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<p>Deep learning-based surrogate models for subsurface flow struggle with spatiotemporal generalization, particularly in time-step extrapolation under dynamic well control conditions. This study proposes a neural network framework embedded with a coarse-grid numerical simulator to enhance predictive generalizability. The approach integrates the computational efficiency of coarse-grid simulators with the high-dimensional mapping capability of deep learning, inherently embedding physical laws (e.g., multiphase flow equations) without relying on traditional loss constraints. A multi-resolution fusion network module bridges low-resolution simulator outputs and high-resolution targets using convolutional neural networks and Fourier neural operators (FNOs) to balance accuracy and flexibility. Evaluations on the Egg model demonstrate a 20% reduction in pressure field prediction errors compared to pure FNO models, with optimized coarse-grid resolution (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(30\times 30\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>30</mn> <mo>×</mo> <mn>30</mn> </mrow> </math></EquationSource> </InlineEquation>) yielding 10<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> faster computation than fine-grid simulations. The proposed framework integrates the computational efficiency of coarse-grid simulators with the high-dimensional mapping capacity of deep learning, where physical laws are inherently embedded through the simulator, thus bypassing traditional loss function constraints and maintaining physical consistency in saturation and pressure forecasts even beyond the training horizons, offering a robust physics-informed solution for real-time reservoir management.</p>

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Coarse-Grid Physics Embedded Neural Operators: Enhanced Extrapolative Generalization for Subsurface Flow Forecasting

  • 期刊论文

  • 发表日期：

    2026年6月21日

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  • Yiheng Zhu,
  • Jianqiao Liu,
  • Jia Liu,
  • Junhui Bai,
  • Huanquan Pan,
  • Junting Wang

摘要

Deep learning-based surrogate models for subsurface flow struggle with spatiotemporal generalization, particularly in time-step extrapolation under dynamic well control conditions. This study proposes a neural network framework embedded with a coarse-grid numerical simulator to enhance predictive generalizability. The approach integrates the computational efficiency of coarse-grid simulators with the high-dimensional mapping capability of deep learning, inherently embedding physical laws (e.g., multiphase flow equations) without relying on traditional loss constraints. A multi-resolution fusion network module bridges low-resolution simulator outputs and high-resolution targets using convolutional neural networks and Fourier neural operators (FNOs) to balance accuracy and flexibility. Evaluations on the Egg model demonstrate a 20% reduction in pressure field prediction errors compared to pure FNO models, with optimized coarse-grid resolution ( \(30\times 30\) 30 × 30 ) yielding 10 \(\times \) × faster computation than fine-grid simulations. The proposed framework integrates the computational efficiency of coarse-grid simulators with the high-dimensional mapping capacity of deep learning, where physical laws are inherently embedded through the simulator, thus bypassing traditional loss function constraints and maintaining physical consistency in saturation and pressure forecasts even beyond the training horizons, offering a robust physics-informed solution for real-time reservoir management.