*Article* **Prediction of Liquefaction-Induced Lateral Displacements Using Gaussian Process Regression**

**Mahmood Ahmad 1,2 , Maaz Amjad <sup>3</sup> , Ramez A. Al-Mansob 1,\* , Paweł Kami ´nski <sup>4</sup> , Piotr Olczak <sup>5</sup> , Beenish Jehan Khan <sup>6</sup> and Arnold C. Alguno <sup>7</sup>**


**Abstract:** During severe earthquakes, liquefaction-induced lateral displacement causes significant damage to designed structures. As a result, geotechnical specialists must accurately estimate lateral displacement in liquefaction-prone areas in order to ensure long-term development. This research proposes a Gaussian Process Regression (GPR) model based on 247 post liquefaction in-situ free face ground conditions case studies for analyzing liquefaction-induced lateral displacement. The performance of the GPR model is assessed using statistical parameters, including the coefficient of determination, coefficient of correlation, Nash–Sutcliffe efficiency coefficient, root mean square error (*RMSE*), and ratio of the *RMSE* to the standard deviation of measured data. The developed GPR model predictive ability is compared to that of three other known models—evolutionary polynomial regression, artificial neural network, and multi-layer regression available in the literature. The results show that the GPR model can accurately learn complicated nonlinear relationships between lateral displacement and its influencing factors. A sensitivity analysis is also presented in this study to assess the effects of input parameters on lateral displacement.

**Keywords:** lateral displacement; liquefaction; Gaussian process regression; sensitivity analysis; machine learning
