Feature-Modulated UFNO for Improved Prediction of Multiphase Flow in Porous Media

TL;DR

This paper targets accurate surrogate modeling for subsurface multiphase flow by addressing two weaknesses of the UFNO: how scalar inputs are incorporated and how training loss weights error spatially. It introduces UFNO-FiLM, which uses a FiLM layer to condition spatial features with decoupled scalar inputs and a spatially weighted loss to prioritize physically important regions. Empirical results on a radially symmetric CO$_2$-water dataset show a $21\%$ reduction in gas-saturation MAE compared with UFNO, with notable gains in MAE and SSIM and strong performance in data-scarce regimes. While the method excels for high-frequency saturation dynamics, benefits for smoother pressure fields are limited, motivating future extensions to more complex 3D reservoir settings.

Abstract

The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy over FNO, it inefficiently treats scalar inputs (e.g., temperature, injection rate) as spatially distributed fields by duplicating their values across the domain. This forces the model to process redundant constant signals within the frequency domain. Additionally, its standard loss function does not account for spatial variations in error sensitivity, limiting performance in regions of high physical importance. We introduce UFNO-FiLM, an enhanced architecture that incorporates two key innovations. First, we decouple scalar inputs from spatial features using a Feature-wise Linear Modulation (FiLM) layer, allowing the model to modulate spatial feature maps without introducing constant signals into the Fourier transform. Second, we employ a spatially weighted loss function that prioritizes learning in critical regions. Our experiments on subsurface multiphase flow demonstrate a 21\% reduction in gas saturation Mean Absolute Error (MAE) compared to UFNO, highlighting the effectiveness of our approach in improving predictive accuracy.

Figures (7)

• Figure 1: Architecture of the UFNO-FiLM model. The FiLM layer modulates spatial feature maps based on scalar inputs, while the spatially weighted loss improves predictive accuracy.
• Figure 2: Comparison of training and validation curves for Attention UNet, FNO, UFNO, and UFNO-FiLM. (a) Training curves show the loss decreases over epochs. (b) Validation curves highlight that UFNO-FiLM achieves the lowest validation error.
• Figure 3: Comparison of MAE and SSIM between predictions and ground truth at different injection times for FNO, UFNO, and UFNO-FiLM. The results show that UFNO-FiLM outperforms the other models by achieving lower MAE and higher SSIM values.
• Figure 4: Qualitative comparison of UFNO and UFNO-FiLM predictions at several injection times. Each block shows the ground truth, model predictions, and associated error maps. UFNO-FiLM exhibits visibly reduced errors and improved reconstruction of plume structure.
• Figure 5: Additional qualitative comparison on a different test sample. UFNO-FiLM again shows improved predictive accuracy and reduced spatial errors compared with UFNO.