds, while maintaining high accuracy.

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