The atrial fibrillation burden (AFB) is defined as the percentage of time spend in atrial fibrillation (AF) over a long enough monitoring period. Recent research has demonstrated the added prognosis value that becomes available by using the AFB as compared with the binary diagnosis. We evaluate, for the first time, the ability to estimate the AFB over long-term continuous recordings, using a deep recurrent neutral network (DRNN) approach. Methods: The models were developed and evaluated on a large database of p=2,891 patients, totaling t=68,800 hours of continuous electrocardiography (ECG) recordings acquired at the University of Virginia heart station. Specifically, 24h beat-to-beat time series were obtained from a single portable ECG channel. The network, denoted ArNet, was benchmarked against a gradient boosting (XGB) model, trained on 21 features including the coefficient of sample entropy (CosEn) and AFEvidence. Data were divided into training and test sets, while patients were stratified by the presence and severity of AF. The generalizations of ArNet and XGB were also evaluated on the independent test PhysioNet LTAF database. Results: the absolute AF burden estimation error |E_AF|, median and interquartile, on the test set, was 1.2 (0.1-6.7) for ArNet and 3.1 (0.0-11.7) for XGB for AF individuals. Generalization results on LTAF were consistent with E_AF of 2.6 (1.1-14.7) for ArNet and 3.6 (1.0-16.7) for XGB. Conclusion: This research demonstrates the feasibility of AFB estimation from 24h beat-to-beat interval time series utilizing recent advances in DRNN. Significance: The novel data-driven approach enables robust remote diagnosis and phenotyping of AF.