EAAI Journal 2026 Journal Article
A hybrid couple-task surrogate operator with Fourier space–time encoding and multi-field attention for solving three-dimensional reservoir seepage equations in heterogeneous media
- Ren-Yao Lin
- Tao Song
- Jian Li
Reservoir seepage modeling involves solving high-dimensional, multi-physics coupled partial differential equations, where both efficient computation and stable quality are critical for engineering applications. Neural operators offer higher computational efficiency than numerical solvers. However, in multi-physics coupling prediction scenarios, existing methods struggle to characterize complex spatiotemporal correlations and capture the coupling evolution characteristics between multiple fluid fields, while also facing challenges such as high computational and storage costs. To address these issues, this paper proposes a coupled task surrogate operator network combining Fourier spatiotemporal encoding and a coupled attention mechanism, aiming to reliably solve the three-dimensional multi-field coupled reservoir seepage equations. This operator first uses Fourier transform to encode spatiotemporal information to enhance the representation ability of data across spatiotemporal scales. Second, it utilizes a coupled task architecture to share spatiotemporal features to learn the potential correlations between different physical fields and the simultaneous spatial domain. Finally, an adaptive multi-field coupled attention mechanism is employed to enhance the ability to capture crucial correlation information and spatiotemporal changes between multiple physical fields in reservoir fluids. Experiments validate the operator’s effectiveness in terms of Fourier encoding, coupled task, and applicability to multiple scenarios. The results show that the proposed model more accurately describes the nonlinear behavior of reservoir fluids: Fourier coding enhancement reduces prediction error by over 95. 0% compared to the baseline model; combining coupled attention and a multi-field prediction framework not only improves the quality of multi-field predictions but also reduces inference time by 70. 9% and memory consumption by 22. 0%; under various types of Gaussian stochastic initial state fields, the operator exhibits stronger robustness and stability compared to the representative benchmark models, reducing multi-field errors by an average of 70. 0%. This study provides a new approach with engineering application potential for efficient and robust data-driven simulation of three-dimensional reservoir seepage problems.