Side-channel attacks (SCA) have been studied for several decades, which resulted in many techniques that use statistical models to extract system information from side channels. More recently, machine learning has shown significant promise to advance the ability for SCAs to expose vulnerabilities. Artificial neural networks (ANN) can effectively learn nonlinear relationships between features within a side channel. In this paper, we propose a multi-architecture data aggregation technique to profile power traces for a system with an embedded processor that is based on three types of deep NNs, namely, multi-layer perceptrons (MLP), convolutional neural networks (CNN), and recurrent neural networks (RNN). This is one of the first works to explore the inter-architecture portability of NNs and SCAs. We demonstrate the robustness of the ANNs performing power-based SCAs on multiple architecture configurations with different architectural features, such as L1/L2 caches' size and associativity, and system memory size.