Probabilistic indirect models for undrained shear strength: addressing significant data missing and variability with advanced imputation and machine learning techniques

arXiv cs.LG Papers
machine-learning probabilistic-models geotechnical-engineering data-imputation neural-networks extreme-gradient-boosting

Summary

This research paper develops probabilistic indirect models for predicting undrained shear strength in geotechnical engineering, using advanced data imputation and machine learning techniques to handle missing data and variability. The proposed MHA-enhanced PNN model demonstrates superior performance in accuracy and uncertainty quantification compared to other methods.

arXiv:2608.13934v1 Announce Type: new Abstract: Accurate prediction of undrained shear strength (su) is crucial for geotechnical design, but is often hampered by substantial uncertainty in traditional empirical methods. This study uses the CLAY/10/7490 global database to develop probabilistic indirect models to predict su based on Atterberg limits and piezocone cone penetration (CPTU) measurements. Firstly, the dataset has a high missing data rate and variability. We test three imputation methods - multivariate normal (MN), multiple imputation by chained equations (MICE), and miss forest (MF) - to fill the missing values. To validate their effectiveness, a Probabilistic Extreme Gradient Boosting (PXGB) model is developed, and the imputation methods are evaluated by comparing the PXGB's performance when trained on the imputed datasets against that on the original incomplete data. Secondly, the indirect model is built by integrating a multi-head attention (MHA) mechanism into an artificial neural network (ANN) to enhance information extraction from limited data, which leads to the MHA-based probabilistic neural networks (MHA-PNN) model. The models' performance, alongside a conventional MN-based prediction model, was evaluated using root mean square error (RMSE), coefficient of determination (R2), mean absolute percentage error (MAPE), conditional interval width (wCI), and coverage rate (CR). Results demonstrate that the proposed MN-enhanced MHA-PNN model substantially outperforms other models in both prediction accuracy and uncertainty quantification. These findings highlight the potential of this integrated strategy for building robust probabilistic indirect models in geotechnical applications, particularly when confronted with sparse and incomplete datasets.
Original Article
View Cached Full Text

Cached at: 08/17/26, 10:17 AM 

# Probabilistic indirect models for undrained shear strength: addressing significant data missing and variability with advanced imputation and machine learning techniques
Source: [https://arxiv.org/abs/2608.13934](https://arxiv.org/abs/2608.13934)
[View PDF](https://arxiv.org/pdf/2608.13934)

> Abstract:Accurate prediction of undrained shear strength \(su\) is crucial for geotechnical design, but is often hampered by substantial uncertainty in traditional empirical methods\. This study uses the CLAY/10/7490 global database to develop probabilistic indirect models to predict su based on Atterberg limits and piezocone cone penetration \(CPTU\) measurements\. Firstly, the dataset has a high missing data rate and variability\. We test three imputation methods \- multivariate normal \(MN\), multiple imputation by chained equations \(MICE\), and miss forest \(MF\) \- to fill the missing values\. To validate their effectiveness, a Probabilistic Extreme Gradient Boosting \(PXGB\) model is developed, and the imputation methods are evaluated by comparing the PXGB's performance when trained on the imputed datasets against that on the original incomplete data\. Secondly, the indirect model is built by integrating a multi\-head attention \(MHA\) mechanism into an artificial neural network \(ANN\) to enhance information extraction from limited data, which leads to the MHA\-based probabilistic neural networks \(MHA\-PNN\) model\. The models' performance, alongside a conventional MN\-based prediction model, was evaluated using root mean square error \(RMSE\), coefficient of determination \(R2\), mean absolute percentage error \(MAPE\), conditional interval width \(wCI\), and coverage rate \(CR\)\. Results demonstrate that the proposed MN\-enhanced MHA\-PNN model substantially outperforms other models in both prediction accuracy and uncertainty quantification\. These findings highlight the potential of this integrated strategy for building robust probabilistic indirect models in geotechnical applications, particularly when confronted with sparse and incomplete datasets\.

## Submission history

From: Shaoheng Dai \[[view email](https://arxiv.org/show-email/e85d6a5e/2608.13934)\] **\[v1\]**Fri, 14 Aug 2026 04:15:16 UTC \(3,770 KB\)

Similar Articles

Evaluating Machine Learning Models for Post-Wildfire Debris-Flow Prediction

arXiv cs.LG

This paper systematically evaluates 15 machine learning models, including the TabPFN foundation model, for post-wildfire debris-flow prediction using USGS basin-scale data, finding TabPFN achieves the best performance (threat score 0.637) and that synthetic data augmentation improves most models.

Physics-Informed Machine Learning for Short-Term Flood Prediction

arXiv cs.LG

Researchers propose a Physics-Informed Machine Learning (PIML) framework that integrates hydrological constraints into an LSTM loss function to improve short-term flood forecasting, particularly in data-scarce regimes. A 'Trend Alignment' constraint enforcing consistency between precipitation and discharge trends improves Nash-Sutcliffe Efficiency and eliminates unphysical predictions during extreme events.