2026 · Completed
Adaptive Sampling for Darcy Flow Surrogate Models
Developed AROnet, a discrete neural operator for transient Darcy flows, and paired it with latent-space adaptive sampling to improve predictions when simulation data is limited.
Research problem
- Transient single-phase and two-phase Darcy flows in heterogeneous porous media normally require expensive numerical simulations for each parameter realization. A useful surrogate must predict evolving pressure and saturation fields from limited labeled simulations.
AROnet: a discrete spatiotemporal operator
- Built an attention residual operator network (AROnet) on a U-Net-based encoder-decoder. Its branch network encodes spatial parameter fields, while a time-embedding trunk network lets the model predict flow fields at queried time steps.
- Used transmissibility tensors derived from finite-volume discretization as model inputs instead of raw permeability fields, giving the network a representation more directly connected to Darcy flow.
Adaptive sampling in latent space
- Projected high-dimensional parameter fields into a lower-dimensional PCA latent space, then used prediction errors to emphasize regions where the current surrogate performed poorly.
- Fit a Gaussian mixture model to error-weighted latent samples, selected its component count with the Bayesian information criterion, and generated new training samples for the next optimization round.
Validation and results
- Validated the approach on 2D and 3D single-phase flow and two-phase pressure and saturation prediction tasks.
- In the 2D single-phase comparison with 300 training samples, AROnet reduced mean relative pressure error from 3.22 × 10⁻³ for ARUnet to 2.94 × 10⁻³.
- In the 3D single-phase experiment with 300 samples, GMM adaptive sampling reduced mean relative error from 2.03 × 10⁻³ with random sampling to 1.21 × 10⁻³.
- A separate 2D input ablation found that transmissibility inputs reduced mean relative error by 31% and producing-well relative error by 77% compared with permeability inputs.