AbstractSurvival analysis is a fundamental area of focus in biomedical research, particularly in the context of personalized medicine. This prominence is due to the increasing prevalence of large and high‐dimensional datasets, such as omics and medical image data. However, the literature on nonlinear regression algorithms and variable selection techniques for interval‐censoring is either limited or nonexistent, particularly in the context of neural networks. Our objective is to introduce a novel predictive framework tailored for interval‐censored regression tasks, rooted in Accelerated Failure Time (AFT) models. Our strategy comprises two key components: (i) a variable selection phase leveraging recent advances on sparse neural network architectures; (ii) a regression model targeting prediction of the interval‐censored response. To assess the performance of our novel algorithm, we conducted a comprehensive evaluation through both numerical experiments and real‐world applications that encompass scenarios related to diabetes and physical activity. Our results outperform traditional AFT algorithms, particularly in scenarios featuring nonlinear relationships.