The research, conducted by Furquan Ahmad of the National Institute of Technology Patna in India and Warit Wipulanusat of Thammasat University in Thailand, addresses a long-standing challenge in geotechnical engineering. Predicting the factor of safety against liquefaction requires untangling complex nonlinear interactions among soil properties, seismic loading conditions, and in-situ measurements. Traditional simplified procedures, developed over decades from case histories of past earthquakes, rely on empirical charts and hand calculations that can miss subtle parameter interactions. Machine learning offers a way forward, but conventional neural networks are often criticized as opaque black boxes, and their training can be slow and unstable. The new framework tackles both problems at once, pairing a fast-learning network architecture with a transparent layer of explainability analysis.

At the heart of the framework is the Extreme Learning Machine, or ELM, a type of single-hidden-layer feedforward neural network introduced in the mid-2000s. Unlike conventional neural networks that iteratively adjust all their internal weights through backpropagation, an ELM assigns its hidden-layer weights randomly and then solves for the output weights analytically in a single step. This makes training dramatically faster while often achieving excellent generalization. However, the random initialization of hidden-layer parameters can leave performance on the table. The researchers solved this by coupling the ELM with four metaheuristic optimization algorithms, each inspired by different natural processes: the Adaptive Opposition Slime Mould Algorithm, Harris Hawks Optimization, Particle Swarm Optimization, and the Reptile Search Algorithm. These algorithms search the space of possible network parameters to find configurations that minimize prediction error, effectively tuning the network far beyond what random initialization alone could achieve.

Each optimizer brings a distinct search philosophy. Particle Swarm Optimization, one of the oldest and most widely used metaheuristics, mimics the social behavior of bird flocks, with candidate solutions sharing information about promising regions of the search space. Harris Hawks Optimization models the cooperative hunting strategies of hawks, dynamically switching between exploration and exploitation phases to chase down optimal solutions. The Reptile Search Algorithm draws on the hunting and social behaviors of crocodiles, while the Adaptive Opposition Slime Mould Algorithm simulates the oscillating foraging patterns of slime moulds, enhanced with an opposition-based learning mechanism that evaluates candidate solutions and their mirrored counterparts to accelerate convergence. By benchmarking all four against the same ELM backbone and the same dataset, the study provides a fair head-to-head comparison of how each optimizer shapes predictive performance.

Before any model training began, the researchers applied a disciplined feature screening process grounded in information theory. Using a database of 309 case histories based on cone penetration test, or CPT, measurements, they employed Mutual Information Analysis and Shannon Entropy Analysis to quantify how much information each candidate input variable carries about the liquefaction outcome. Mutual information measures the reduction in uncertainty about one variable given knowledge of another, while Shannon entropy, a concept borrowed from communication theory, quantifies the inherent uncertainty or information content of a variable. This pre-processing step ensures that the models focus on genuinely informative features rather than redundant or noisy ones, a critical consideration when working with real-world geotechnical data that often contains correlated measurements.

The performance results are striking. The best model, ELM-AOSMA, achieved coefficients of determination of 0.9912 on the training dataset and 0.9900 on the testing dataset, with root mean square errors of just 0.0146 and 0.0160 respectively. In practical terms, an R-squared value approaching 0.99 means the model explains nearly all of the variance in the liquefaction factor of safety across the case database, leaving only a tiny fraction unexplained. The models were validated through 5-fold cross-validation, a robust technique in which the data is partitioned into five subsets and the model is repeatedly trained and tested on different combinations to guard against overfitting. Beyond the headline metrics, the evaluation battery included the Nash-Sutcliffe coefficient, weighted mean absolute percentage error, and the A20-index, which measures the proportion of predictions falling within twenty percent of observed values.

The study also went beyond standard statistical scores with a suite of diagnostic analyses. Regression Error Characteristic curves were used to visualize the trade-off between prediction tolerance and the fraction of samples accurately predicted, while rank analysis and curve fitting analysis compared the relative standing of the four hybrid models. Convergence analysis tracked how quickly each optimizer approached its best solution, and computational efficiency was measured directly. ELM-AOSMA converged within approximately 400 iterations while requiring the lowest computational time of the four models, at 220.68 seconds. For engineers who may need to run liquefaction assessments across many sites or within probabilistic reliability frameworks that demand thousands of repeated evaluations, this combination of accuracy and speed is a meaningful advantage over slower, more computationally demanding alternatives.

Perhaps the most consequential contribution is the framework’s commitment to explainability. Using SHapley Additive exPlanations, a technique from cooperative game theory that allocates credit for each prediction to individual input features, and Partial Dependence with Individual Conditional Expectation analysis, which traces how predictions change as each variable varies, the researchers identified the dominant drivers of liquefaction behavior. Four parameters emerged as the most influential: the effective vertical stress, denoted sigma prime v; the normalized and cleaned cone penetration tip resistance, qc1Ncs; the total vertical stress, sigma v; and the magnitude scaling factor, MSF, which adjusts cyclic stress ratios for earthquakes of different magnitudes. This hierarchy aligns with established geotechnical understanding, since liquefaction resistance fundamentally depends on how tightly soil particles are confined and how densely they are packed, but the explainable AI analysis quantifies these relationships in a way empirical charts cannot.

The implications for practice extend to performance-based geotechnical design and reliability-oriented assessment. Modern seismic design codes increasingly demand not just a binary safe-or-unsafe verdict but a quantified factor of safety that can feed into probabilistic risk calculations. A model that is both highly accurate and computationally lightweight can serve as a surrogate within Monte Carlo simulations or first-order reliability methods, where the simplified empirical procedures would be evaluated tens of thousands of times. The interpretability layer also matters for professional acceptance: engineers are understandably reluctant to trust black-box predictions for safety-critical infrastructure, and SHAP-based attribution gives them a window into the reasoning behind each assessment, enabling sanity checks against engineering judgment.

The work arrives amid a broader wave of machine learning adoption in geotechnical engineering, with researchers applying hybrid models to slope stability, sheet pile walls, embankment performance in seismic zones, and liquefaction potential mapping in regions from the Indo-Gangetic plain to Kolkata. What distinguishes this study is its end-to-end rigor: information-theoretic feature selection, systematic optimizer benchmarking, cross-validated performance evaluation, and explainable AI diagnostics all integrated within a single framework. As earthquake-prone cities continue to grow and climate-driven changes alter groundwater conditions that govern soil saturation, tools that can rapidly and transparently assess liquefaction risk will become increasingly valuable. The ELM-AOSMA framework demonstrates that the next generation of geotechnical prediction tools need not force a choice between accuracy, speed, and interpretability; with careful design, they can deliver all three at once.

Subject of Research: Hybrid machine learning prediction of seismic soil liquefaction using cone penetration test data

Article Title: An information-theoretic and explainable hybrid extreme learning machine framework for seismic soil liquefaction assessment

Article References: Ahmad, F., & Wipulanusat, W. (2026). An information-theoretic and explainable hybrid extreme learning machine framework for seismic soil liquefaction assessment. Earth Science Informatics, 19(11), Article 195. https://doi.org/10.1007/s12145-026-02248-x

Image Credits: AI Generated

DOI: 10.1007/s12145-026-02248-x

Keywords: soil liquefaction, earthquake engineering, extreme learning machine, metaheuristic optimization, SHAP explainability, cone penetration test, mutual information, Shannon entropy, geotechnical engineering, machine learning, factor of safety, seismic hazard