Synthetic Data Generation and Comparative Evaluation of Machine Learning Models for Predicting the Biomechanical Behavior of the Human Cornea

Abstract

The analysis of the biomechanical behavior of the human cornea is crucial for various clinical applications, such as planning refractive surgeries and diagnosing diseases like keratoconus. Numerical simulations, like the Finite Element Method (FEM), are powerful tools for these analyses but can be computationally expensive, limiting extensive parameter explorations or real-time optimizations. Surrogate models based on Machine Learning (ML) emerge as a promising alternative but require representative datasets for training. This study details a methodology for generating synthetic data (N=10,000) to replicate the functional relationships and variability observed in a previous FEM simulation study of corneal mechanical behavior under different mesh configurations and loading conditions \cite{Almeida2017}. The performance of 19 ML regression algorithms was comparatively evaluated in predicting three key variables: the Simulated Corneal Displacement, the simulation Processing Time, and the Simulation Percentage Error (SSE). Predictor variables included applied pressure, (simulated) patient age, and FEM mesh characteristics (number of nodes and elements). The results demonstrated that models based on tree ensembles (Extra Trees, Random Forest, LightGBM, XGBoost) and KNeighbors Regressor achieved exceptional performance in predicting the simulated displacement ($R^2 > 0.999, RMSE < 0.001 mm$), validating their potential as accurate surrogate models. For the time and error variables, inherently linked to the discrete scenario configuration in the synthetic data, several models reached $R^2 \approx$ 1.0. The research validates the approach of generating simulation-informed synthetic data as an effective method to enable the robust training and selection of ML models for complex problems in computational biomechanics.