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The increasing use of Internet-of-Things (IoT) devices for monitoring a wide spectrum of applications, along with the challenges of “big data” streaming support they often require for data analysis, is nowadays pushing for increased attention to the emerging edge computing paradigm. In particular, smart approaches to manage and analyze data directly on the network edge, are more and more investigated, and artificial intelligence (AI)-powered edge computing is envisaged to be a promising direction. In this article, we focus on data centers (DCs) and supercomputers (SCs), where a new generation of high-resolution monitoring systems is being deployed, opening new opportunities for analysis like anomaly detection and security, but introducing new challenges for handling the vast amount of data it produces. In detail, we report on a novel lightweight and scalable approach to increase the security of DCs/SCs, which involves AI-powered edge computing on high-resolution power consumption. The method—called pAElla —targets real-time malware detection (MD), it runs on an out-of-band IoT-based monitoring system for DCs/SCs, and involves power spectral density of power measurements, along with autoencoders. Results are promising, with an F1-score close to 1, and a false alarm and malware miss rate close to 0%. We compare our method with State-of-the-Art (SoA) MD techniques and show that, in the context of DCs/SCs, pAElla can cover a wider range of malware, significantly outperforming SoA approaches in terms of accuracy. Moreover, we propose a methodology for online training suitable for DCs/SCs in production, and release open data set and code.