A reduced-order derivative-informed neural operator for subsurface fluid-flow

2025-09-16

AI Summary

To address the low gradient accuracy and high computational cost of surrogate models in subsurface multiphase flow simulation, this paper proposes DeFINO—a reduced-order neural operator framework. Methodologically, DeFINO introduces a sensitivity-driven, low-rank compression scheme for derivative information using the Fisher Information Matrix (FIM), enabling data-driven modal projection without explicit Jacobian computation—thus avoiding quadratic complexity growth. It further integrates Fourier Neural Operators (FNOs) with a derivative-aware training strategy to jointly optimize flow-field prediction fidelity and gradient estimation accuracy. Evaluated on synthetic subsurface flow scenarios, DeFINO achieves comparable forward prediction accuracy while significantly reducing gradient error and computational overhead. Consequently, it markedly improves efficiency and scalability for permeability inversion and uncertainty quantification tasks.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In these applications, the fidelity of the surrogate's gradients with respect to system parameters is crucial, as the accuracy of downstream tasks, such as optimization and Bayesian inference, relies directly on the quality of the derivative information. Recent advances in physics-informed methods have leveraged derivative information to improve surrogate accuracy. However, incorporating explicit Jacobians can become computationally prohibitive, as the complexity typically scales quadratically with the number of input parameters. To address this limitation, we propose DeFINO (Derivative-based Fisher-score Informed Neural Operator), a reduced-order, derivative-informed training framework. DeFINO integrates Fourier neural operators (FNOs) with a novel derivative-based training strategy guided by the Fisher Information Matrix (FIM). By projecting Jacobians onto dominant eigen-directions identified by the FIM, DeFINO captures critical sensitivity information directly informed by observational data, significantly reducing computational expense. We validate DeFINO through synthetic experiments in the context of subsurface multi-phase fluid-flow, demonstrating improvements in gradient accuracy while maintaining robust forward predictions of underlying fluid dynamics. These results highlight DeFINO's potential to offer practical, scalable solutions for inversion problems in complex real-world scenarios, all at substantially reduced computational cost.

Problem

• Develops efficient neural operator for subsurface fluid-flow simulation
• Improves gradient accuracy for optimization and Bayesian inference
• Reduces computational cost of derivative-informed surrogate modeling

Innovation

• Reduced-order derivative-informed neural operator training
• Fourier neural operators with Fisher Information Matrix
• Jacobian projection onto dominant eigen-directions