Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems

The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical simulations of these systems are notoriously computationally expensive due to geological heterogeneity, high resolution requirements, and the tight coupling of physical processes with distinct propagation time scales. Here we propose the $\textbf{Adaptive Physics Transformer}$ (APT), a geometry-, mesh-, and physics-agnostic neural operator that explicitly addresses these challenges. APT fuses a graph-based encoder to extract high-resolution local heterogeneous features with a global attention mechanism to resolve long-range physical impacts. Our results demonstrate that APT outperforms state-of-the-art architectures in subsurface tasks across both regular and irregular grids with robust super-resolution capabilities. Notably, APT is the first architecture that learns directly from HR-adaptive mesh refinement simulations. We also demonstrate APT's favorable scaling behavior and cross-dataset learning capability, positioning it as a robust and scalable backbone for large-scale subsurface foundation model development.

The Earth's subsurface provides essential energy that our modern society runs on, and it is also where we can permanently store carbon dioxide to help mitigate climate change. To do any of this safely, engineers simulate how fluids and heat move through underground rock—but these simulations are very slow and costly. Rock properties very significantly from one point to the next and several physical processes unfold at very different speeds. We developed the Adaptive Physics Transformer (APT), an AI model that reproduces these simulations in a fraction of the simulation time. Unlike earlier methods, it is not tied to a particular underground setting, grid shape, or set of physics: a single model captures both fine local detail and how a change in one location impacts the whole system. It is also the first such model that can learn from "adaptive" simulations, which adjusts computational effort according to the flow complexity. APT outperforms leading methods across diverse subsurface problems and can sharpen coarse predictions into detailed ones. With APT, one model can learn from many datasets at once, it offers a foundation for general-purpose AI tools to study the Earth's subsurface—accelerating progress on carbon storage, geothermal energy, and resource management.