Wearable devices are transforming healthcare by providing continuous, real-time physiological data for monitoring and analysis. However, data often suffer from noise and significant missing values due to operational constraints and user compliance. Traditional approaches address these issues through data imputation during pre-processing, introducing biases and inaccuracies. We propose a novel method enabling Recurrent Neural Networks (RNNs) to inherently handle missing data without imputation. By implementing teacher-forcing during Backpropagation Through Time (BPTT) when data are available and switching to autonomous mode otherwise, our approach leverages RNNs' dynamics to model physiological signals accurately. We demonstrate our method's effectiveness using the Lorenz 63 system as a surrogate dataset, achieving robust reconstructions with 80% missing data.