mlsanityData to 7 Oct 2026

Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network

arXiv 2110.10080 ↗First posted 12 Oct 2021physics.geo-ph cs.LG physics.comp-phcited by 5

Not on the map. Why?

Abstract (arXiv)

The theory-guided convolutional neural network (TgCNN) framework, which can incorporate discretized governing equation residuals into the training of convolutional neural networks (CNNs), is extended to two-phase porous media flow problems in this work. The two principal variables of the considered problem, pressure and saturation, are approximated simultaneously with two CNNs, respectively. Pressure and saturation are coupled with each other in the governing equations, and thus the two networks are also mutually conditioned in the training process by the discretized governing equations, which also increases the difficulty of model training. The coupled and discretized equations can provide valuable information in the training process. With the assistance of theory-guidance, the TgCNN surrogates can achieve better accuracy than ordinary CNN surrogates in two-phase flow problems. Moreover, a piecewise training strategy is proposed for the scenario with varying well controls, in which the TgCNN surrogates are constructed for different segments on the time dimension and stacked together to predict solutions for the whole time-span. For scenarios with larger variance of the formation property field, the TgCNN surrogates can also achieve satisfactory performance. The constructed TgCNN surrogates are further used for inversion of permeability fields by combining them with the iterative ensemble smoother (IES) algorithm, and sufficient inversion accuracy is obtained with improved efficiency.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 15 of its 34 references that are in the map. First posted on arXiv 12 Oct 2021.

Builds on

15 of 34 references.

References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  3. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  4. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  5. 2019PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEscited by 116
  6. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  7. 2019Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transportcited by 60
  8. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
  9. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  10. 2019Deep Learning of Subsurface Flow via Theory-guided Neural Networkcited by 32
  11. 2014Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximationscited by 17
  12. 2020Efficient Uncertainty Quantification for Dynamic Subsurface Flow with Surrogate by Theory-guided Neural Networkcited by 17
3 more
  1. 2020Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Examplecited by 13
  2. 2020Weak Form Theory-guided Neural Network (TgNN-wf) for Deep Learning of Subsurface Single and Two-phase Flowcited by 12
  3. 2020Theory-guided Auto-Encoder for Surrogate Construction and Inverse Modelingcited by 12

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 0; 2026: 2.

5 papers.

  1. 2023Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controlscited by 4
  2. 2023Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controlscited by 4
  3. 2023Graph Network Surrogate Model for Subsurface Flow Optimizationcited by 4
  4. 2026Machine learning for sustainable geoenergy: uncertainty, physics and decision-ready inferencecited by 0
  5. 2026AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flowcited by 0