# Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements

arXiv: https://arxiv.org/abs/2205.12684 · HTML: https://mlsanity.com/paper/2205.12684/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 6 of 6)

- [DR-RNN: A deep residual recurrent neural network for model reduction](https://mlsanity.com/paper/1709.00939/) (2017)
- [Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example](https://mlsanity.com/paper/2007.15580/) (2020)
- [Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks](https://mlsanity.com/paper/1810.10422/) (2018)
- [Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements](https://mlsanity.com/paper/2005.08868/) (2020)
- [A Deep Learning Approach to the Inversion of Borehole Resistivity Measurements](https://mlsanity.com/paper/1810.04522/) (2018)
- [Modeling extra-deep electromagnetic logs using a deep neural network](https://mlsanity.com/paper/2005.08919/) (2020)

## Built on by (most cited first, 3 of 3)

- [High-Precision Geosteering via Reinforcement Learning and Particle Filters](https://mlsanity.com/paper/2402.06377/) (2024)
- [Strategic Geosteering Workflow with Uncertainty Quantification and Deep Learning: A Case Study on the Goliat Field](https://mlsanity.com/paper/2210.15548/) (2022)
- [Automated machine learning for borehole resistivity measurements](https://mlsanity.com/paper/2207.09849/) (2022)

## Abstract (arXiv)

The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting for uncertainties. However, they rely on the repeated evaluation of the computational models, and deep neural network (DNN) based proxies can be useful to address this computational bottleneck. This paper studies the effects of the approximate nature of the deep learned models and associated model errors during the inversion of extra-deep borehole electromagnetic (EM) measurements, which are critical for geosteering. Using a deep neural network (DNN) as a forward model allows us to perform thousands of model evaluations within seconds, which is very useful for quantifying uncertainties and non-uniqueness in real-time. While significant efforts are usually made to ensure the accuracy of the DNN models, it is known that they contain unknown model errors in the regions not covered by the training data. When DNNs are utilized during inversion of EM measurements, the effects of the model errors could manifest themselves as a bias in the estimated input parameters and, consequently, might result in a low-quality geosteering decision. We present numerical results highlighting the challenges associated with the inversion of EM measurements while neglecting model error. We further demonstrate the utility of a recently proposed flexible iterative ensemble smoother in reducing the effect of model bias by capturing the unknown model errors, thus improving the quality of the estimated subsurface properties for geosteering operation. Moreover, we describe a procedure for identifying inversion multimodality and propose possible solutions to alleviate it in real-time.