Acute Kidney Injury (AKI) is one of the most frequent postoperative complications and is associated with both short- and long-term mortality. Improved prediction of AKI is crucial and may help clinicians prevent and mitigate its adverse effects. In this paper, we explore the use of machine learning methods to predict postoperative AKI. Our analysis centers on the ensemble-based random forest (RF) classifier, which operates on static clinical variables, and a novel deep learning architecture that incorporates intraoperative time series data along with the static variables. The architecture uses a dual-attention mechanism to select both features and time intervals relevant for AKI prediction. We evaluate our models on the publicly available VitalDB database of 3, 640 patients who underwent non-cardiac surgery. The RF outperformed existing machine learning classifiers in the AKI literature (AUROC: 0.86, AUPRC: 0.54). In addition, the RF identified a robust set of preoperative variables that can be screened in a simple blood test. While the deep learning model achieved slightly lower performance (AUROC: 0.84, AUPRC: 0.44), the attention weights provide important intraoperative information, which can be monitored by clinicians during surgery. Taken together, our results highlight the promise of machine learning for AKI prediction and take the first steps towards developing clinically translatable models.