A Discrete Neural Operator with Adaptive Sampling for Surrogate Modeling of Parametric Transient Darcy Flows in Porous Media
This work addresses efficient simulation of fluid flow in porous media for applications like reservoir engineering, but it is incremental as it builds on existing neural operator methods with specific improvements.
The study tackled surrogate modeling of transient Darcy flow in porous media by proposing a discrete neural operator that integrates temporal encoding, operator learning, and UNet, achieving higher prediction accuracy than the SOTA attention-residual-UNet structure and enhancing accuracy with transmissibility matrices and adaptive sampling.
This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to approximate the mapping between vector spaces of random parameter and spatiotemporal flow fields. The new discrete neural operator can achieve higher prediction accuracy than the SOTA attention-residual-UNet structure. Derived from the finite volume method, the transmissibility matrices rather than permeability is adopted as the inputs of surrogates to enhance the prediction accuracy further. To increase sampling efficiency, a generative latent space adaptive sampling method is developed employing the Gaussian mixture model for density estimation of generalization error. Validation is conducted on test cases of 2D/3D single- and two-phase Darcy flow field prediction. Results reveal consistent enhancement in prediction accuracy given limited training set.