Print Email Facebook Twitter Application of Deep Neural Networks to the Operator Space of Nonlinear PDE for Physics-Based Proxy Modelling Title Application of Deep Neural Networks to the Operator Space of Nonlinear PDE for Physics-Based Proxy Modelling Author Hadjisotiriou, George (Student TU Delft) Mansour Pour, K. (TU Delft Reservoir Engineering) Voskov, D.V. (TU Delft Reservoir Engineering; Stanford University) Date 2023 Abstract In this study, we utilize deep neural networks to approximate operators of a nonlinear partial differential equation (PDE), within the Operator-Based Linearization (OBL) simulation framework, and discover the physical space for a physics-based proxy model with reduced degrees of freedom. In our methodology, observations from a high-fidelity model are utilized within a supervised learning scheme to directly train the PDE operators and improve the predictive accuracy of a proxy model. The governing operators of a pseudo-binary gas vaporization problem are trained with a transfer learning scheme. In this two-stage methodology, labeled data from an analytical physics-based approximation of the operator space are used to train the network at the first stage. In the second stage, a Lebesgue integration of the shocks in space and time is used in the loss function by the inclusion of a fully implicit PDE solver directly in the neural network's loss function. The Lebesgue integral is used as a regularization function and allows the neural network to discover the operator space for which the difference in shock estimation is minimal. Our Physics-Informed Machine Learning (PIML) methodology is demonstrated for an isothermal, compressible, two-phase multicomponent gas-injection problem. Traditionally, neural networks are used to discover hidden parameters within the nonlinear operator of a PDE. In our approach, the neural network is trained to match the shocks of the full-compositional model in a 1D homogeneous model. This training allows us to significantly improve the prediction of the reduced-order proxy model for multi-dimensional highly heterogeneous reservoirs. With a relatively small amount of training, the neural network can learn the operator space and decrease the error of the phase-state classification of the compositional transport problem. Furthermore, the accuracy of the breakthrough time prediction is increased therefore improving the usability of the proxy model for more complex cases with more nonlinear physics. Subject united states governmentmachine learningupstream oil & gasartificial intelligencevoskovequationneural networksimulationcompositional simulationfigure To reference this document use: http://resolver.tudelft.nl/uuid:66ed157b-abe8-42ad-bcac-4b686630c163 DOI https://doi.org/10.2118/212217-MS Publisher Society of Petroleum Engineers Embargo date 2023-09-21 ISBN 9781613998717 Source SPE Reservoir Simulation Conference 2023 Proceedings Papers Event SPE Reservoir Simulation Conference 2023, 2023-03-28 → 2023-03-30, Galveston Island Convention Center, Galveston, United States Series Society of Petroleum Engineers - SPE Reservoir Simulation Conference, RSC 2023 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type conference paper Rights © 2023 George Hadjisotiriou, K. Mansour Pour, D.V. Voskov Files PDF spe_212217_ms.pdf 7.94 MB Close viewer /islandora/object/uuid:66ed157b-abe8-42ad-bcac-4b686630c163/datastream/OBJ/view