Accelerating hybrid ANN–ODE frameworks using surrogate machine learning and metaheuristic optimization for predicting recurrent venous thromboembolism

Accurate and computationally efficient modeling of complex biological processes remains a major challenge in personalized medicine. This study introduces a hybrid framework that replaces the computationally intensive ordinary differential equation (ODE) system in hybrid artificial neural network–ODE (ANN–ODE) models with machine learning (ML) surrogate models. Using clinical and hematological data, the framework estimates patient-specific kinetic parameters of the coagulation cascade and predicts the endogenous thrombin potential (ETP), which serves as a discriminative threshold for classifying recurrent venous thromboembolism (RVTE) risk. Fourteen ML algorithms and eight metaheuristic optimization algorithms (MOAs) were systematically evaluated to identify optimal model–optimizer combinations. Among all candidates, the artificial neural network (ANN) acts as the best surrogate, yielding a root mean squared error (RMSE) below 0.3 for both the training and test sets. The ANN coupled with the Grey Wolf Optimizer (ANN–GWO) achieved the best performance, maintaining a relative accuracy of 97.97% compared with full ODE simulations, while reducing optimization time by over 99%. Particle swarm optimization (PSO) also exhibited competitive performance, confirming the robustness of swarm-based search strategies. These results demonstrate that replacing mechanistic ODE systems with machine-learning surrogates can substantially reduce computational complexity without sacrificing predictive accuracy. The proposed ANN–GWO and ANN–PSO models provide efficient, accurate, and scalable computational tools for RVTE prediction and personalized medicine. The findings support the use of ANNs as surrogate models and highlight GWO and PSO as robust and reliable optimizers for RVTE prediction within the tested hybrid framework. This guidance is particularly relevant for further extensions and improvements of the hybrid framework that require low computational cost without compromising accuracy, such as backward and forward selection of clinical features and kinetic parameters.