# Efficient Uncertainty Quantification for Dynamic Subsurface Flow with Surrogate by Theory-guided Neural Network

arXiv: https://arxiv.org/abs/2004.13560 · HTML: https://mlsanity.com/paper/2004.13560/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2020.

## Built on by (most cited first, 17 of 17)

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- [Deep Reinforcement Learning for Constrained Field Development Optimization in Subsurface Two-phase Flow](https://mlsanity.com/paper/2104.00527/) (2021)
- [Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network](https://mlsanity.com/paper/2110.10080/) (2021)
- [Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network](https://mlsanity.com/paper/2111.08691/) (2021)
- [Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fields](https://mlsanity.com/paper/2407.09728/) (2024)
- [Empowering Bayesian Neural Networks with Functional Priors through Anchored Ensembling for Mechanics Surrogate Modeling Applications](https://mlsanity.com/paper/2409.05234/) (2024)
- [Deep learning based closed-loop optimization of geothermal reservoir production](https://mlsanity.com/paper/2204.08987/) (2022)
- [Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net](https://mlsanity.com/paper/2205.00134/) (2022)
- [Uncertainty quantification of two-phase flow in porous media via coupled-TgNN surrogate model](https://mlsanity.com/paper/2205.14301/) (2022)
- [AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flow](https://mlsanity.com/paper/2604.11945/) (2026)
- [Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage](https://mlsanity.com/paper/2608.02629/) (2026)

## Abstract (arXiv)

Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty quantification for dynamic subsurface flow with a surrogate constructed by the Theory-guided Neural Network (TgNN). The TgNN here is specially designed for problems with stochastic parameters. In the TgNN, stochastic parameters, time and location comprise the input of the neural network, while the quantity of interest is the output. The neural network is trained with available simulation data, while being simultaneously guided by theory (e.g., the governing equation, boundary conditions, initial conditions, etc.) of the underlying problem. The trained neural network can predict solutions of subsurface flow problems with new stochastic parameters. With the TgNN surrogate, the Monte Carlo (MC) method can be efficiently implemented for uncertainty quantification. The proposed methodology is evaluated with two-dimensional dynamic saturated flow problems in porous medium. Numerical results show that the TgNN based surrogate can significantly improve the efficiency of uncertainty quantification tasks compared with simulation based implementation. Further investigations regarding stochastic fields with smaller correlation length, larger variance, changing boundary values and out-of-distribution variances are performed, and satisfactory results are obtained.