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Battery-powered mobile devices (e.g., smartphones, AR/VR glasses, and various IoT devices) are increasingly being used for AI training due to their growing computational power and easy access to valuable, diverse, and real-time data. On-device training is highly energy-intensive, making accurate energy consumption estimation crucial for effective job scheduling and sustainable AI. However, the heterogeneity of devices and the complexity of models challenge the accuracy and generalizability of existing methods. This paper proposes AMPERE, a generic approach for energy consumption estimation in deep neural network (DNN) training. First, we examine the layer-wise energy additivity property of DNNs and strategically partition the entire model into layers for fine-grained energy consumption profiling. Then, we fit Gaussian Process (GP) models to learn from layer-wise energy consumption measurements and estimate a DNN's overall energy consumption based on its layer-wise energy additivity property. We conduct extensive experiments with various types of models across different real-world platforms. The results demonstrate that AMPERE has effectively reduced the Mean Absolute Percentage Error (MAPE) by up to 30%. Moreover, AMPERE is applied in guiding energy-aware pruning, successfully reducing energy consumption by 50%, thereby further demonstrating its generality and potential.