proxy models
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2021 ◽  
Shivam Kalra ◽  
Junfeng Wen ◽  
Jesse Cresswell ◽  
Maksims Volkovs ◽  
Hamid Tizhoosh

Abstract Institutions in highly regulated domains such as finance and healthcare often have restrictive rules around data sharing. Federated learning is a distributed learning framework that enables multi-institutional collaborations on decentralized data with improved protection for each collaborator’s data privacy. In this paper, we propose a communication-efficient scheme for decentralized federated learning called ProxyFL, or proxy-based federated learning. Each participant in ProxyFL maintains two models, a private model, and a publicly shared proxy model designed to protect the participant’s privacy. Proxy models allow efficient information exchange among participants using the PushSum method without the need of a centralized server. The proposed method eliminates a significant limitation of canonical federated learning by allowing model heterogeneity; each participant can have a private model with any architecture. Furthermore, our protocol for communication by proxy leads to stronger privacy guarantees using differential privacy analysis. Experiments on popular image datasets, and a pan-cancer diagnostic problem using over 30,000 high-quality gigapixel histology whole slide images, show that ProxyFL can outperform existing alternatives with much less communication overhead and stronger privacy.

2021 ◽  
Carlo Cristiano Stabile ◽  
Marco Barbiero ◽  
Giorgio Fighera ◽  
Laura Dovera

Abstract Optimizing well locations for a green field is critical to mitigate development risks. Performing such workflows with reservoir simulations is very challenging due to the huge computational cost. Proxy models can instead provide accurate estimates at a fraction of the computing time. This study presents an application of new generation functional proxies to optimize the well locations in a real oil field with respect to the actualized oil production on all the different geological realizations. Proxies are built with the Universal Trace Kriging and are functional in time allowing to actualize oil flows over the asset lifetime. Proxies are trained on the reservoir simulations using randomly sampled well locations. Two proxies are created for a pessimistic model (P10) and a mid-case model (P50) to capture the geological uncertainties. The optimization step uses the Non-dominated Sorting Genetic Algorithm, with discounted oil productions of the two proxies, as objective functions. An adaptive approach was employed: optimized points found from a first optimization were used to re-train the proxy models and a second run of optimization was performed. The methodology was applied on a real oil reservoir to optimize the location of four vertical production wells and compared against reference locations. 111 geological realizations were available, in which one relevant uncertainty is the presence of possible compartments. The decision space represented by the horizontal translation vectors for each well was sampled using Plackett-Burman and Latin-Hypercube designs. A first application produced a proxy with poor predictive quality. Redrawing the areas to avoid overlaps and to confine the decision space of each well in one compartment, improved the quality. This suggests that the proxy predictive ability deteriorates in presence of highly non-linear responses caused by sealing faults or by well interchanging positions. We then followed a 2-step adaptive approach: a first optimization was performed and the resulting Pareto front was validated with reservoir simulations; to further improve the proxy quality in this region of the decision space, the validated Pareto front points were added to the initial dataset to retrain the proxy and consequently rerun the optimization. The final well locations were validated on all 111 realizations with reservoir simulations and resulted in an overall increase of the discounted production of about 5% compared to the reference development strategy. The adaptive approach, combined with functional proxy, proved to be successful in improving the workflow by purposefully increasing the training set samples with data points able to enhance the optimization step effectiveness. Each optimization run performed relies on about 1 million proxy evaluations which required negligible computational time. The same workflow carried out with standard reservoir simulations would have been practically unfeasible.

2021 ◽  
Mark Zhao ◽  
Ryosuke Okuno

Abstract Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions. The proxy fugacity model was trained by artificial neural networks (ANN) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng- Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. The proxy model is applied to multiphase flash calculations (phase-split and stability), where the cubic equation solutions and fugacity coefficient calculations are bypassed when the Peng-Robinson EOS has one root. The original fugacity coefficient is analytically calculated when the EOS has more than one root, but this occurs only occasionally at reservoir conditions. A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling. To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.

2021 ◽  
Anna E. Gubanova ◽  
Bulat A. Khabibullin ◽  
Denis M. Orlov ◽  
Dmitry A. Koroteev

