Application of graph and spectral neural operators for accelerated modeling of reservoir fluid dynamics

UDK: 681.518:622.276.031:532.5.001

DOI: 10.24887/0028-2448-2025-12-118-122

Key words: neural operator, architectures Multipole Graph Kernel Network (MGKN) and Latent Neural Operator (LNO), reservoir simulation, acceleration of calculations, relative L1 error

Authors: B.M. Latypov (Ufa State Petroleum Technological University, RF, Ufa); A.M. Andrianova (Gazprom Neft Companу Group, RF, Saint Petersburg); R.A. Bondorov (Ufa State Petroleum Technological University, RF, Ufa); N.A. Zyryanov (Saint Petersburg State University, RF, Saint Petersburg)

This paper investigates the application of neural operators for accelerated modeling of reservoir fluid dynamics in field development tasks. Two state-of-the-art architectures – the Multipole Graph Kernel Network (MGKN) and the Latent Neural Operator (LNO) – are compared in terms of predictive accuracy and inference speed for forecasting the spatio-temporal evolution of pressure and water saturation of fields. The models were trained on a dataset generated by an industrial reservoir simulator, comprising 2620 well configurations and 37 time steps, and validated on a test set of 360 configurations with analysis over the first 12 time steps. Model performance is evaluated using the relative L1 error, which measures the average normalized deviation of predictions from reference solutions across all spatial nodes, time steps, and scenarios. The results show that both architectures accurately reproduce the spatio-temporal behavior of the reservoir system. The LNO model achieves nearly two times lower error in pressure prediction compared to MGKN and demonstrates a substantially higher computational efficiency, with inference time around 0,05 seconds on GPU. Despite a gradual accumulation of error during autoregressive forecasting, the models maintain acceptable stability over short-term horizons. Overall, LNO provides an advantageous balance between accuracy and computational performance, confirming the potential of neural operators for interactive optimization and large-scale scenario analysis in reservoir engineering.

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