Surrogate Model for Field Optimization Using Beta-VAE Based Regression
Authors: Kumar Ajitabh 
Published: February 2022

Abstract
Oilfield development related decisions are made using reservoir simulation-based optimization study in which different production scenarios and well controls are compared. Such simulations are computationally expensive and so surrogate models are used to accelerate studies. Deep learning has been used in past to generate surrogates, but such models often fail to quantify prediction uncertainty and are not interpretable. In this work, beta-VAE based regression is proposed to generate simulation surrogates for use in optimization workflow. beta-VAE enables interpretable, factorized representation of decision variables in latent space, which is then further used for regression. Probabilistic dense layers are used to quantify prediction uncertainty and enable approximate Bayesian inference.
A single optimization run requires thousands of compute-expensive simulation runs to calculate a real valued objective function such as net present value or weighted cumulative fluid production. Surrogate models may be used in place of full-physics simulation to accelerate optimization studies or quickly analyze different scenarios. With this goal in mind, beta-VAE based regression is used in which factorized representation in latent space makes the model interpretable while probabilistic layers determine the prediction uncertainty. Latent factors are disentangled by increasing value of beta which enhances interpretability at the cost of larger reconstruction error. Probabilistic dense layers assist in modeling high-dimensional decision variables and ascertaining uncertainty. Latent representation is further used as input in regression, and both VAE as well as regression networks are trained jointly. This ensures that encoder finds meaningful latent representation that is useful for downstream supervised learning task.
Olympus benchmark is used to validate our approach with test case comprising of 72 well control and 18 well placement related decision variables. Two separate objective functions namely weighted cumulative fluid production and net present value of cash flow are used. As beta value is increased from value of one which corresponds to original VAE, latent variable representation first improves and then diffuses for even higher value. Thus, proper selection of beta value could make the factors independent and hence interpretable. Probabilistic dense layers enable modeling of complex, high-dimensional, and trainable priors as well as quantification of prediction uncertainty. Both predicted objective function value and associated uncertainty can be used to decide whether predictions are acceptable or full simulation should be made for a case. Thus, optimization study can be accelerated without compromising the quality of results.
Surrogate model developed using beta-VAE based regression finds interpretable and relevant latent representation. A reasonable value of beta ensures a good balance between factor disentanglement and reconstruction. Probabilistic dense layer helps in quantifying predicted uncertainty for objective function, which is then used to decide whether full-physics simulation is required for a case.