Domain-informed explainable boosting machines for trustworthy lateral spread predictions

Cheng-Hsi Hsiao; Krishna Kumar; Ellen M. Rathje

cs.LGMar 17, 2026

Domain-informed explainable boosting machines for trustworthy lateral spread predictions

Authors: Cheng-Hsi Hsiao, Krishna Kumar, Ellen M. Rathje

Abstract

Explainable Boosting Machines (EBMs) provide transparent predictions through additive shape functions, enabling direct inspection of feature contributions. However, EBMs can learn non-physical relationships that reduce their reliability in natural hazard applications. This study presents a domain-informed framework to improve the physical consistency of EBMs for lateral spreading prediction. Our approach modifies learned shape functions based on domain knowledge. These modifications correct non-physical behavior while maintaining data-driven patterns. We apply the method to the 2011 Christchurch earthquake dataset and correct non-physical trends observed in the original EBM. The resulting model produces more physically consistent global and local explanations, with an acceptable tradeoff in accuracy (4--5%).

Figures & tables

Figure 1: Spatial distribution of 2011 Christchurch earthquake showing lateral spreading Yes/No sites.

Panel of Figure 2 — Figure 2: Distribution of input features and outliers analysis.

Figure 3: Relationship between the score $s$ and probability $P(y=1)$ through the logistic function. The classification threshold $P=0.5$ corresponds to $s=0$ .

Figure 4: Round-robin training for univariate shape functions.

Panel of Figure 5 — Figure 5: Shape function examples. (a)(b) 1D shape function examples for $f_{1}$ and $f_{2}$ . The x axis is the feature value and the y axis is the score. (d) 2D shape function example for $f_{1,2}$ . The color denotes the score. The red point denotes the example point with feature value $x_{1}=5$ and $x_{2}=0.5$ .

	RF	XGB	EBM
Learning rate	-	0.1	0.01
Max iteration	-	-	5,000
Max leaves	-	-	3
Early stopping	-	-	50
# Estimators	50	100	-
Max depth	9	8	-

Table 1: Model configuration and testing performance for lateral spreading in Christchurch.

Panel of Figure 6 — Figure 6: Univariate score curves from the EBM

Panel of Figure 7 — Figure 7: Examples of look-up graphs generated by EBM, with arrows highlighting non-physical behaviors.

Panel of Figure 8 — Figure 8: The original and modified univariate function.

Panel of Figure 9 — Figure 9: Synthesis of the modified bivariate function for GWD and PGA.

Panel of Figure 10 — Figure 10: Mixing the original interaction map and the synthetic map.

	Original EBM		Domain-Informed EBM
Dataset	Validation	Testing	Validation	Testing
Accuracy	0.80	0.80	0.76	0.75
Precision	0.80	0.82	0.72	0.72
Recall	0.71	0.70	0.70	0.71
F1-score	0.76	0.75	0.71	0.71
AUC	0.87	0.88	0.80	0.80

Table 2: EBM models performance on validation and testing dataset.

Panel of Figure 11 — Figure 11: Confusion matrices of the original EBM and the domain-informed EBM on the testing dataset.

Panel of Figure 12 — Figure 12: Feature importance in the training data.

Figure 13: Beeswarm plot for RF (top left), XGB (top right), Original EBM (bottom left), and Domain-informed EBM (bottom right). Each dot in the plot represents a datapoint from the training data. The color denotes the feature values, and the x-axis denotes the SHAP values

Panel of Figure 14 — Figure 14: The distribution of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) results for (a) original EBM and (b) domain-informed EBM. (c) The improved and degraded cases after the modification. The label XX- YY denotes the prediction changing from XX to YY after the modification (e.g., an FP change to TN is FP - TN.

Figure 15: Local explanation for Site 2639. The modified features are marked in italic style, and the feature values are shown in the brackets.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 16 — Figure 16: Bivariate function maps from the original EBM.

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Formal verification of tree-based machine learning models for lateral spreading

Krishna Kumar

aOden Institute of Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA

Formal Verification

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Machine learning models for geotechnical hazard prediction can achieve high accuracy while learning physically inconsistent relationships from sparse or biased training data. Current remedies (post-hoc explainability, such as SHAP and LIME, and training-time constraints) either diagnose individual predictions approximately or restrict model capacity without providing exhaustive guarantees. This paper encodes trained tree ensembles as logical formulas in a Satisfiability Modulo Theories (SMT) solver and checks physical specifications across the entire input domain, not just sampled points. Four geotechnical specifications (water table depth, PGA monotonicity, distance safety, and flat-ground safety) are formalized as decidable logical formulas and verified via SMT against both XGBoost ensembles and Explainable Boosting Machines (EBMs) trained on the 2011 Christchurch earthquake lateral spreading dataset (7,291 sites, four features). The SMT solver either produces a concrete counterexample where a specification fails or proves that no violation exists. The unconstrained EBM (80.1% accuracy) violates all four specifications. A fully constrained EBM (67.2%) satisfies three of four specifications, demonstrating that iterative constraint application guided by verification can progressively improve physical consistency. A Pareto analysis of 33 model variants reveals a persistent trade-off, as none of the variants studied achieve both greater than 80% accuracy and full compliance with the specified set. SHAP analysis of specification counterexamples shows that the offending feature can rank last, demonstrating that post-hoc explanations do not substitute for formal verification. These results establish a verify-fix-verify engineering loop and a formal certification for deploying physically consistent ML models in safety-critical geotechnical applications.

Abstract

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