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Statistically Accurate and Robust Generative Prediction of Rock Discontinuities with A Tabular Foundation Model

Han Meng, Gang Mei, Hong Tian, Nengxiong Xu, Jianbing Peng

TL;DR

This work tackles the challenge of inferring stochastic rock discontinuities from sparse surface observations by evaluating three generative strategies: Monte Carlo, deep generative models (GAN and DDPM), and a TabPFN-based tabular foundation model designed for small data. Across ten diverse datasets, the TabPFN approach consistently delivers higher fidelity in reproducing single-parameter statistics, inter-parameter correlations, and multivariate distribution patterns, while maintaining robustness under data scarcity. The study demonstrates the limitations of traditional Monte Carlo in capturing correlations and the data-dependence of deep generative models, establishing TabPFN as a simple, effective, and generalizable solution for generative prediction of rock discontinuities. These findings advance quantitative characterization of rock mass structures and support safer, data-driven geotechnical design, especially when surface observations are minimal.

Abstract

Rock discontinuities critically govern the mechanical behavior and stability of rock masses. Their internal distributions remain largely unobservable and are typically inferred from surface-exposed discontinuities using generative prediction approaches. However, surface-exposed observations are inherently sparse, and existing generative prediction approaches either fail to capture the underlying complex distribution patterns or lack robustness under data-sparse conditions. Here, we proposed a simple yet robust approach for statistically accurate generative prediction of rock discontinuities by utilizing a tabular foundation model. By leveraging the powerful sample learning capability of the foundation model specifically designed for small data, our approach can effectively capture the underlying complex distribution patterns within limited measured discontinuities. Comparative experiments on ten datasets with diverse scales and distribution patterns of discontinuities demonstrate superior accuracy and robustness over conventional statistical models and deep generative approaches. This work advances quantitative characterization of rock mass structures, supporting safer and more reliable data-driven geotechnical design.

Statistically Accurate and Robust Generative Prediction of Rock Discontinuities with A Tabular Foundation Model

TL;DR

This work tackles the challenge of inferring stochastic rock discontinuities from sparse surface observations by evaluating three generative strategies: Monte Carlo, deep generative models (GAN and DDPM), and a TabPFN-based tabular foundation model designed for small data. Across ten diverse datasets, the TabPFN approach consistently delivers higher fidelity in reproducing single-parameter statistics, inter-parameter correlations, and multivariate distribution patterns, while maintaining robustness under data scarcity. The study demonstrates the limitations of traditional Monte Carlo in capturing correlations and the data-dependence of deep generative models, establishing TabPFN as a simple, effective, and generalizable solution for generative prediction of rock discontinuities. These findings advance quantitative characterization of rock mass structures and support safer, data-driven geotechnical design, especially when surface observations are minimal.

Abstract

Rock discontinuities critically govern the mechanical behavior and stability of rock masses. Their internal distributions remain largely unobservable and are typically inferred from surface-exposed discontinuities using generative prediction approaches. However, surface-exposed observations are inherently sparse, and existing generative prediction approaches either fail to capture the underlying complex distribution patterns or lack robustness under data-sparse conditions. Here, we proposed a simple yet robust approach for statistically accurate generative prediction of rock discontinuities by utilizing a tabular foundation model. By leveraging the powerful sample learning capability of the foundation model specifically designed for small data, our approach can effectively capture the underlying complex distribution patterns within limited measured discontinuities. Comparative experiments on ten datasets with diverse scales and distribution patterns of discontinuities demonstrate superior accuracy and robustness over conventional statistical models and deep generative approaches. This work advances quantitative characterization of rock mass structures, supporting safer and more reliable data-driven geotechnical design.

Paper Structure

This paper contains 19 sections, 5 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Approaches for generative prediction (generation) of rock discontinuities
  4. Conventional statistical approach: the Monte Carlo method
  5. Generative deep learning-based approach: GAN and DDPM
  6. Foundation model-based approach: TabPFN
  7. Evaluation metrics
  8. Qualitative assessment
  9. Quantitative evaluation
  10. Results
  11. Experimental Scenario I: Discontinuities with relatively more samples and clear statistical regularity
  12. Experimental Scenario II: Discontinuities with relatively more samples and unclear statistical regularity
  13. Experimental Scenario III: Discontinuities with relatively less samples and clear statistical regularity
  14. Experimental Scenario IV: Discontinuities with relatively less samples and unclear statistical regularity
  15. Discussion
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Accurate and robust generative prediction of rock discontinuities with a tabular foundation model
  • Figure 2: Experimental scenario I--example from the Oernlia Slope: comparison of observed and generated discontinuities using three types of approaches (histograms, box plots, and scatter plots).
  • Figure 3: Experimental scenario II--example from the Valle Slope: comparison of observed and generated discontinuities using three types of approaches (histograms, box plots, and scatter plots).
  • Figure 4: Experimental scenario III--example from the Oernlia Slope: comparison of observed and generated discontinuities using three types of approaches (histograms, box plots, and scatter plots)
  • Figure 5: Experimental scenario IV--example from the Valle Slope: comparison of observed and generated discontinuities using three types of approaches (histograms, box plots, and scatter plots)