Abstract To reduce inefficient costs and environmental risks, oil companies strive to optimize the process of hydrocarbon production at all stages of field development, including geological and technical works at wells. In particular, it is important to predict fluid production with high accuracy. 3D hydrodynamic modeling is a generally accepted technique for solving this problem. It provides reliable results but requires many input data, computational resources, and time for calculations. Since the decision-making process has to be reactive, it is necessary to develop a simultaneously precise and prompt predictive instrument for quick forecasts of liquid production. The most promising tools for these purposes are proxy models based on solving the material balance equation. They adapt to the existing historical data even without PVT properties and reservoir data. Some of the most popular approaches are proxy models such as Capacitance Resistance Models (CRM). CR-type model is a material balance-based flow model, which provides preferable transmissibility trends, the presence of sealing or leaking faults with compressibility effects in consideration, and dissipation between injector-producer pairs. It is a data-driven model with adjustable time constants and interwell connectivity parameters. Before the model tuning, all parameters must be initialized with analytical or random approximations, and then they can be found by an appropriate optimization procedure. Historical-based Capacitance Models can be applied to poorly studied fields. Besides, they give an opportunity to rapidly optimize field development strategy by making calculations with different well exploitation parameters. They only require historical data of hydrocarbon production volumes, injection profiles, and bottom-hole pressure dynamics as input data. One of the main is that properties in the interwell space are estimated approximately and considered to be constant throughout the entire development history. However, this is a weak assumption in the case of including well interventions and stimulations. Thus, the main goal of this work is to adjust coefficients online to changes in well operation modes, introducing new wells or shut-in the existing ones. Since the governing equation includes the considered CRM improvement, users can perform optimization over different timespans, including "special" intervals. As a result, weighting connectivity parameters of the model can be depicted on a map of well interactions versus time.

2021 ◽  
Lingies Santhirasekaran ◽  
Derric Ong ◽  
Farren Kaylyn Foo ◽  
Bonavian Hasiholan

Abstract Over the past decades, Assisted History Matching has been the new norm for history matching that leverages the rapid advancement in digital computational performance. Continuous advancements such as parallel computing and GPU accelerates numerical simulation which overcomes the cumbersome experience of working with large fine-scaled model that mainly concerns the simulation time and intervention of engineers. As more interest emerges around artificial intelligence in the optimisation process, this paper explores the Artificial Intelligence algorithm to optimize two proxy modelling techniques: Quadratic Polynomial and Artificial Neural Network proxy model. These techniques are compared with stochastic optimisation method known as Differential Evolution algorithm on their efficiency of optimizing the objective functions, time taken, and knowledge investment needed by engineer, given today's hardware technology. This paper starts off by using Latin hypercube experimental design to generate first ensemble of simulation cases to generate proxy models to match the historical cumulative oil and water production by well level. The quality of both proxy modelling techniques is evaluated using R2 coefficient and proxy plot. Proxy models are then further validated by creating real simulation models from variants generated via Monte Carlo Analysis. The history matching quality and practicality were compared between the AI algorithm that runs optimizer on top of existing proxy models, and Differential Evolution algorithm in optimizing the regional porosity and permeability multipliers. The ANN proxy model prevailed over quadratic proxies to mimic the numerical reservoir model output with high degree of accuracy. The black-box nature of the ANN proxies limits the interpretability of predicted model when compared quadratic proxies where the formula for the proxy model can be obtained. Quadratic approximations are more flexible, simplistic in nature, and requires less computational cost to be constructed. Despite that, its prediction quality maybe subjected to the degree of non-linearity in the simulation model. The use of AI algorithm vastly reduces the number of full reservoir simulation required to achieve the minimum objective function at a shorter timeframe, which is proved to be the strength of such method. However, AI optimisation is highly susceptible to be trapped in local minimum. This paper proved the superiority of Differential Evolution algorithm over AI, that it may avoid being trapped in local minimum to achieve high degree of prediction accuracy for the history matching given the larger number of iterations required. This paper provides a preliminary understanding of optimisation workflow and how to go about each optimisation strategies: quadratic polynomial proxy, ANN proxy, stochastic optimisation, artificial intelligence techniques, and a novel approach of converting proxy predicted variants into real simulation cases to evaluate proxy quality. Hence establishes engineers’ expectation by appraising the pros and cons of each optimisation strategies.

Cuthbert Shang Wui Ng ◽  
Ashkan Jahanbani Ghahfarokhi ◽  
Menad Nait Amar

AbstractWith the aid of machine learning method, namely artificial neural networks, we established data-driven proxy models that could be utilized to maximize the net present value of a waterflooding process by adjusting the well control injection rates over a production period. These data-driven proxies were maneuvered on two different case studies, which included a synthetic 2D reservoir model and a 3D reservoir model (the Egg Model). Regarding the algorithms, we applied two different nature-inspired metaheuristic algorithms, i.e., particle swarm optimization and grey wolf optimization, to perform the optimization task. Pertaining to the development of the proxy models, we demonstrated that the training and blind validation results were excellent (with coefficient of determination, R2 being about 0.99). For both case studies and the optimization algorithms employed, the optimization results obtained using the proxy models were all within 5% error (satisfied level of accuracy) compared with reservoir simulator. These results confirm the usefulness of the methodology in developing the proxy models. Besides that, the computational cost of optimization was significantly reduced using the proxies. This further highlights the significant benefits of employing the proxy models for practical use despite being subject to a few constraints.

2021 ◽  
Julia Rosenzweig ◽  
Joachim Sicking ◽  
Sebastian Houben ◽  
Michael Mock ◽  
Maram Akila

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