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

πŸ“… 2026-02-10
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This work addresses the high computational cost of high-fidelity physical simulation in subsurface energy systems, which arises from geological heterogeneity, strong multi-physics coupling, and the demand for high spatial resolution. To overcome these challenges, the authors propose the Adaptive Physics Transformer (APT), a neural operator that integrates a graph encoder to capture local heterogeneous features and introduces a global–local fused attention mechanism to model long-range physical interactions. APT is geometry-, mesh-, and physics-agnostic, and uniquely enables direct learning from adaptive mesh refinement simulations. It demonstrates superior generalization across datasets and tasks, outperforms existing methods on both structured and unstructured grids, and exhibits exceptional super-resolution capabilities, thereby establishing a new paradigm for large-scale subsurface foundation models.

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πŸ“ Abstract
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 directly learns from adaptive mesh refinement simulations. We also demonstrate APT's capability for cross-dataset learning, positioning it as a robust and scalable backbone for large-scale subsurface foundation model development.
Problem

Research questions and friction points this paper is trying to address.

subsurface energy systems
computational expense
geological heterogeneity
multi-physics coupling
high-resolution simulation
Innovation

Methods, ideas, or system contributions that make the work stand out.

Adaptive Physics Transformer
neural operator
global-local attention
adaptive mesh refinement
subsurface energy systems
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