Random Features Learning in Incremental Machine Learning: Fast Non-Linear Preconditioning for History Matching

History matching in reservoir engineering aligns model parameters with observed data to improve forecasts by iteratively adjusting parameters like porosity and permeability. Traditional methods, such as ensemble modeling, are computationally expensive for complex reservoirs due to repeated simulations. Machine learning (ML) addresses these challenges by creating surrogate models, like deep neural networks, to predict reservoir outputs and reduce computational demands. However, training such models for ensemble-based history matching remains difficult due to large datasets and generalization issues.

ML can also optimize solver parameters, as seen in simulators like OPM Flow, which use neural networks to manage non-linear stiffness during well events. For example, the Hybrid Newton method improves initial guesses, reducing iterations, while the local hybrid Newton method focuses on near-well regions. However, the latter incurs high offline costs for data generation and training.

We propose a two-step strategy: ensemble-based history matching generates parameter distributions for supervised learning, enabling neural networks to accelerate Newton’s method. The Sample Where It Matters strategy reduces CPU training time. Adapting the local hybrid Newton method for the OPM Flow simulator with simplified black-oil equations, this approach integrates history matching to create nested parameter distributions. Fully connected neural networks and SWIM ensure efficient CPU training.