Title: A Novel A.I Enhanced Reservoir Characterization with a Combined Mixture of Experts -- NVIDIA Modulus based Physics Informed Neural Operator Forward Model

Abstract: We have developed an advanced workflow for reservoir characterization, effectively addressing the challenges of reservoir history matching through a novel approach. This method integrates a Physics Informed Neural Operator (PINO) as a forward model within a sophisticated Cluster Classify Regress (CCR) framework. The process is enhanced by an adaptive Regularized Ensemble Kalman Inversion (aREKI), optimized for rapid uncertainty quantification in reservoir history matching. This innovative workflow parameterizes unknown permeability and porosity fields, capturing non-Gaussian posterior measures with techniques such as a variational convolution autoencoder and the CCR. Serving as exotic priors and a supervised model, the CCR synergizes with the PINO surrogate to accurately simulate the nonlinear dynamics of Peaceman well equations. The CCR approach allows for flexibility in applying distinct machine learning algorithms across its stages. Updates to the PINO reservoir surrogate are driven by a loss function derived from supervised data, initial conditions, and residuals of governing black oil PDEs. Our integrated model, termed PINO-Res-Sim, outputs crucial parameters including pressures, saturations, and production rates for oil, water, and gas. Validated against traditional simulators through controlled experiments on synthetic reservoirs and the Norne field, the methodology showed remarkable accuracy. Additionally, the PINO-Res-Sim in the aREKI workflow efficiently recovered unknown fields with a computational speedup of 100 to 6000 times faster than conventional methods. The learning phase for PINO-Res-Sim, conducted on an NVIDIA H100, was impressively efficient, compatible with ensemble-based methods for complex computational tasks.