InterPore2026

Beyond Spectral Bias in Geothermal Heat Transport: A Comparative Analysis of Fourier Neural Operators and DeepONet Architectures in Heterogeneous Media

19 May 2026, 14:20

15m

Oral Presentation (MS15) Machine Learning in Porous Media MS15

Speaker

Antonio Ortiz Romero (IDAEA-CSIC)

Description

Deep geothermal energy exploitation relies heavily on predicting heat transport within highly heterogeneous porous formations. The multi-scale nature of subsurface geology (ranging from pore-scale variances to reservoir-scale fracture networks) coupled with the non-linear interaction between Darcy flow and advective-diffusive heat transfer, renders traditional numerical solvers computationally prohibitive for real-time optimization and many-query uncertainty quantification. Scientific Machine Learning, specifically Operator Learning, offers a promising path to overcome this bottleneck by learning mesh-independent solution operators.

In this work, we present a rigorous analysis of two leading operator learning paradigms: Fourier Neural Operators (FNO) and Deep Operator Networks (DeepONet). We utilize a high-fidelity benchmark of dipole flow and heat transport simulations in stochastically generated heterogeneous media to evaluate the capacity of these architectures to act as reliable surrogates for the management of geothermal reservoirs. We present an exhaustive comparative analysis of both architectures, focusing not just on global error metrics, but on the spatial and spectral distribution of residuals. Furthermore, we investigate the internal mechanisms of both models to understand their respective failure modes. By explicitly mapping how each architecture encodes physical heterogeneity, we propose novel strategies to mitigate spectral bias, enabling hybrid architectures that reconcile global spectral efficiency with the local resolution necessary for robust geothermal digital twins.

Our primary contribution is the demonstration and quantification of ``spectral bias'' in standard FNO architectures. While FNOs exhibit exceptional performance in diffusion-dominated regimes, our results reveal a structural inability to resolve high-frequency spatial features in advection-dominated scenarios. Specifically, the intrinsic frequency truncation in FNO layers acts as a low-pass filter, leading to significant localized errors around singularities (injection/production wells) and sharp thermal fronts. This smoothing effect compromises the physical fidelity required for operational decision-making in geothermal doublets.

Comparatively, Deep Operator Networks (DeepONet) utilize a dual Branch and Trunk structure that learns an adaptive basis, theoretically offering superior resolution for local singularities compared to the fixed Fourier basis of FNOs (Lu et al., 2021). However, recent analyses indicate that while DeepONets offer geometric flexibility, standard MLP-based trunks suffer from their own spectral bias, leading to slower convergence when resolving multimodal global fields compared to spectral methods (Wang et al., 2021; Rahaman et al., 2019). To reconcile these trade-offs, we propose a novel hybrid strategy inspired by recent `global-local' operator learning paradigms (Wen et al., 2022; Jiang et al., 2024). Our approach integrates FNOs to efficiently resolve the dominant global transport dynamics with a localized DeepONet correction module, specifically targeted to capture the high-frequency residuals at injection wells. This architecture aims to bridge the computational speed of spectral methods with the physical fidelity required for high-Péclet geothermal reservoir management.