A Machine Learning Model for Beam Deflection Curve Prediction A Random Forest Approach with Multi-Material Validation

Abstract

Numerical simulation of complex engineering systems, such as those modeled using the Finite Element Method (FEM) or the Discrete Element Method (DEM), is often computationally intensive, limiting extensive parametric studies or optimization efforts. Surrogate models offer a promising alternative by enabling accelerated predictions. This work presents the development and rigorous validation of a machine learning (ML)-based methodology for creating surrogate models capable of predicting full structural deformation curves, point-by-point. To isolate and validate the ML approach, the classic case of a cantilever beam under a concentrated load at its free end was employed, for which the analytical solution, based on Euler-Bernoulli theory (including self-weight effects), is well established. A synthetic dataset was programmatically generated by calculating the analytical deflection at 51 equally spaced points along the beam length (from $x=0$ to $x=L= 2.0 \, \text{m}$) for 13 distinct materials (varying Young’s modulus, density, Poisson’s ratio, and yield strength), resulting in 663 records for a fixed beam geometry. A Random Forest regression model, trained on 80\% of the dataset (530 points), was developed to map material properties and spatial position $x$ to local deflection $y$. Evaluation on the test set (133 points) demonstrated high predictive accuracy, achieving a coefficient of determination ($R^2$) of 0.9991, a mean absolute error (MAE) of $0.2105 \, \text{mm}$, and a root mean squared error (RMSE) of $0.4605 \, \text{mm}$. An Out-of-Bag (OOB) $R^2$ score of 0.9983 further corroborated the model's generalization capability. The importance of this validation step, prior to applying the methodology to complex simulations where responses are obtained at discrete points, is discussed. The results demonstrate that the proposed methodology is robust and promising for developing fast and accurate surrogates for discretized structural response prediction.